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image for course Introduction To Solving Ordinary Differential Equations

Introduction To Solving Ordinary Differential Equations

Learn the fundamentals of solving first-order ordinary differential equations (ODEs) using MATLAB. Write ODE functions, apply initial conditions, and use ODE solvers to obtain and visualize numerical solutions. By the end of the course, you'll be able to solve a variety of real-world problems modeled by first-order ODEs.

Course modules

Introduction

Familiarize yourself with ordinary differential equations and the course.

Lessons:
  • Course Overview
  • Learning Outcomes and Prerequisites

What is an Ordinary Differential Equation?

Get started with ordinary differential equations (ODEs) and their solutions.

Lessons:
  • Numerical Derivatives
  • Introducing the Ordinary Differential Equation
  • Vocabulary for Differential Equations
  • Solutions to Differential Equations
  • Compare Numerical and Analytical Results to Real-World Data

Solve First-Order ODEs Numerically

Learn the basics of the ODE Object workflow and obtain a solution to an ODE.

Lessons:
  • The ODE Object Workflow
  • Initialize an ODE Object
  • Find and Visualize the Solution to an ODE

Write ODE Functions

Learn the syntax and structure for writing ODE functions.

Lessons:
  • The Structure of an ODE Function
  • Write an ODE Function
  • Types of ODE Functions
  • Write an ODE Function File
  • Pass Additional Parameters to an ODE Function

Course Projects

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

Lessons:
  • Compound Interest
  • Land a Probe on Mars

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 Linear Algebra with MATLAB

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

Solve Higher-Order ODEs

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

Solve Systems of First-Order ODEs

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

MATLAB Onramp

Get started quickly with the basics of MATLAB.

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