Differential Equations and Transformations

The resources below revisit complex Maths topics included your STEM course. Watch the videos and work through the exercises to boost your knowledge and understanding. If you need to 'dig deeper', please check the Higher section on the previous page or if you are looking for something more specific, use "Ctrl+F" for a faster search.

Enjoy your learning!

Differential equations

First-order differential equations

• Video: An Introduction to First order Linear Differential Equations
• HELM Workbook: First order differential equations (with solutions)

Second-order differential equations

• Video: Second Order Linear Differential Equations
• HELM Workbook: Second order differential equations (with solutions)

Use of differential equations

• Video: Differential equations, a tourist's guide
• Exercise booklet: Modelling with differential equations
• Exercise booklet: Applications of differential equations

Fourier Transforms

Introduction

• Video: Introduction to the Fourier Transform
• HELM Workbook: An introduction to Fourier transformations

Properties of Fourier transforms

• Video: Properties of Fourier Transform
• HELM Exercise Workbook on Fourier transformations

Special Fourier transform pairs

• Video: What is the Fourier Transform?
• HELM Exercises on FTs

Periodic functions

• Video: Intro to FOURIER SERIES: The Big Idea
• HELM Workbook on Periodic Functions

Representing periodic functions by Fourier series

• Video: Fourier Series introduction
• HELM Workbook on representing functions

Even and odd functions

• Video: Computing the Fourier Series of EVEN or ODD Functions
• HELM Workbook on Even and Odd Functions

Convergence

• Video: Fourier Series - the Fourier Convergence Theorem
• HELM Workbook on Convergence

Partial Differential equations

Introduction

• Video: Partial Differential Equations Overview
• HELM Workbook on Partial Differential Equations

Solutions using separation of variables

• Video: Separation of Variables
• HELM Workbook on Solutions using separations of variables

Solution using Fourier series

• Video: Using Fourier Series to Find a Particular Solution to an ODE
• HELM Workbook on 2-periodic Fourier series