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Lambda Lambda Lambda
-
<function <lambda> at 0x7fdad4e06480>
+
<function <lambda> at 0x7fbb647f6200>
 4
 

 

@@ -1112,7 +1112,7 @@ 
Lambda Lambda Lambda
-
<function <lambda> at 0x7fdad4e06200>
+
<function <lambda> at 0x7fbba4019440>
 5
 

 

@@ -1129,7 +1129,7 @@ 
Lambda Lambda Lambda
-
<function <lambda> at 0x7fdad4e062a0>
+
<function <lambda> at 0x7fbb647f6340>
 5
 5
 

@@ -1150,7 +1150,7 @@ 
Lambda Lambda Lambda
 

 

-
<function <lambda> at 0x7fdad4e06340>
+
<function <lambda> at 0x7fbb647f6020>
 1
 3
 6
@@ -1326,7 +1326,7 @@ 
Creating arrays in python
/tmp/ipykernel_1855/3002503601.py:4: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
+
/tmp/ipykernel_1842/3002503601.py:4: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
   print(np.row_stack([a, b]))
 

 

@@ -1779,7 +1779,7 @@ 
Indexing vectors and arrays in Python
-1.7950016288086892
 

 

-
/tmp/ipykernel_1855/518394352.py:3: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_1842/518394352.py:3: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   print(np.trapz( x[x > 2], y[x > 2]))
 

 

@@ -1876,17 +1876,17 @@ 
3D arrays#
 

 

-
[[[0.5476759  0.3187746  0.88242603]
-  [0.04201148 0.3107921  0.06749891]
-  [0.71861984 0.95930351 0.43440104]]
+
[[[0.20114173 0.78957013 0.90321075]
+  [0.22052675 0.22851006 0.89396718]
+  [0.50508075 0.34204208 0.33682147]]
 
- [[0.1454874  0.60072783 0.45501144]
-  [0.20656186 0.11965505 0.4332491 ]
-  [0.95939429 0.97698476 0.21397559]]
+ [[0.43953453 0.5692659  0.64330352]
+  [0.70936523 0.87371169 0.31148072]
+  [0.39352461 0.61141827 0.4327842 ]]
 
- [[0.42694521 0.84762176 0.75276863]
-  [0.12219024 0.78224364 0.79227382]
-  [0.58754432 0.85776127 0.7448481 ]]]
+ [[0.81473398 0.87740287 0.20524145]
+  [0.88280938 0.83577573 0.83025906]
+  [0.46015632 0.21074422 0.66137439]]]
 

 

 

@@ -1900,11 +1900,11 @@ 
3D arrays#
 

 

-
[[0.5476759  0.04201148 0.71861984]
- [0.1454874  0.20656186 0.95939429]
- [0.42694521 0.12219024 0.58754432]]
-[0.5476759  0.1454874  0.42694521]
-[0.45501144 0.4332491  0.21397559]
+
[[0.20114173 0.22052675 0.50508075]
+ [0.43953453 0.70936523 0.39352461]
+ [0.81473398 0.88280938 0.46015632]]
+[0.20114173 0.43953453 0.81473398]
+[0.64330352 0.31148072 0.4327842 ]
 

 

 

diff --git a/blog/differential-equations.html b/blog/differential-equations.html
index f3af956..adca8b3 100644
--- a/blog/differential-equations.html
+++ b/blog/differential-equations.html
@@ -1618,7 +1618,7 @@ 
Linear algebra approaches to solving systems of constant coefficient ODEs
 

 

-
/tmp/ipykernel_1910/2289625004.py:4: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
+
/tmp/ipykernel_1896/2289625004.py:4: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
   T = np.row_stack([t, t])
 

 

diff --git a/blog/interpolation.html b/blog/interpolation.html
index 5ced758..aabcb4d 100644
--- a/blog/interpolation.html
+++ b/blog/interpolation.html
@@ -916,9 +916,9 @@ 
Interpolation with splines
/tmp/ipykernel_1941/1138919460.py:26: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
+
/tmp/ipykernel_1925/1138919460.py:26: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
   plt.title('Max point = ({0:1.2f}, {1:1.2f})'.format(float(xmax),
-/tmp/ipykernel_1941/1138919460.py:27: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
+/tmp/ipykernel_1925/1138919460.py:27: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
   float(f(xmax))));
 

 

diff --git a/blog/linear-algebra.html b/blog/linear-algebra.html
index 3d446b5..d877d2f 100644
--- a/blog/linear-algebra.html
+++ b/blog/linear-algebra.html
@@ -1178,7 +1178,7 @@ 
Determining linear independence of a set of vectors

 

-
/tmp/ipykernel_1966/3718588497.py:6: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
+
/tmp/ipykernel_1951/3718588497.py:6: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
   A = np.row_stack([v1, v2, v3])
 

 

@@ -1231,7 +1231,7 @@ 
Another example
[7.57773162 5.99149259]
 

 

-
/tmp/ipykernel_1966/73961882.py:7: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
+
/tmp/ipykernel_1951/73961882.py:7: DeprecationWarning: `row_stack` alias is deprecated. Use `np.vstack` directly.
   A = np.row_stack([v1, v2])
 

 

diff --git a/blog/math.html b/blog/math.html
index ebfeed5..51c4ea0 100644
--- a/blog/math.html
+++ b/blog/math.html
@@ -673,9 +673,9 @@ 
Numeric derivatives by differences
-
 Forward difference took 0.000216 seconds
- Backward difference took 0.000188 seconds
- Centered difference took 0.000234 seconds
+
 Forward difference took 0.000345 seconds
+ Backward difference took 0.000194 seconds
+ Centered difference took 0.000235 seconds
 

 

 ../_images/e82a955efa2e01fb55f09524ce9405030516d0ae15614c934dfaf2d14380e228.png
@@ -775,7 +775,7 @@ 
2-point vs. 4-point numerical derivatives
-../_images/a30bf00a5204e6d17835fb5f5ffc9f9f08bcc055617d0828094286f2b0b68dca.png
+../_images/729dfe3171a20031ea23a8d2a0463e001a80256f6a34a07f5b25cfe0ba7f4c4f.png
 

 

 
@@ -900,7 +900,7 @@ 
Derivatives by FFT
-../_images/b294a66f4893e385c8b0825ee55fa107babe8973e425c1a90ed2d04ac92108f4.png
+../_images/63f40c6dd9b56d83ad5c4d954392d42f12507cea8be3773dc57d6715c03dd194.png
 

 

 
@@ -1280,7 +1280,7 @@ 
Numerical data integration
4.25 0.0625
 

 

-
/tmp/ipykernel_1991/1388173814.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_1976/1388173814.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   i2 = np.trapz(y, x)
 

 

@@ -1323,7 +1323,7 @@ 
Numerical data integration
4.000408121620243
 

 

-
/tmp/ipykernel_1991/1343167527.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_1976/1343167527.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   print(np.trapz(y2, x2))
 

 

@@ -1363,7 +1363,7 @@ 
Combining numerical data with quad
/tmp/ipykernel_1991/1681875887.py:13: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_1976/1681875887.py:13: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   print(np.trapz(yfine, xfine))
 

 

@@ -1774,7 +1774,7 @@ 
The trapezoidal method of integration
-
time elapsed = 0.0007312297821044922 sec
+
time elapsed = 0.0010030269622802734 sec
 1.9999983517708524
 

 

@@ -1795,7 +1795,7 @@ 
The trapezoidal method of integration
-
time elapsed = 0.0001850128173828125 sec
+
time elapsed = 0.00022840499877929688 sec
 1.9999934070923728
 

 

@@ -1814,7 +1814,7 @@ 
The trapezoidal method of integration
-
time elapsed = 8.893013000488281e-05 sec
+
time elapsed = 7.390975952148438e-05 sec
 1.999993407092373
 

