Applied Analysis

Applied Analysis

1. Complex Analysis
   i. Complex variables and complex valued functions
   ii. Analytic functions and integration along contours
   iii. Residue calculus
   iv. Extreme-, stationary- and saddle-point methods (bonus
2. Fourier Analysis
   i. Fourier tranform and inverse Fourier transform
   ii. Properties of 1d Fourier transform
   iii. Dirac's delta-function
   iv. Closed form representation for select Fourier transforms
   v. Fourier series: introduction
   vi. Properties of the Fourier series
   vii. Riemann-Lebesgue lemma
   viii. Gibbs phenomenon
   ix. Laplace transform
   x. From differential to algebraic equations with Fourier transform, Fourier series and Laplace transform