Syllabus
- Introduction
- Modelling and Error Analysis
- Mathematical Model
- A Simple Mathematical Model
- Approximations and Round-Off Errors
- Significant Figures
- Accuracy and Precision
- Error Definitions
- Round-Off Errors
- Truncation Errors and the Taylor Series
- The Taylor Series
- Error Propagation
- Total Numerical Error
- Mathematical Model
- Taking derivatives
- General discussion of derivatives with computers
- Forward difference
- Central difference and higher order methods
- Higher order derivatives
- Solution of nonlinear equations [excel]
- Bisection method
- Newton’s method
- Method of secants
- Brute force method
- Interpolation [excel]
- Lagrange interpolation
- Neville’s algorithm
- Linear interpolation
- Polynomial interpolation
- Cubic spline
- Matrices [Matriks-1] [Matriks-2]
- Linear systems of equations
- Gaussian elimination
- Standard libraries
- Eigenvalue problem
- Curve Fitting
- Linear Regression [excel]
- Polynomial Regression
- Multiple Linear Regression
- General Linear Least Squares
- Nonlinear Regression
- Numerical integration [excel]
- Introduction to numerical integration
- The simplest integration methods
- More advanced integration
- Ordinary differential equation
- Introduction
- The simple Euler method [ODE-Euler]
- The modified Euler method
- Runge–Kutta method [excel-1] [excel-2]
- Adaptive step size Runge–Kutta
- Partial differential equations [excel]