# Advanced mathematical methods

> Study complex analysis, residues, Fourier series, PDE boundary conditions and convexity through focused lessons.

Prerequisites: Complex arithmetic and partial derivatives.

Short self-study course; not an accredited qualification or a complete university syllabus.

## Lessons

- [Holomorphic functions and Cauchy-Riemann equations](https://studybrix.com/en/courses/advanced-mathematical-methods/a-complex-analysis/index.md): advanced; 8 questions.
- [Poles, residues and contour integrals](https://studybrix.com/en/courses/advanced-mathematical-methods/a-residues/index.md): advanced; 8 questions.
- [Fourier coefficients and convergence](https://studybrix.com/en/courses/advanced-mathematical-methods/a-fourier/index.md): advanced; 8 questions.
- [PDE modes, boundaries and initial data](https://studybrix.com/en/courses/advanced-mathematical-methods/a-pde-boundaries/index.md): advanced; 8 questions.
- [Convexity and constrained optimization](https://studybrix.com/en/courses/advanced-mathematical-methods/a-convexity/index.md): advanced; 8 questions.