1 General Programming
1.1 MATLAB: General properties
1.2 MATLAB: General usage
1.3 MATLAB: Variables and elementary operations
1.4 MATLAB: Functions
1.5 Algorithms
1.6 Representation of numbers: Binary and hexadecimal
1.7 Representation of numbers: Floating point numbers
1.8 Representation of numbers: Truncation and rounding
1.9 Numerical Errors: Examples of common appearing
1.10 Numerical Errors: Basic definitions
1.11 Numerical Errors: Due to finite-precision floating-point arithmetic
2 Interpolation
2.1 Introduction
2.2 Polynomial interpolation: Introduction
2.3 Polynomial interpolation: Calculation according to Lagrange
2.4 Polynomial interpolation: Calculation according to Newton
2.5 Cubic spline interpolation
3 Finding Zeros
3.1 Introduction
3.2 Fixed Points: A Footing for Iterative Methods
3.3 Interval Bisection Method
3.4 Secant Algorithm
3.5 Brackening
3.6 Newton Algorithm
4 Numerical Optimization
4.1 Introduction
4.2 Golden Section Search in One Dimension
4.3 Linear Least Squares
4.4 Linear Least Squares: Matrix formulation
4.5 Linear Least Squares: Example and remark
5 Systems of Linear Equations
5.1 Introduction
5.2 Gaussian Elimination Method
5.3 Partial Pivoting
6 Numerical Integration
6.1 Introduction
6.2 Trapezoidal Rule
6.3 Simpson’s Rule
7 Integration of Ordinary Differential Equations
7.1 Introduction
7.2 Euler’s Method
7.3 Runge–Kutta Method
7.4 Stiff sets of differential equations
8 Monte-Carlo-Simulation
8.1 Introduction
8.2 Detailed balance condition and Metropolis algorithm
8.3 Random walk
9 Exercises
9.1 Exercise 1
9.2 Exercise 2
9.3 Exercise 3
9.4 Exercise 4
9.5 Exercise 5
9.6 Exercise 6
9.7 Exercise 7
9.8 Exercise 8