 

@@ -2009,7 +2009,7 @@ 
Function integration by the Romberg method
/tmp/ipykernel_1991/1760157840.py:9: DeprecationWarning: `scipy.integrate.romberg` is deprecated as of SciPy 1.12.0and will be removed in SciPy 1.15.0. Please use`scipy.integrate.quad` instead.
+
/tmp/ipykernel_1976/1760157840.py:9: DeprecationWarning: `scipy.integrate.romberg` is deprecated as of SciPy 1.12.0and will be removed in SciPy 1.15.0. Please use`scipy.integrate.quad` instead.
   print(romberg(np.sin, a, b))
 

 

@@ -2038,7 +2038,9 @@ 
Solve the quadratic equation
 
[(-b - sqrt(-4*a*c + b**2))/(2*a), (-b + sqrt(-4*a*c + b**2))/(2*a)]
-⎡        _____________          _____________⎤
+

+

+
⎡        _____________          _____________⎤
 ⎢       ╱           2          ╱           2 ⎥
 ⎢-b - ╲╱  -4⋅a⋅c + b    -b + ╲╱  -4⋅a⋅c + b  ⎥
 ⎢─────────────────────, ─────────────────────⎥
diff --git a/blog/nonlinear-algebra.html b/blog/nonlinear-algebra.html
index 199fc1d..9430521 100644
--- a/blog/nonlinear-algebra.html
+++ b/blog/nonlinear-algebra.html
@@ -765,10 +765,10 @@ 
Method of continuity for nonlinear equation solving
 

 

-
/tmp/ipykernel_2021/4022852329.py:19: RuntimeWarning: The iteration is not making good progress, as measured by the 
+
/tmp/ipykernel_2004/4022852329.py:19: RuntimeWarning: The iteration is not making good progress, as measured by the 
   improvement from the last ten iterations.
   y1, = fsolve(tmp, x0)
-/tmp/ipykernel_2021/4022852329.py:19: RuntimeWarning: The iteration is not making good progress, as measured by the 
+/tmp/ipykernel_2004/4022852329.py:19: RuntimeWarning: The iteration is not making good progress, as measured by the 
   improvement from the last five Jacobian evaluations.
   y1, = fsolve(tmp, x0)
 

diff --git a/blog/plotting.html b/blog/plotting.html
index 345fb93..e7e8391 100644
--- a/blog/plotting.html
+++ b/blog/plotting.html
@@ -1173,7 +1173,7 @@ 
Peak annotation in matplotlib
-
/tmp/ipykernel_2075/256016704.py:19: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2059/256016704.py:19: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   area = np.trapz(i[ind], w[ind])
 

 

diff --git a/blog/programming.html b/blog/programming.html
index 1d25248..dd962d9 100644
--- a/blog/programming.html
+++ b/blog/programming.html
@@ -795,7 +795,7 @@ 
Unique entries in a vector
-
['abracadabra', 'c', 'd', 'a', 'b']
+
['d', 'b', 'a', 'c', 'abracadabra']
 

 

 

@@ -1168,12 +1168,12 @@ 
About your python
-
uname_result(system='Linux', node='fv-az1205-349', release='6.5.0-1022-azure', version='#23~22.04.1-Ubuntu SMP Thu May  9 17:59:24 UTC 2024', machine='x86_64')
+
uname_result(system='Linux', node='fv-az1109-780', release='6.5.0-1023-azure', version='#24~22.04.1-Ubuntu SMP Wed Jun 12 19:55:26 UTC 2024', machine='x86_64')
 Linux
 ('64bit', 'ELF')
 x86_64
-fv-az1205-349
-Linux-6.5.0-1022-azure-x86_64-with-glibc2.35
+fv-az1109-780
+Linux-6.5.0-1023-azure-x86_64-with-glibc2.35
 x86_64
 ('main', 'Jun 25 2024 18:25:01')
 3.11.9
@@ -1238,7 +1238,7 @@ 
About your python
 
initially inside /home/runner/work/pycse/pycse/pycse-jb/pycse___python_computations_in_science_and_engineering/blog
 inside /home/runner/work/pycse/pycse/pycse-jb/pycse___python_computations_in_science_and_engineering/blog/data
-['PT.txt', 'example4.xls', 'antoine_data.dat', 'example4.xlsx', 'test.docx', 'debug.txt', 'antoine_database.mat', 'testdata.txt', 'gc-data-21.txt', 'debug-3.txt', 'example3.xls', 'debug-2.txt', 'raman.txt', 'example.xlsx', 'debug-4.txt', 'example2.xls']
+['example4.xlsx', 'antoine_data.dat', 'debug-4.txt', 'debug-2.txt', 'example.xlsx', 'example2.xls', 'example4.xls', 'test.docx', 'antoine_database.mat', 'gc-data-21.txt', 'debug-3.txt', 'raman.txt', 'PT.txt', 'testdata.txt', 'example3.xls', 'debug.txt']
 Exception caught:  <class 'Exception'>
 Running final code
 finally inside /home/runner/work/pycse/pycse/pycse-jb/pycse___python_computations_in_science_and_engineering/blog
diff --git a/blog/statistics.html b/blog/statistics.html
index 9af8be1..9577662 100644
--- a/blog/statistics.html
+++ b/blog/statistics.html
@@ -1124,9 +1124,9 @@ 
Addition and subtraction
-../_images/70a6f807ae33389814ac8aebfde4344d76f972a0d186005f7e6899ba2b46584e.png
-
0.5019639801268565
-0.5016767590391439
+../_images/5bde168daa4140145b77ff8f26f9188ec2595dca480eb7d4605a76365d0af5cc.png
+
0.5061913303232849
+0.4953129860305366
 0.5
 

 

@@ -1150,7 +1150,7 @@ 
Multiplication
-
11.893816748497734
+
11.940087050183678
 11.872657663724665
 

 

@@ -1169,7 +1169,7 @@ 
Division
 

 

 

-
0.294772574854224
+
0.29602035868747906
 0.2898598062432779
 

 

@@ -1194,7 +1194,7 @@ 
exponents
-
1.7377897715068298
+
1.7029730713441298
 1.7236544062149992
 

 

@@ -1208,7 +1208,7 @@ 
exponents
-
0.007539640663547944
+
0.007445647369221156
 0.007483647387490024
 

 

@@ -1236,7 +1236,7 @@ 
the chain rule in error propagation
-
3.6301096459668702
+
3.6348443621705666
 3.6180105030251086
 

 

@@ -1494,7 +1494,7 @@ 
Another approach to error propagation
-
Ca(exit) = 0.005011172235348289+/-0.00016896237271451172
+
Ca(exit) = 0.005010409261084926+/-0.00016694459925285874
 

 

 

@@ -1526,7 +1526,7 @@ 
Random thoughts
-
n = 0.30248634939616625
+
n = 0.39944543050232983
 you lose.
 

 

@@ -1551,10 +1551,10 @@ 
Random thoughts
-
You won 5049 times (50.490000%)
+
You won 5057 times (50.570000%)
 

 

-../_images/251095d1355e94ddb6161af56a7934f03d4f1e807116332c65d3617906ff196d.png
+../_images/3d2002be363e512ec01a2e1925e6494a9ba5d7f76271b5cad4a77b1b108e14c2.png
 

 

 
As you can see you win slightly more than you lost.

