## Calculus of variations

What is the Euler-Lagrange equationHow to calculate the functional derivative

What are the various application of the functional derivative

How to evaluate the first integral

How to use the Lagrangian function

How to use the Noether's theorem

## Linear Ordinary Differential Equations

How to determine existence and uniqueness of solutions to linear ODEsHow to put an ODE in normal form

How to solve inhomogeneous equations

How to solve differential equations with singular points

## Linear Differential Operators

What is a formal operator## Green functions

How to solve inhomogeneous linear equationsHow to construct Green functions

How to apply Lagrange's identity

## Partial differential equations

How to classify PDEs## Mathematics of real waves

What is the relationship between the speed of propagation and the frequency of a wave## Special functions and complex variables

What is the Gamma functionHow to solve linear differential equations with coefficients that are meromorphic functions