Interactive Computational Mathematics Tutorial
Learn essential skills for solving computational math problems in MATLAB
This tutorial introduces you to the use of MATLAB® and Optimization Toolbox™ for solving numeric computation problems. It includes a section on using Optimization Toolbox™ for determining critical points using various algorithms built-in to MATLAB. Select sections based on your experience with computational math. Click on any section link to begin.
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Academic Tutorial (approximately 195 minutes)
Computational Mathematics Tutorial Introduction 4:11
Introduces the examples and shows how to download them.
Linear Algebra (60 minutes)
Learn the basics of solving linear systems in MATLAB.
- Introduction to Linear Algebra 1:35
See the examples that will be used in the subsequent sections.
- Solving Linear Systems 16:26
Learn how to carry out basic matrix algebra to solve problems in MATLAB.
- Eigenvalue Decomposition 22:44
Learn how to carry out eigenvalue decomposition in MATLAB.
- Singular Value Decomposition 14:55
Learn how to carry out singular value decomposition in MATLAB.
Solving Ordinary Differential Equations (60 minutes)
Learn to solve ordinary differential equations (ODEs) numerically in MATLAB.
- Introduction to Solving Ordinary Differential Equations 4:57
See the spacecraft example used throughout this module and different methods used to analyze or solve first-order ODEs.
- Numerical Solution to ODEs 18:21
Obtain numerical solutions for first-order ODEs in MATLAB.
- Solving First-Order Systems 13:11
Reduce higher-order ODEs and higher-order systems of ODEs to a first-order system.
- MATLAB ODE Solver Options 17:15
Set solver options for ODE solvers in MATLAB, specifically with regard to event handling. Determine which solver to use when the system is stiff.
Data Fitting and Working with Nonlinear Equations (50 minutes)
Implement data fitting methods and analyze nonlinear equations in MATLAB.
- Introduction to Data Fitting and Working with Nonlinear Equations 1:56
See the daily electricity consumption data used throughout this module.
- Data-Driven Models 27:16
Apply interpolation and curve fitting using least squares to the data.
- Solving Nonlinear Equations 18:29
Model and tune common compensators to meet design requirements.