Notes
Selected notes and teaching materials, organized by topic and language.
Calculus, Analysis, and ODE
- Functions of a real variable
- Continuity and differentiation
- Parametrizations and loci
- Critical points
- Multiple integrals
- Vector fields
- Review of linear algebra
- Differentiation
- Introduction to manifolds
- Critical points
- Riemann integral
- Stokes' theorem
- Basic concepts
- Abel's identity
- Power series solutions
- Frobenius series solutions
- The Laplace transform
- Computer arithmetic
- Power series
- Baire's theorem
- Constant coefficient linear differential equations
Complex Analysis
- Complex numbers
- Complex differentiability
- Power series
- Elementary functions
- Fundamental theorems
- Isolated singularites
- Harmonic functions
- Power series, analyticity and elementary functions
- Foundations of Cauchy's function theory
- Isolated singularities and the residue theorem
- The Riemann mapping theorem
- Picard's theorems
Partial Differential Equations
- The Cauchy-Kovalevskaya theorem
- The Cauchy-Kovalevskaya theorem
- Elementary introduction to distributions
- Introduction to distributions
- First order equations
- First order equations
- Harmonic functions
- Harmonic functions
- Perron's method
- The Dirichlet problem
- Poisson's equation
- Multipole expansions in two dimensions
- Basic examples of PDEs
Mongolian Materials
English is the main language of the site. Mongolian notes are included as first-class teaching materials where they fit the public archive.