Video

MATLAB has some good ODE solvers, but you'll need to understand the big ideas before digging into the syntax. Here's a short, simple intro with the information you'll need.

There are two different kinds of finite difference solutions for differential equations, implicit and explicit. Explicit is easier to program, but might not be stable. Implicit is stable, but might require more calculations. Here's an example showing the difference.

First and second order differential equations show up everywhere in both engineering and physics. Here's a short introduction to solving them with MATLAB

Many of the objects and circuits we use are described by 1st and 2nd order differential equations. Here's a simple intro describing how those equations behave.

MATLAB has a symbolic Laplace Transform function that can be handy. The syntax is a little involved, but simple and powerful once you learn it. I show some results in Mathcad Prime since it's easier to look at, then switch to MATLAB.

Laplace transforms are often used to solve differential equations because they reduce solving a differential equation to just algebra. The best part is that it's not even that hard once you understand the big idea. Very cool.

Initial value problems are everywhere in engineering and physics. Here's how to solve an initial value problem based on a rocket accelerating. The solution is based on finite difference, particularly a forward difference.

Initial value problems are ones in which you know a starting point. The differential equation dictates the points that follow. I present an example the shows the acceleration of a rocket.

MATLAB is a great way to solve differential equations. You can use finite differences or one of the built in solvers.

Diff eqs are just equations with slopes in them, so the solution to one is a function rather than a number (numbers don't have slopes). All physical laws are expressed as differential equations, so they are important.

MATLAB has some very helpful tools for Laplace transforms. This video shows how to do them in MATLAB using the symbolic functions. I also show in Mathcad how the kernel function differs from the Fourier transform.

This is a simple introduction to Laplace transforms. They are related to Fourier transforms and are very handy for solving differential equations.

Here's a simple explanation of how to calculate Fourier transforms in Mathcad and MATLAB. I show the results graphically, so the results are clear.

The Fourier transform is just everywhere in engineering and science. Here's how it is developed from complex Fourier series.

ENGT 509 25-2 Fourier Series in MATLAB

ENGT 509 25-1 Fourier Series

ENGT 509 24-2 Integral Transforms in MATLAB

ENGT 509 24-1 Integral Transforms

ENGT 509 22-2 Machin Like Formulae in MATLAB

ENGT 509 22-1 Machin Like Formulae

ENGT 509 23-2 Vectorizing MATLAB

ENGT 509 23-1 Vectorizing MATLAB - Intro

ENGT 509 21-2 Calculating Pi in MATLAB

ENGT 509 21-1 Algorithms for Calculating Pi

ENGT 509 20-2 Algorithms in MATLAB - Newton's Method

ENGT 509 20-1 Intro to Algorithms - Newton's Method

ENGT 509 19-2 Infinite Series in MATLAB

ENGT 509 19-1 Infinite Series Intro

ENGT 509 18-2 Functions of Complex Numbers MATLAB