A cheatsheet for the Analysis 3 course (401-0353-00L), taken in fall 2025. The content is based primarily on the official lecture notes for the course.
Some mistakes are guaranteed; if you find any, please open an issue/pull request.
- Method of characteristics for first-order PDEs
- Conservation laws, shock waves, and Burgers' equation
- Classification of second-order PDEs (hyperbolic, parabolic, elliptic)
- Heat and wave equations with Dirichlet, Neumann, and mixed boundary conditions
- Separation of variables and eigenfunction expansions
- Elliptic problems in rectangular and circular domains
- Harmonic functions and maximum principles
- Appendix with trigonometric identities, Fourier series orthogonality, and derivative/antiderivative formulas
Requires a LaTeX distribution (TeX Live, MikTeX, etc.):
# compile main.tex using pdflatex or lualatex
pdflatex main.tex- Multiple runs may be necessary for references, table of contents, and cross-references.
- Kevin Frunz - basically wrote most of the cheatsheet, including Separation of Variables and Elliptic Problems
- EstaticEclipse - helped with proofreading and fixes
MIT License (LICENSE) - feel free to use, modify, share.