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Solving Ordinary Differential Equations with MATLAB

## Modules

## Lessons

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Course Overview

Course Outline What is an Ordinary Differential Equation? Introduce differential equations, and what it means to find a solution. Solving ODEs Numerically Use MATLAB ODE solvers to find and
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Course Example – The Shuttle Launch

The Shuttle Launch Here's an example of an application of the math discussed in this course. What could you do if you wanted to estimate the velocity of the space
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Introducing the Differential Equation

Imagine you could take pictures of a shuttle launch infinitely fast, so you could measure its height at any time and use the ratio to approximate its velocity. As you take
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Solutions to Differential Equations

Space Shuttle Ballistic Trajectory Let's return to the problem of finding the velocity of the space shuttle. If the shuttle followed a ballistic trajectory (that is, like a ball
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Using MATLAB ODE Solvers

Reference: MATLAB ODE Solver Syntax Calling ode45 and Interpreting the Outputs In this interaction, you'll solve the differential equation dy/dt=sin(t) from t=0 to t=4π with the initial condition y(0)=0. You will use the ode45 function and interpret
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Writing ODE Functions

The Structure of an ODE Function The ODE function is a MATLAB function that represents the ODE for use in a MATLAB ODE solver, like ode45. The ODE function
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Obtaining a General Solution Structure

ODE Solution Structures Typically, ode45 produces two output variables: a vector for the independent variable and a vector of the corresponding dependent variable. What if you want to know
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Review – Solving ODEs Numerically

MATLAB ODE Solver Syntax ode45 with two outputs ode45 with one output Structure of an ODE function The ODE function is a MATLAB function that represents the ODE
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Course Example – The SIR Model

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Implementing a First-Order System of ODEs

Implementing a System of ODEs in MATLAB Vector-Valued ODEs To use a MATLAB ODE solver like ode45, the ODE function must have one output variable and one input dependent
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Using ode45 to Solve Systems of ODEs

Using MATLAB ODE Solvers with Systems of ODEs You can solve a system of ODEs numerically in much the same way you solved a single scalar ODE, using the
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Review – Solving Systems of ODEs Numerically

You can solve a system of differential equations using ode45 just like you would for a single differential equation. The main differences are the input Y0 and the output YSol