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This is a former project of mine where I was compiling my notes from various classes, notable textbooks, and independent explorations. I never polished the notes into a textbook, but that might be an interesting project if I ever have the opportunity. Please feel free to email me any mistakes you notice or comments you have about this compendium.
- SpacesandProperties.pdf : An enumeration of the most common spaces seen in Applied Math, and descriptions of their defining traits.
- CompressibleFluidsNotes.pdf : Introduces the theory and physics behind shock hydrodynamics
- Appendix.pdf : Common identities, useful results, and summaries of the most critical theorems.
- IntroductoryAnalysis.pdf : Introductory results and theories from real analysis, set theory, topology, and calculus.
- PrinciplesofAppliedMath.pdf : Operator theory, eigenspaces, fourier analysis
- LinearAlgebra.pdf : Everything you have ever wanted to know about matrices.
- NumericalAnalysis.pdf : Currently this includes error analysis, convergence, and a few numerical methods.
- OrdinaryDifferentialEquations.pdf : Advanced theory of ordinary differential equations.
- PartialDifferentialEquations.pdf : Advanced theory of partial differential equations.
- FiniteDifferenceMethods.pdf : Introduces the theory behind Finite Difference Methods.
- FiniteElementMethods.pdf : Introduces the theory behind Finite Element Methods.