@@ -1570,10 +1570,10 @@ 
Random thoughts
-
96
-[ 3 50 27]
-[[52 20]
- [52 58]]
+
87
+[67 53 86]
+[[13 20]
+ [47 60]]
 

 

 

@@ -1591,8 +1591,8 @@ 
Random thoughts
-
0.9979647463824574
-[ 1.32222053 -0.05607502]
+
1.111332262894601
+[0.88495284 0.82255345]
 

 

 

@@ -1615,7 +1615,7 @@ 
Random thoughts
-../_images/e5cee18c55d481be39ac0ccd7d40ddb5eecb31e4bdf5ae744e0fbb47e5906f3a.png
+../_images/6e7cc860b8bea612ed4708a43614344199b5ad9ebb30a3ed3c345703a501e291.png
 

 

 
What fraction of points lie between plus and minus one standard deviation of the mean?

@@ -1638,8 +1638,8 @@ 
Random thoughts
-
67.860000% of samples are within +- 1 standard deviations of the mean
-95.460000% of samples are within +- 2 standard deviations of the mean
+
68.480000% of samples are within +- 1 standard deviations of the mean
+95.560000% of samples are within +- 2 standard deviations of the mean
 

 

 

diff --git a/blog/worked-examples.html b/blog/worked-examples.html
index 9a613e0..b07c6eb 100644
--- a/blog/worked-examples.html
+++ b/blog/worked-examples.html
@@ -1432,7 +1432,7 @@ 
Linear equality constraints for atomic mass conservation
/tmp/ipykernel_2167/1892264215.py:6: RuntimeWarning: invalid value encountered in log
+
/tmp/ipykernel_2151/1892264215.py:6: RuntimeWarning: invalid value encountered in log
   G = np.sum(nj * (Gjo / R / T + np.log(nj / Enj)))
 

 

@@ -1548,9 +1548,9 @@ 
The Gibbs free energy of a reacting mixture and the equilibrium composition<
 

 

 

-
/tmp/ipykernel_2167/2870202885.py:20: RuntimeWarning: divide by zero encountered in log
+
/tmp/ipykernel_2151/2870202885.py:20: RuntimeWarning: divide by zero encountered in log
   diffg += R * T * x1 * np.log(x2 * P / P0)
-/tmp/ipykernel_2167/2870202885.py:20: RuntimeWarning: invalid value encountered in multiply
+/tmp/ipykernel_2151/2870202885.py:20: RuntimeWarning: invalid value encountered in multiply
   diffg += R * T * x1 * np.log(x2 * P / P0)
 

 

@@ -1576,9 +1576,9 @@ 
The Gibbs free energy of a reacting mixture and the equilibrium composition<
 
0.46959618248998036
 

 

-
/tmp/ipykernel_2167/2870202885.py:20: RuntimeWarning: divide by zero encountered in log
+
/tmp/ipykernel_2151/2870202885.py:20: RuntimeWarning: divide by zero encountered in log
   diffg += R * T * x1 * np.log(x2 * P / P0)
-/tmp/ipykernel_2167/2870202885.py:20: RuntimeWarning: invalid value encountered in multiply
+/tmp/ipykernel_2151/2870202885.py:20: RuntimeWarning: invalid value encountered in multiply
   diffg += R * T * x1 * np.log(x2 * P / P0)
 

 

@@ -2019,9 +2019,9 @@ 
Constrained minimization to find equilibrium compositions
/tmp/ipykernel_2167/1928982228.py:17: RuntimeWarning: invalid value encountered in log
+
/tmp/ipykernel_2151/1928982228.py:17: RuntimeWarning: invalid value encountered in log
   d * np.log(P) + yI * d * np.log(yI) +
-/tmp/ipykernel_2167/1928982228.py:18: RuntimeWarning: invalid value encountered in log
+/tmp/ipykernel_2151/1928982228.py:18: RuntimeWarning: invalid value encountered in log
   yB * d * np.log(yB) + yP1 * d * np.log(yP1) + yP2 * d * np.log(yP2))
 

 

@@ -2373,9 +2373,9 @@ 
Numerically calculating an effectiveness factor for a porous catalyst bead

 

-
/tmp/ipykernel_2167/4291268947.py:40: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2151/4291268947.py:40: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   eta_numerical = (np.trapz(k * Ca * 4 * np.pi * (r**2), r)
-/tmp/ipykernel_2167/4291268947.py:41: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+/tmp/ipykernel_2151/4291268947.py:41: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   / np.trapz(k * CAs * 4 * np.pi * (r**2), r))
 

 

@@ -3698,9 +3698,9 @@ 
What region is a point in
-
/tmp/ipykernel_2167/339476128.py:64: RuntimeWarning: invalid value encountered in scalar divide
+
/tmp/ipykernel_2151/339476128.py:64: RuntimeWarning: invalid value encountered in scalar divide
   m1 = y1 / x1
-/tmp/ipykernel_2167/339476128.py:64: RuntimeWarning: divide by zero encountered in scalar divide
+/tmp/ipykernel_2151/339476128.py:64: RuntimeWarning: divide by zero encountered in scalar divide
   m1 = y1 / x1
 

 

diff --git a/book/00-intro.html b/book/00-intro.html
index 0dcfeef..508cc58 100644
--- a/book/00-intro.html
+++ b/book/00-intro.html
@@ -816,7 +816,7 @@ 
scipy#<
           906177281,  1325485569,  1443712780,  1963025921, -2063369727,
             6098177,   553716061,   856765187,   588325653,    53813521,
            16973318,  -704760322,  1593690581,  -470014715,   872205571,
-           27328168,       50016,   730350720,  -802356008,    80751876],
+           27328168,       50016,    92013158,         678,         683],
        dtype=int32),
  'alist': array([0.00000000e+00, 2.25000000e+00, 7.67216743e-04, 2.10783652e-03,
         4.30872995e-03, 7.48622952e-03, 1.17307690e-02, 1.71108947e-02,
@@ -843,20 +843,20 @@ 
scipy#<
         2.14321575e-312, 2.10077583e-312, 2.01589600e-312, 2.33419537e-312,
         2.01589600e-312, 2.33419537e-312, 2.22809558e-312, 2.14321575e-312,
         2.41907520e-312, 2.33419537e-312, 9.97338022e-313, 2.35541533e-312,
-        2.27053550e-312, 1.64726287e+265]),
- 'rlist': array([2.05718868e-001, 9.12099070e-001, 6.94227648e-310, 6.94227600e-310,
-        6.94227580e-310, 6.94227648e-310, 6.94227600e-310, 6.94227580e-310,
-        6.94227648e-310, 6.94227600e-310, 6.94227581e-310, 6.94227648e-310,
-        6.94227600e-310, 6.94227581e-310, 6.94227648e-310, 6.94227600e-310,
-        6.94227581e-310, 6.94227648e-310, 6.94227600e-310, 6.94227581e-310,
-        6.94227648e-310, 6.94227600e-310, 6.94227581e-310, 6.94227648e-310,
-        6.94227600e-310, 6.94227581e-310, 6.94227648e-310, 6.94227600e-310,
-        6.94227581e-310, 6.94227648e-310, 6.94227600e-310, 6.94227581e-310,
-        6.94227648e-310, 6.94227600e-310, 6.94227581e-310, 6.94227648e-310,
-        6.94227600e-310, 6.94227581e-310, 6.94227648e-310, 6.94227600e-310,
-        6.94227581e-310, 6.94227648e-310, 6.94227600e-310, 6.94227581e-310,
-        6.94227648e-310, 6.94227600e-310, 6.94227581e-310, 6.94227648e-310,
-        6.94227600e-310, 6.94227581e-310]),
+        2.27053550e-312, 5.37710476e+228]),
+ 'rlist': array([2.05718868e-001, 9.12099070e-001, 6.94724204e-310, 6.94724155e-310,
+        6.94724136e-310, 6.94724204e-310, 6.94724155e-310, 6.94724136e-310,
+        6.94724204e-310, 6.94724155e-310, 6.94724136e-310, 6.94724204e-310,
+        6.94724155e-310, 6.94724136e-310, 6.94724204e-310, 6.94724155e-310,
+        6.94724136e-310, 6.94724204e-310, 6.94724155e-310, 6.94724136e-310,
+        6.94724204e-310, 6.94724155e-310, 6.94724136e-310, 6.94724204e-310,
+        6.94724155e-310, 6.94724136e-310, 6.94724204e-310, 6.94724155e-310,
+        6.94724136e-310, 6.94724204e-310, 6.94724155e-310, 6.94724136e-310,
+        6.94724204e-310, 6.94724155e-310, 6.94724136e-310, 6.94724204e-310,
+        6.94724155e-310, 6.94724136e-310, 6.94724204e-310, 6.94724155e-310,
+        6.94724136e-310, 6.94724204e-310, 6.94724155e-310, 6.94724136e-310,
+        6.94724204e-310, 6.94724155e-310, 6.94724136e-310, 6.94724204e-310,
+        6.94724155e-310, 6.94724136e-310]),
  'elist': array([7.86630709e-09, 1.01263339e-14, 0.00000000e+00, 0.00000000e+00,
         0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
         0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
@@ -882,7 +882,7 @@ 
scipy#<
 

