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image for course Solve Higher-Order ODEs

Solve Higher-Order ODEs

Solve higher-order ordinary differential equations (ODEs) in MATLAB by transforming them into systems of first-order ODEs. Learn how to write ODE functions for higher-order problems, define initial conditions, and interpret solutions.

Course modules

Introduction

Familiarize yourself with higher-order ordinary differential equations and the course.

Lessons:
  • Course Overview
  • Learning Outcomes and Prerequisites

Identify Higher-Order ODEs

Learn how to identify and numerically approximate higher-order derivatives.

Lessons:
  • What Are Higher-Order ODEs?
  • Approximate Higher-Order Derivatives

Initial Conditions and Solutions for Higher-Order Problems

Learn how to define the initial conditions for higher-order problems, and use ODE objects to find and interpret solutions.

Lessons:
  • Solve Higher-Order ODEs using ODE Objects
  • Initial Conditions and the Solution Array
  • Set Initial Conditions and Interpret the Solution Array

Second-Order Problems as First-Order Systems

Rewrite second-order ODEs as first-order systems, solve them, and interpret the solutions.

Lessons:
  • Rewrite Second-Order ODE as First-Order Systems
  • Write an ODE Function for a Second-Order ODE
  • Apply a Second-Order ODE to Vibrations

Third-Order Problems as First-Order Systems

Rewrite third-order ODEs as first-order systems, solve them, and interpret the solutions.

Lessons:
  • Rewrite Third-Order ODEs as First-Order Systems
  • Write an ODE Function for a Third-Order ODE
  • Apply a Third-Order ODE to Motion with Jerk

Course Projects

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

Lessons:
  • Model The Tacoma Narrows Bridge
  • Predict the Expansion of the Universe

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

Introduction to Finite Element Analysis with MATLAB

Learn to solve real-world engineering problems with finite element analysis.

Solving Nonlinear Equations with MATLAB

Use root finding methods to solve nonlinear equations.

Introduction to Linear Algebra with MATLAB

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

Solve Systems of First-Order ODEs

Learn to solve and analyze systems of differential equations in MATLAB.

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