# Differential equations
---
1. Elementary ODEs
Integrating factor

Exact equation
Bernoulli equation
Riccati equation

Method of undetermined coefficients
Annihilator method
Differential operators
Picard's theorem
2. Linear ODEs
Wronskian
Abel's formula
Variation of Parameters (VOP)
Series method
Method of Frobenius
Bessel functions
Modified Bessel functions
Airy functions
3. Laplace transform
Laplace transform
Heaviside step function
Convolution theorem (Laplace transform)
Confluent hyergeometric series
3. PDEs
Separation of variables
Maximum principle
Harnack's theorem
4. Sturm-Liouville theory
Operator are an object from functional analysis; familiar with differential operators is required for this chapter.
- Sturm-liouville operator





\part{Advanced}
\chapter{$D$-modules}
Holonomic function