 

 

-
/tmp/ipykernel_2199/843280888.py:2: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2182/843280888.py:2: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   (np.trapz(integrand(x1), x1) - I) / I
 

 

diff --git a/book/02-integration-1.html b/book/02-integration-1.html
index 167c16d..728e3a5 100644
--- a/book/02-integration-1.html
+++ b/book/02-integration-1.html
@@ -727,7 +727,7 @@ 
numpy.trapz
-
/tmp/ipykernel_2252/3604360318.py:4: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2229/3604360318.py:4: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   np.trapz(y, x)
 

 

@@ -953,7 +953,7 @@ 
Estimating the volume of a plug flow reactor
/tmp/ipykernel_2252/4086341036.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2229/4086341036.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   vol = np.trapz(y[0:i+1], X[0:i+1])
 

 

@@ -990,7 +990,7 @@ 
Estimating the volume of a plug flow reactor
/tmp/ipykernel_2252/427682055.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2229/427682055.py:6: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   vol = np.trapz(y[0:i+1], X[0:i+1])
 

 

@@ -1162,7 +1162,7 @@ 
Numerical quadrature - or integration of functions
 

 

-
/tmp/ipykernel_2252/36719416.py:4: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.
+
/tmp/ipykernel_2229/36719416.py:4: IntegrationWarning: The maximum number of subdivisions (50) has been achieved.
   If increasing the limit yields no improvement it is advised to analyze 
   the integrand in order to determine the difficulties.  If the position of a 
   local difficulty can be determined (singularity, discontinuity) one will 
diff --git a/book/03-fode-1.html b/book/03-fode-1.html
index 12e6821..5d237de 100644
--- a/book/03-fode-1.html
+++ b/book/03-fode-1.html
@@ -631,7 +631,7 @@ 
Homogeneous, first-order linear differential equations
 
(array([0., 0., 0., 0.]),
  array([1., 1., 1., 1.]),
- array([4.64764453e-310, 0.00000000e+000, 4.64704087e-310, 4.64704087e-310]))
+ array([4.66942207e-310, 0.00000000e+000, 4.66871187e-310, 4.66871188e-310]))
 

 

 

@@ -775,7 +775,7 @@ 
Homogeneous, first-order linear differential equations
 

 

-
<matplotlib.legend.Legend at 0x7fcb597a9bd0>
+
<matplotlib.legend.Legend at 0x7f8db3355710>
 

 

 ../_images/0d992e05e05f92dc53b78d747da1fa725f1cb6fc66247847be3c6e338ba12bc2.png
@@ -1114,7 +1114,7 @@ 
scipy.integrate.solve_ivp
-
<matplotlib.legend.Legend at 0x7fcb574c5b90>
+
<matplotlib.legend.Legend at 0x7f8db10ba0d0>
 

 

 ../_images/0f3cb0f20de8a66563583063f2afeb51738e8b0db5b5ace82e7cb68a5289387e.png
diff --git a/book/07-nla-1.html b/book/07-nla-1.html
index c5fdadc..8488a6e 100644
--- a/book/07-nla-1.html
+++ b/book/07-nla-1.html
@@ -854,7 +854,7 @@ 
Derivatives of functions
-
/tmp/ipykernel_2362/1845505028.py:6: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+
/tmp/ipykernel_2342/1845505028.py:6: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   derivative(f, x0, dx=1e-6), 3 * x0**2  # the numerical and analytical derivative
 

 

@@ -899,9 +899,9 @@ 
Derivatives of functions
-
/tmp/ipykernel_2362/1563071673.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+
/tmp/ipykernel_2342/1563071673.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   d0 = derivative(func, x0, dx=dx)
-/tmp/ipykernel_2362/1563071673.py:10: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+/tmp/ipykernel_2342/1563071673.py:10: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   dnew = derivative(func, x0, dx=dx)
 

 

@@ -937,9 +937,9 @@ 
Derivatives of functions
-
/tmp/ipykernel_2362/1563071673.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+
/tmp/ipykernel_2342/1563071673.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   d0 = derivative(func, x0, dx=dx)
-/tmp/ipykernel_2362/1563071673.py:10: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+/tmp/ipykernel_2342/1563071673.py:10: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   dnew = derivative(func, x0, dx=dx)
 

 

@@ -982,7 +982,7 @@ 
fsolve#

 

-
/tmp/ipykernel_2362/1619064557.py:9: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
+
/tmp/ipykernel_2342/1619064557.py:9: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
   print(f'{float(ans):1.2f}')
 

 

@@ -1212,7 +1212,7 @@ 
Parameterized objective functions
-
/tmp/ipykernel_2362/2335501430.py:17: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
+
/tmp/ipykernel_2342/2335501430.py:17: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
   fa_exit[i] = ans
 

 

diff --git a/book/08-nla-2.html b/book/08-nla-2.html
index b2db8de..451493d 100644
--- a/book/08-nla-2.html
+++ b/book/08-nla-2.html
@@ -721,7 +721,7 @@ 
Cubic equations of state
-
/tmp/ipykernel_2387/406724879.py:1: ComplexWarning: Casting complex values to real discards the imaginary part
+
/tmp/ipykernel_2367/406724879.py:1: ComplexWarning: Casting complex values to real discards the imaginary part
   float(R[0])
 

 

@@ -799,7 +799,7 @@ 
Other useful things to remember about polynomials
 

 

-
/tmp/ipykernel_2387/174692805.py:3: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2367/174692805.py:3: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   np.trapz(Y, X)
 

 

@@ -836,7 +836,7 @@ 
Other useful things to remember about polynomials
 

 

-
130 μs ± 340 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
+
129 μs ± 411 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
 

 

 

@@ -853,7 +853,7 @@ 
Other useful things to remember about polynomials
 

 

-
6.26 μs ± 76.3 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)
+
6.23 μs ± 34 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)
 

 

 

@@ -885,7 +885,7 @@ 
Other useful things to remember about polynomials
 

 

-
<function integrand at 0x7f3d946436a0>
+
<function integrand at 0x7ff7a4623240>
 

 

 

@@ -1077,7 +1077,7 @@ 
Systems of nonlinear equations
-../_images/8c9de484c2d962680f586e667537303cff57fea4a71b49bdf26d30c06bfbbd28.png
+../_images/5c57ac8f62734b1116b8d31686c0f6e680d7c2b693891896ae301033cd8f24d0.png
 

 

 

@@ -1095,12 +1095,12 @@ 
Systems of nonlinear equations
-
Failed at guess [-7.973799239785311, 6.397399727103775].
+
Failed at guess [-9.394454424418573, -0.7907650725827731].
 The iteration is not making good progress, as measured by the 
-  improvement from the last ten iterations.
+  improvement from the last five Jacobian evaluations.
 

