Contents
1 Complex Numbers
 1.1 Basic Properties
 1.2 Polar Form of Complex Numbers
 1.3 The Exponential Function
 1.4 Euler’s Formula
 1.5 Trigonometric and Hyperbolic Functions
2 Second Order Linear Differential Equations
 2.1 Ordinary 2nd Order Linear Differential Equations
 2.2 ODE with constant coefficients I
 2.3 2nd order ODE with constant coefficients II
 2.4 Inhomogeneous Equations
 2.5 * Green’s function approach
3 Functions of more than one variable
 3.1 Functions of several variables
 3.2 Partial Derivatives
 3.3 Curves on Surfaces
 3.4 The Gradient
4 Series and Limits
 4.1 Finite and Infinite Series
 4.2 Taylor–Series
 4.3 Taylor–Expansion of Functions
 4.4 Further Examples for Series and Limits
5 Two–by–Two Matrices
 5.1 Two-by-Two Matrices: Introduction
 5.2 Two–by–Two Matrices: Linear Mappings
 5.3 Two–by–Two Matrices: Index Notation and Multiplication
 5.4 Inverse of a Matrix
 5.5 Eigenvalues and eigenvectors