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