 

-
array([4.50509916e-12, 1.80068573e-11])
+
array([4.50050952e-12, 2.11725820e-11])
 

 

 

diff --git a/book/09-bvp.html b/book/09-bvp.html
index cabaae2..9e514be 100644
--- a/book/09-bvp.html
+++ b/book/09-bvp.html
@@ -1076,7 +1076,7 @@ 
Concentration profile in a particle
0.008249311811255714
 

 

-
/tmp/ipykernel_2428/1627362779.py:2: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
+
/tmp/ipykernel_2398/1627362779.py:2: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
   print(np.trapz(c**2, sol.x))
 

 

diff --git a/book/10-min-max.html b/book/10-min-max.html
index 3a48f70..c71ee17 100644
--- a/book/10-min-max.html
+++ b/book/10-min-max.html
@@ -664,7 +664,7 @@ 
Find the derivative, and solve for where it is zero
 

 

-
/tmp/ipykernel_2453/2917585576.py:4: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+
/tmp/ipykernel_2425/2917585576.py:4: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   return derivative(f, x, dx=1e-6)
 

 

@@ -707,9 +707,9 @@ 
Newton-Raphson method of minima finding
-
/tmp/ipykernel_2453/4103338182.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+
/tmp/ipykernel_2425/4103338182.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   yp = derivative(f, x0, dx=1e-6, n=1)
-/tmp/ipykernel_2453/4103338182.py:8: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+/tmp/ipykernel_2425/4103338182.py:8: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   ypp = derivative(f, x0, dx=1e-6, n=2)
 

 

diff --git a/book/11-regression.html b/book/11-regression.html
index ceab0b0..5dd013b 100644
--- a/book/11-regression.html
+++ b/book/11-regression.html
@@ -818,7 +818,7 @@ 
Regression of data is a form of function minimization
 

 

-
/tmp/ipykernel_2478/3278399195.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
+
/tmp/ipykernel_2450/3278399195.py:7: DeprecationWarning: scipy.misc.derivative is deprecated in SciPy v1.10.0; and will be completely removed in SciPy v1.12.0. You may consider using findiff: https://github.com/maroba/findiff or numdifftools: https://github.com/pbrod/numdifftools
   dEdV = derivative(proxy, V, args=(pars,), dx=1e-6)
 

 

diff --git a/book/15-intro-linear-algebra.html b/book/15-intro-linear-algebra.html
index 5877192..2f36786 100644
--- a/book/15-intro-linear-algebra.html
+++ b/book/15-intro-linear-algebra.html
@@ -1257,7 +1257,7 @@ 
The determinant
-
np.float64(-1.7014402080809936)
+
np.float64(0.8547619360717147)
 

 

 

@@ -1276,9 +1276,9 @@ 
The inverse
-
array([[  9.57458374,  -5.61782028,  -5.47715205],
-       [-16.8622985 ,   9.64542903,  11.87393974],
-       [  7.04731281,  -2.62804695,  -5.98302998]])
+
array([[-6.55133034,  0.4286837 ,  2.3328957 ],
+       [-2.35403998, -1.02816124,  2.02920082],
+       [ 6.87169103,  0.8933169 , -2.51336017]])
 

 

 

@@ -1292,9 +1292,9 @@ 
The inverse
-
[[ 1. -0.  0.]
+
[[ 1.  0. -0.]
  [ 0.  1. -0.]
- [ 0. -0.  1.]]
+ [-0.  0.  1.]]
 

 

 

@@ -1569,7 +1569,7 @@ 
Solving linear algebraic equations
-../_images/15f74efc9f5020eae016b210713528971242e7d90642d5eedcebf3ea0c48d8fa.png
+../_images/f8fb685424dcfbf7e93eb76ba9ac4644630abbd238b9b5065c0c340bd2aa1818.png
 

 

 
As usual, there is a function we can use to solve this.

@@ -1604,7 +1604,7 @@ 
Solving linear algebraic equations
-../_images/752d6b1545f1b6fad72a2d99986c1e7ec680a38112b6fe125b2447e055b19133.png
+../_images/2bc2595525828df5de393d9784136a118acb1b872e87fd68c8e5597da63cdc4c.png
 

 

 
You can see by inspection that solve must not be using an inverse to solve these equations; if it did, it would take much longer to solve them. It is remarkable that we can solve ~5000 simultaneous equations here in about 1 second!

diff --git a/book/17-linear-algebra-2.html b/book/17-linear-algebra-2.html
index e2c85ed..6fd979a 100644
--- a/book/17-linear-algebra-2.html
+++ b/book/17-linear-algebra-2.html
@@ -721,7 +721,7 @@ 
Interpolation libraries
 

 

-
/tmp/ipykernel_2625/3098855599.py:5: RuntimeWarning: The iteration is not making good progress, as measured by the 
+
/tmp/ipykernel_2601/3098855599.py:5: RuntimeWarning: The iteration is not making good progress, as measured by the 
   improvement from the last ten iterations.
   fsolve(obj, 7)
 

@@ -817,9 +817,9 @@ 
Eigenvalues
-
array([[1.17034789, 1.12852431, 1.13538358],
-       [1.12852431, 0.20479578, 0.93771711],
-       [1.13538358, 0.93771711, 1.85899232]])
+
array([[1.85294056, 0.3741679 , 1.16139508],
+       [0.3741679 , 1.40558989, 1.5372893 ],
+       [1.16139508, 1.5372893 , 0.74941638]])
 

 

 

@@ -834,7 +834,7 @@ 
Eigenvalues
-
array([ 1.44373348, -0.4636214 , -0.00922275])
+
array([ 3.44746413, -0.43591453, -0.89261489])
 

 

 

@@ -846,7 +846,8 @@ 
Eigenvalues
-
array([1.78350089, 0.51593133, 0.1015698 ])
+
array([1.55633319+0.j       , 0.09420867+0.2004125j,
+       0.09420867-0.2004125j])
 

 

 

@@ -860,7 +861,7 @@ 
Eigenvalues
-
(np.float64(0.9708893270114745), np.float64(0.9708893270114745))
+
(np.float64(2.1189347076957206), np.float64(2.1189347076957206))
 

 

 

@@ -874,7 +875,7 @@ 
Eigenvalues
-
np.float64(0.9708893270114737)
+
np.float64(2.1189347076957206)
 

 

 

@@ -888,7 +889,7 @@ 
Eigenvalues
-
(np.float64(0.006173210069733394), np.float64(0.006173210069733389))
+
(np.float64(1.3414213957101666), np.float64(1.3414213957101675))
 

 

 

@@ -902,10 +903,10 @@ 
Eigenvalues
-
(array([ 1.44373348, -0.4636214 , -0.00922275]),
- array([[ 0.55569268,  0.82770729, -0.07814269],
-        [ 0.46797412, -0.38909203, -0.79347817],
-        [ 0.68717237, -0.40436126,  0.60356119]]))
+
(array([ 3.44746413, -0.43591453, -0.89261489]),
+ array([[ 0.36772665,  0.88027133,  0.29983245],
+        [ 0.53632987,  0.06264024, -0.84168074],
+        [ 0.759689  , -0.47031754,  0.44908132]]))
 

 

 

@@ -919,7 +920,7 @@ 
Eigenvalues
-
(np.float64(0.9999999999999997), np.float64(0.9999999999999999))
+
(np.float64(1.0000000000000002), np.float64(0.9999999999999999))
 

 

 

