Self-made MATLAB Toolbox for numerical analysis.
Chapter 2 MATLAB Programming
Chapter 3 Solving Equations: 1. Symbolic Computation 2. Numerical Computation: (1) Bisection Method (2) Fixed-Point Iteration Method (3) Newton's Method (4) The Secant Method
Chapter 4 Interpolation: 1. Lagrange Interpolation Method 2. Newton's Divided Differences 3. Hermite Interpolation 4. Cubic Spline Interpolation
Chapter 5 Least Squares: 1. Linear Least Squares: (1) The Normal Equation (2) QR Factorization 2. Nonlinear Least Squares: (1) Gauss-Newton Method (2) Levenberg-Marquardt Method
Chapter 6 Differentiation and Integration: 1. Symbolic Computation 2. Numerical Computation: (1) Numerical Differentiation: a. Finite Difference Formulas b. Richardson Extrapolation (2) Numerical Integration: a. Newton-Cotes Methods b. Romberg Integration
Chapter 7 Ordinary Differential Equations: 1. Symbolic Computation 2. Numerical Computation: (1) Scalar Difference Equations: a. Euler's Method b. The Trapezoid Method c. Runge-Kutta Methods (2) Systems of Differential Equations: a. Runge-Kutta Methods b. Implicit Trapezoid Method
Chapter 8 Boundary Value Problems: 1. Symbolic Computation 2. Numerical Computation: (1) Shooting Method (2) Finite Difference Methods a. Linear boundary value problems b. Nonlinear boundary value problems (3) Finite Element Method
Chapter 9 Optimization: 1. One-Dimensional Minimization: (1) Golden Section Search (2) Newton's Method (3) Inaccurate Linear Search 2. Unconstrained Optimization: (1) Steepest Descent Method (2) Newton's Method (3) Quasi-Newton Method 3. Linear Programming:
Chapter 10 Fourier Analysis: 1. Fourier analysis: (1) Fourier Series (2) Fourier Transform (3) Discrete Time Fourier Transform (DTFT) (4) Discrete Fourier Transform (DFT) (5) Fast Fourier Transform (FFT)
Final Project: Trajectory planning and attitude optimazation for UAV by NURBS Spline and Interpolation in SE(3).
I also provide a GUI and demo for this project by MATLAB Simulink