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image for course Solve Systems of First-Order ODEs

Solve Systems of First-Order ODEs

Explore how to model and solve systems of ordinary differential equations (ODEs) in MATLAB. Learn how to write vector-valued ODE functions, define vector-valued initial conditions, and use ODE solvers to obtain and interpret solutions. By the end of the course, you’ll be equipped to analyze coupled dynamic systems in engineering and science.

Course modules

Introduction

Familiarize yourself with systems of ordinary differential equations and the course.

Lessons:
  • Course Overview
  • Learning Outcomes and Prerequisites

Solve Systems of ODEs Numerically

Define initial conditions, and work with the solution for a system of ODEs.

Lessons:
  • How to Solve a System of ODEs
  • Initial Conditions and the Solution Array
  • Interpret the Solution Array
  • Solve a System of Two ODEs
  • Solve a System of Three ODEs
  • Test Your Knowledge

Write ODE Vector-Valued ODE Functions

Learn how to write ODE functions for systems of ODEs.

Lessons:
  • Represent a System of ODEs as a Vector-Valued ODE
  • Implement ODE Functions for Systems of ODEs
  • Test Your Knowledge

Course Projects

Apply your knowledge of systems of first-order differential equations to challenging projects.

Lessons:
  • Zombie Outbreak
  • Penguin Launcher

Conclusion

Learn next steps and give feedback on the course.

Lessons:
  • Summary
  • Additional Resources
  • Survey

Format:Self-paced

Language:English

Language

  • Hands-on exercises with automated feedback
  • Access to MATLAB through your web browser
  • Shareable progress report and course certificate

Solve Higher-Order ODEs

Learn to solve higher-order differential equations by transforming them into systems of first-order differential equations.

Optimization Onramp

Learn the basics of solving optimization problems in MATLAB using the problem-based approach.

Introduction to Linear Algebra with MATLAB

Use matrix methods to solve systems of linear equations and perform eigenvalue decomposition.

Introduction To Solving Ordinary Differential Equations

Learn to solve and analyze first-order differential equations using MATLAB.

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