@@ -931,8 +932,8 @@ 
Eigenvalues
-
(array([0.44983279, 0.45915949, 0.67329851]),
- array([ 0.80227213,  1.19498873, -0.11281721]))
+
(array([1.10018882, 1.16497644, 2.43475858]),
+ array([1.26772444, 3.03470383, 1.0336616 ]))
 

 

 

@@ -945,8 +946,8 @@ 
Eigenvalues
-
(array([0.80227213, 0.67562991, 0.99209376]),
- array([0.80227213, 0.67562991, 0.99209376]))
+
(array([1.26772444, 1.84897799, 2.61900058]),
+ array([1.26772444, 1.84897799, 2.61900058]))
 

 

 

@@ -959,8 +960,8 @@ 
Eigenvalues
 
[np.float64(0.9999999999999999),
- np.float64(0.9999999999999999),
- np.float64(1.0)]
+ np.float64(1.0),
+ np.float64(0.9999999999999999)]
 

 

 

@@ -1007,10 +1008,10 @@ 
Eigenvalues
-
(array([-0.4636214 , -0.00922275,  1.44373348]),
- array([[ 0.82770729, -0.07814269,  0.55569268],
-        [-0.38909203, -0.79347817,  0.46797412],
-        [-0.40436126,  0.60356119,  0.68717237]]))
+
(array([-0.89261489, -0.43591453,  3.44746413]),
+ array([[ 0.29983245,  0.88027133,  0.36772665],
+        [-0.84168074,  0.06264024,  0.53632987],
+        [ 0.44908132, -0.47031754,  0.759689  ]]))
 

 

 

diff --git a/book/18-linear-regression.html b/book/18-linear-regression.html
index e950097..b1ac889 100644
--- a/book/18-linear-regression.html
+++ b/book/18-linear-regression.html
@@ -1134,11 +1134,10 @@ 
LASSO regression
 0.00032
+
 0.00032      0.09    -0.01    -0.00    -0.16    -0.62     0.80     2.16     0.79    -4.96    -0.51     1.66
 

 

-
      0.09    -0.01    -0.00    -0.16    -0.62     0.80     2.16     0.79    -4.96    -0.51     1.66
-    0.01     -0.19    -0.00    -0.00    -0.00     1.02     0.39     0.00    -0.00    -1.75    -2.08     1.85
+
    0.01     -0.19    -0.00    -0.00    -0.00     1.02     0.39     0.00    -0.00    -1.75    -2.08     1.85
     0.32      0.28     0.29     0.00     0.00    -0.00    -0.00     0.00    -0.00    -1.99    -0.00     0.60
 

 

diff --git a/book/23-gp.html b/book/23-gp.html
index 158c9c6..8344491 100644
--- a/book/23-gp.html
+++ b/book/23-gp.html
@@ -780,7 +780,7 @@ 
GPR by example
-
array([0.75492506, 0.76470167])
+
array([0.76103205, 0.7707987 ])
 

 

 

@@ -796,7 +796,7 @@ 
GPR by example
-../_images/aa64411db34156f55c946719e7f45775487e8594553e72b2eca8d88b3acd5b2f.png
+../_images/49cdfe902247f10f4518d6b322a2605d8b06c2bc25b347bebf2f763134c4ebc1.png
 

 

 
That is not bad, but clearly not great. With a \(\lambda=0.15\), only one data point is contributing to the estimate, the other points have only small contributions because they are far from points we are estimating. This is a feature of the assumption we made about the covariance with \(\lambda\). This means we do not have enough data to make a very good estimate. We can see this if we try this with a much more dense data set.

@@ -830,7 +830,7 @@ 
GPR by example
Known data step size is 0.05
 

 

-../_images/c5171bf4d8699298b143372af92378882bc67880f1cf2711d738d1601b0363e4.png
+../_images/6e8635e458dfe36a662324bb7e880b7acfd631b8bb0fdbbb2990929873775423.png
 

 

 
Now you can see that we do very well in estimating the values. The length scale here might even be considered too short, since it is evident we are fitting trends in the noise.

@@ -861,7 +861,7 @@ 
GPR by example
Known data step size is 0.05
 

 

-../_images/01e866ae06e9106b01ee314feaede8249138dcff900194cf5b04505059389c33.png
+../_images/c291cdf1da7c22fd6b0138dbc39780ad522b7667421e2778c67cdec9ae67dbea.png
 

 

 

@@ -925,7 +925,7 @@ 
Underfitting in GPR
-../_images/71e18cf49013af1d37ffa54391963296c3de76399120793bbf21a8255826098e.png
+../_images/3c479c790345ee140b1f543b5c65916baa5c553b1b755c10ad77ab796b8a2c9e.png
 

 

 
@@ -950,7 +950,7 @@ 
Overfitting in GPR
-../_images/896e167518fec75ed78f94ae1f96026d74318b26ac7341edea6dd206202f384e.png
+../_images/9e803b6dc9401c783cd9fd590de03f3e943b231f8ad868b11532d644df84072a.png
 

 

 
@@ -991,10 +991,10 @@ 
Finding the hyperparameters in GPR
-
array([1.        , 0.06584185])
+
array([1.        , 0.07049851])
 

 

-../_images/c36b0cae2601e3cefedab1829c398b0cc7aaa57d4d998813d71d08c27332a536.png
+../_images/8f3a7bf246cdc8d2356396ea9d6fb00a2b79ac3bad200af6acc399c384e1e598.png
 

 

 

@@ -1029,10 +1029,10 @@ 
Finding the hyperparameters in GPR
-
array([1.        , 0.21198213, 0.20200693])
+
array([ 1.        ,  0.2116936 , -0.19268527])
 

 

-../_images/3f4c01cb219bbd22668e2a580c6790823d1a201f73c402fcc11543f3d3d414a3.png
+../_images/613bd80e8c4f11be200629f2f6c89be4f1a323ca653c16e005656249e95d212b.png
 

 

 
Note that we still see some wiggles in the fit, indicating some minor degree of overfitting with the optimal hyperparameters. That is happening because we fit to all the data, and do not use any to estimate how good our fits are. You can use train/test data splits for GPR for this purpose as well, but it is out of the scope of the lecture today.

@@ -1067,7 +1067,7 @@ 
An example with a linear kernel
-../_images/8e293ffff887cc3ca90e0262c8c5f57673f2f23a8a918724477c09819bcb7d47.png
+../_images/9b197510ef3a06b6511845f29792f9d9f567a4263f0a4078fc1a8d64c206797c.png
 

 

 
As before, we setup a log likelihood function and maximize it to get estimates for the parameters.

@@ -1090,15 +1090,15 @@ 
An example with a linear kernel
  message: Optimization terminated successfully.
   success: True
    status: 0
-      fun: 7.635285850604611
-        x: [-4.468e-06  6.449e-01 -1.488e+00]
-      nit: 28
-      jac: [ 2.801e-06  9.120e-06 -9.477e-06]
- hess_inv: [[ 6.097e+00  5.913e-05  1.944e-02]
-            [ 5.913e-05  3.121e-02  1.668e-02]
-            [ 1.944e-02  1.668e-02  4.863e-02]]
-     nfev: 148
-     njev: 37
+      fun: 7.472045608184835
+        x: [ 2.014e-05  6.449e-01 -1.482e+00]
+      nit: 30
+      jac: [-2.861e-06 -5.007e-06  5.841e-06]
+ hess_inv: [[ 3.680e+00  5.002e-03  1.012e-02]
+            [ 5.002e-03  2.671e-02  1.830e-02]
+            [ 1.012e-02  1.830e-02  5.557e-02]]
+     nfev: 152
+     njev: 38
 

 

 

