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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