Higher Mathematics 4

Prof. Dr.-Ing. Dieter Kraus

14. Partial Differential Equations (pdf)
   14.1 Fundamental Terms
   14.2 Solution Methods for the Wave Equation
          14.2.1 Initial Value Problem of the Wave Equation
          14.2.2 Initial Value and Initial Boundary Value Problem of the Wave Equation
   14.3  Solution Methods for the Heat Concuction Equation
   14.4 Solution of the Laplace Equation in specific regions
          14.4.1 Solution of the Laplace Equation in a Disc
          14.4.2 Solution of the Laplace Equation in a Sphere
          14.4.3 Solution of the Laplace Equation in a Cylinder

15. Function Theory (pdf)
   15.1 Complex Number Plane
         15.1.1 Sequences and Series in C
         15.1.2 Curves in C
         15.1.3 Regions in C
   15.2 Complex Functions
         15.2.1 Conitnuity of Complex Functions
         15.2.2 Elementary Complex Functions
         15.2.3 Differentiability of Complex Functions
         15.2.4 Inverse Functions
         15.2.5 Conformal Mappings
   15.3 Complex Integration
         15.3.1 Complex Line Integrale
         15.3.2 Cauchy's Integral Theorem
         15.3.3 Cauchy's Integral Formulae
         15.3.4 Primitives
   15.4 Series Expansion of Complex Functions
         15.4.1 Power Series
         15.4.2 Laurent Series
         15.4.3 Isolated Singularities
   15.5 Residue Theorem and its Applications
         15.5.1 Residue Theorem
         15.5.2 Calculation of real Integrals using the Residue Theorem
         15.5.3 Calculation of the inverse Laplace Transform using the Residue Theorem

16. Numerical Mathematics (pdf)
   16.1 Linear Equation Systems
         16.1.1 Gaussian Elimination
         16.1.2 Accuracy Considerations, Error Estimation
         16.1.3 Cholesky Decomposition
   16.2 Nonlinear Equation Systems
         16.2.1 Introduction
         16.2.2 Newton Method
         16.2.3 Damped Newton Method
         16.2.4 Application Example, Calculation of Extrema
   16.3 Eigen Value Calculation for Matrices
         16.3.1 Basics
         16.3.2 von Mises Method
         16.3.3 Wielandt Mehtod
   16.4 Interpolation
         16.4.1 Lagrange Interpolation
         16.4.2 Approximation of a Function by Interpolation Polynomials
         16.4.3 Newton Interpolation
         16.4.4 Hermite Interpolation
         16.4.5 Spline Interpolation
   16.5 Numerics of Partial Differential Equations
         16.5.1 Difference Methods

17. Probability Calculus (pdf)
   17.1 Definitions, Examples
   17.2 Conditional Probabilities,independent Events
   17.3 Random Variables and Distribution Functions
   17.4 Mean Value and Variance
   17.5 Examples for Distribution Functions
         17.5.1 Bernoulli Distribution
         17.5.2 Binomial Distribution
         17.5.3 Poisson Distribution
         17.5.4 Hypergeometric Distribution
         17.5.5 Rectangular/Uniform Distribution
         17.5.6 Exponential Distribution
         17.5.7 Normal Distribution