@@ -1126,7 +1126,7 @@ 
An example with a linear kernel
-../_images/2db3bd6abce984baf6fd32595ea8a55cad60af721e054deb3bd7e5ca9ce187ea.png
+../_images/4ad898a2b1fbacb9a6f447f639a3a1799a56ffdd5d56e7b122e996dc7c179c64.png
 

 

 
Note that now, we get linear extrapolation, because we are using a linear kernel. Note also that the hyperparameters do not mean anything in particular to us. They do not include the slope or intercept. We can work those out pretty easily though. The intercept is just a prediction at \(x=0\):

@@ -1139,7 +1139,7 @@ 
An example with a linear kernel
-
array([2.986537])
+
array([2.97278072])
 

 

 

@@ -1152,7 +1152,7 @@ 
An example with a linear kernel
-
np.float64(2.006532822018294)
+
np.float64(2.006417515086492)
 

 

 

@@ -1186,7 +1186,7 @@ 
Uncertainty quantification in GPR
-../_images/5e3ba782a3bdd0685792e0c8b505d949aa9d947483129211ffedad62c76caedc.png
+../_images/8ed9980079cb50623ea3082acbede22136d0d19e4e8b22419714ab03057078fc.png
 

 

 
@@ -1204,7 +1204,7 @@ 
Combining kernels
-../_images/56ea7954aea57ab2046185ac3cf336971f0021ccd8c1fad01b81f85d8cd7194a.png
+../_images/9451033f12106bf9544e28e31ebd872f5048b24ddc2dabe62035f568790fa329.png
 

 

 
This looks like a sin wave superimposed on a line. A periodic kernel is defined as

@@ -1226,22 +1226,22 @@ 
Combining kernels
-
  message: Desired error not necessarily achieved due to precision loss.
-  success: False
-   status: 2
-      fun: 21.397748604923645
-        x: [ 8.511e-07  4.020e-01 -1.423e+00  6.466e-01  9.376e-01
-            -3.402e-01]
-      nit: 40
-      jac: [-2.384e-07  2.384e-06  2.623e-06  7.153e-07  1.431e-05
-             1.431e-06]
- hess_inv: [[ 9.914e-02 -4.187e-03 ... -3.961e-05  1.421e-02]
-            [-4.187e-03  4.788e-03 ...  5.537e-04  9.237e-04]
+
  message: Optimization terminated successfully.
+  success: True
+   status: 0
+      fun: 35.88700819020977
+        x: [ 9.583e-01  5.792e-06  1.025e+00  1.116e+00  1.010e+00
+             9.022e-03]
+      nit: 21
+      jac: [ 2.384e-06  3.338e-06 -4.768e-07  2.384e-06 -4.768e-07
+             0.000e+00]
+ hess_inv: [[ 1.838e-02  1.101e-02 ... -1.100e-01 -6.600e-01]
+            [ 1.101e-02  1.548e+00 ... -1.783e+00 -1.068e+01]
             ...
-            [-3.961e-05  5.537e-04 ...  2.056e-04  3.684e-04]
-            [ 1.421e-02  9.237e-04 ...  3.684e-04  8.746e-03]]
-     nfev: 711
-     njev: 100
+            [-1.100e-01 -1.783e+00 ...  7.778e+00  4.663e+01]
+            [-6.600e-01 -1.068e+01 ...  4.663e+01  2.795e+02]]
+     nfev: 182
+     njev: 26
 

 

 

@@ -1268,7 +1268,7 @@ 
Combining kernels
-../_images/88f733555a489aa9648e287fd928acd24270bbd947994d0caa17f1719b14754c.png
+../_images/3ca5ed7d495a283a2851fad06fa287db5f2d41d2f8d69e139b58c8549b8ee2d2.png
 

 

 
Note that we get oscillatory + linear extrapolation behavior!

diff --git a/docs/about.html b/docs/about.html
index d153f27..ec842f4 100644
--- a/docs/about.html
+++ b/docs/about.html
@@ -582,12 +582,12 @@ 
About pycse
-
uname_result(system='Linux', node='fv-az1205-349', release='6.5.0-1022-azure', version='#23~22.04.1-Ubuntu SMP Thu May  9 17:59:24 UTC 2024', machine='x86_64')
+
uname_result(system='Linux', node='fv-az1109-780', release='6.5.0-1023-azure', version='#24~22.04.1-Ubuntu SMP Wed Jun 12 19:55:26 UTC 2024', machine='x86_64')
 Linux
 ('64bit', 'ELF')
 x86_64
-fv-az1205-349
-Linux-6.5.0-1022-azure-x86_64-with-glibc2.35
+fv-az1109-780
+Linux-6.5.0-1023-azure-x86_64-with-glibc2.35
 x86_64
 ('main', 'Jun 25 2024 18:25:01')
 3.11.9
diff --git a/docs/beginner.html b/docs/beginner.html
index 17f9a19..e23463f 100644
--- a/docs/beginner.html
+++ b/docs/beginner.html
@@ -870,7 +870,7 @@ 
A better fsolve
-
/tmp/ipykernel_2800/1685161423.py:2: RuntimeWarning: The iteration is not making good progress, as measured by the 
+
/tmp/ipykernel_2772/1685161423.py:2: RuntimeWarning: The iteration is not making good progress, as measured by the 
   improvement from the last ten iterations.
   fsolve(f, 2.5)
 

diff --git a/docs/execution-statistics.html b/docs/execution-statistics.html
index b484e62..e61d84c 100644
--- a/docs/execution-statistics.html
+++ b/docs/execution-statistics.html
@@ -513,225 +513,225 @@ 
Build statistics
blog/basic-python

-
2024-07-10 13:46

+
2024-07-10 14:57

 
force

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3.98

+
3.09

 
✅

 
 
blog/data-analysis

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3.85

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3.76

 
✅

 
 
blog/differential-equations

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10.35

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10.44

 
✅

 
 
blog/interpolation

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1.96

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2.17

 
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blog/linear-algebra

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1.67

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1.74

 
✅

 
 
blog/math

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4.7

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4.52

 
✅

 
 
blog/nonlinear-algebra

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3.28

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2.98

 
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blog/optimization

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2.35

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2.11

 
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blog/plotting

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3.22

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3.17

 
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blog/programming

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1.47

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1.44

 
✅

 
 
blog/statistics

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4.27

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4.01

 
✅

 
 
blog/units

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1.16

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1.09

 
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blog/worked-examples

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11.36

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11.08

 
✅

 
 
book/00-intro

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1.79

 
✅

 
 
book/01-jupyter

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1.73

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1.96

 
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book/02-integration-1

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2.54

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2.67

 
✅

 
 
book/03-fode-1

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2.24

 
✅

 
 
book/04-fode-2

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5.62

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5.55

 
✅

 
 
book/05-nth-odes

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book/07-nla-1

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2.4

 
✅

 
 
book/08-nla-2

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18.26

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17.97

 
✅

 
 
book/09-bvp

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3.02

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2.67

 
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book/11-regression

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book/13-constrained-optimization

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book/15-intro-linear-algebra

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101.76

 
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book/16-linear-algebra

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2.19

 
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book/18-linear-regression

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3.7

 
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book/21-machine-learning

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book/22-ml-2

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book/23-gp

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docs/about

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docs/beginner

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docs/utils

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✅

 
 
diff --git a/searchindex.js b/searchindex.js
index 2d1dfdb..710427c 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"alltitles": {"2-point vs. 4-point numerical derivatives": [[6, "point-vs-4-point-numerical-derivatives"]], "2d arrays": [[0, "d-arrays"]], "3D arrays": [[0, "id2"]], "A better fsolve": [[38, "a-better-fsolve"]], "A harder problem": [[3, "a-harder-problem"]], "A nonlinear BVP": [[2, "a-nonlinear-bvp"]], "A novel way to numerically estimate the derivative of a function - complex-step derivative approximation": [[6, "a-novel-way-to-numerically-estimate-the-derivative-of-a-function-complex-step-derivative-approximation"]], "A simple first order ode evaluated at specific points": [[2, "a-simple-first-order-ode-evaluated-at-specific-points"]], "A worked bvp problem": [[22, "a-worked-bvp-problem"]], "A worked example": [[20, "a-worked-example"]], "About pycse": [[37, "about-pycse"]], "About the Python packages": [[37, "about-the-python-packages"]], "About your python": [[10, "about-your-python"]], "Addition and subtraction": [[11, "addition-and-subtraction"], [27, "addition-and-subtraction"]], "Advanced function creation": [[0, "advanced-function-creation"]], "Advanced mathematical operators": [[0, "advanced-mathematical-operators"]], "Advanced selection of \u03bb": [[30, "advanced-selection-of"]], "Advanced string formatting": [[0, "advanced-string-formatting"]], "An application": [[26, "an-application"]], "An example of polynomial fitting": [[30, "an-example-of-polynomial-fitting"]], "An example with a linear kernel": [[34, "an-example-with-a-linear-kernel"]], "An example with curve_fit": [[24, "an-example-with-curve-fit"]], "Analytically solve a simple ODE": [[6, "analytically-solve-a-simple-ode"]], "Another approach to error propagation": [[11, "another-approach-to-error-propagation"]], "Another example": [[5, "another-example"], [5, "id2"]], "Another interpretation of neural networks": [[32, "another-interpretation-of-neural-networks"]], "Another way to parameterize an ODE - nested function": [[2, "another-way-to-parameterize-an-ode-nested-function"]], "Application in linear boundary value problems": [[28, "application-in-linear-boundary-value-problems"]], "Application in reaction engineering - Steady state CSTR": [[28, "application-in-reaction-engineering-steady-state-cstr"]], "Application to independent chemical reactions.": [[5, "application-to-independent-chemical-reactions"]], "Application to maximizing profit in a PFR": [[23, "application-to-maximizing-profit-in-a-pfr"]], "Application to roots of a polynomial": [[29, "application-to-roots-of-a-polynomial"]], "Applications": [[16, "applications"]], "Applications of lambda functions": [[0, "applications-of-lambda-functions"]], "Applications of linear algebra": [[28, "applications-of-linear-algebra"]], "Applications to optimization": [[29, "applications-to-optimization"]], "Are averages different": [[11, "are-averages-different"]], "Avoiding indexing in lists": [[38, "avoiding-indexing-in-lists"]], "Basic math": [[0, 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"choice-of-activation-functions-in-neural-networks"]], "Combining kernels": [[34, "combining-kernels"]], "Combining numerical data with quad": [[6, "combining-numerical-data-with-quad"]], "Compare the equilibrium constants": [[13, "compare-the-equilibrium-constants"]], "Compare to a loop solution": [[10, "compare-to-a-loop-solution"]], "Compressibility variation from an implicit equation of state": [[31, "compressibility-variation-from-an-implicit-equation-of-state"]], "Compute areas": [[13, "compute-areas"]], "Compute gas phase pressures of each species": [[13, "compute-gas-phase-pressures-of-each-species"]], "Compute mole fractions and partial pressures": [[13, "compute-mole-fractions-and-partial-pressures"]], "Compute the t-score for our data": [[11, "compute-the-t-score-for-our-data"]], "Computing a pipe diameter": [[13, "computing-a-pipe-diameter"]], "Computing determinants from matrix decompositions": [[5, "computing-determinants-from-matrix-decompositions"]], "Computing equilibrium constants": [[13, "computing-equilibrium-constants"]], "Computing the pressure from a solid equation of state": [[31, "computing-the-pressure-from-a-solid-equation-of-state"]], "Concentration profile in a particle": [[22, "concentration-profile-in-a-particle"]], "Concluding remarks": [[35, "concluding-remarks"]], "Conclusions": [[10, "conclusions"]], "Confidence interval on an average": [[11, "confidence-interval-on-an-average"]], "Confidence intervals on the parameters": [[30, "confidence-intervals-on-the-parameters"]], "Conservation of mass in chemical reactions": [[13, "conservation-of-mass-in-chemical-reactions"]], "Constrained minimization": [[26, "constrained-minimization"]], "Constrained minimization to find equilibrium compositions": [[13, "constrained-minimization-to-find-equilibrium-compositions"]], "Constrained optimization": [[8, "constrained-optimization"], [26, "constrained-optimization"]], "Constrained optimization with Lagrange multipliers and autograd": [[31, "constrained-optimization-with-lagrange-multipliers-and-autograd"]], "Construct the Lagrange multiplier augmented function": [[8, "construct-the-lagrange-multiplier-augmented-function"]], "Constructing arrays": [[27, "constructing-arrays"]], "Controlling the format of printed variables": [[0, "controlling-the-format-of-printed-variables"]], "Counting roots": [[7, "counting-roots"]], "Coupled nonlinear equations": [[7, "coupled-nonlinear-equations"]], "Creating arrays in python": [[0, "creating-arrays-in-python"]], "Creating your own functions": [[0, "creating-your-own-functions"]], "Cubic equations of state": [[21, "cubic-equations-of-state"]], "Curve fitting to get overlapping peak areas": [[13, "curve-fitting-to-get-overlapping-peak-areas"]], "Customizing plots after the fact": [[9, "customizing-plots-after-the-fact"]], "Data analysis": [[1, "data-analysis"]], "Debugging/getting help": [[15, "debugging-getting-help"]], "Defining functions in python": [[0, 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line integrals": [[31, "evaluating-line-integrals"]], "Exponential and logarithmic functions": [[0, "exponential-and-logarithmic-functions"]], "Families of solutions to FODEs": [[18, "families-of-solutions-to-fodes"]], "Fancy, built-in colors in Python": [[9, "fancy-built-in-colors-in-python"]], "Find the derivative, and solve for where it is zero": [[23, "find-the-derivative-and-solve-for-where-it-is-zero"]], "Find the minimum distance from a point to a curve.": [[8, "find-the-minimum-distance-from-a-point-to-a-curve"]], "Find the volume of a PFR": [[16, "find-the-volume-of-a-pfr"]], "Finding equilibrium composition by direct minimization of Gibbs free energy on mole numbers": [[13, "finding-equilibrium-composition-by-direct-minimization-of-gibbs-free-energy-on-mole-numbers"]], "Finding equilibrium conversion": [[13, "finding-equilibrium-conversion"]], "Finding independent reactions": [[28, "finding-independent-reactions"]], "Finding maxima": [[23, "finding-maxima"]], "Finding the hyperparameters in GPR": [[34, "finding-the-hyperparameters-in-gpr"]], "Finding the maximum power of a photovoltaic device.": [[8, "finding-the-maximum-power-of-a-photovoltaic-device"]], "Finding the nth root of a periodic function": [[7, "finding-the-nth-root-of-a-periodic-function"]], "Finding the partial derivatives": [[8, "finding-the-partial-derivatives"]], "First guess": [[2, "first-guess"]], "First-order differential equations": [[17, "first-order-differential-equations"]], "Fit a line to numerical data": [[1, "fit-a-line-to-numerical-data"]], "Fitting a numerical ODE solution to data": [[1, "fitting-a-numerical-ode-solution-to-data"]], "Flexible nonlinear models for regression": [[32, "flexible-nonlinear-models-for-regression"]], "Float comparisons": [[42, "float-comparisons"]], "Fourth-order Runge-Kutta method": [[17, "fourth-order-runge-kutta-method"]], "Function extrema": [[23, "function-extrema"]], "Function integration by the Romberg method": [[6, 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