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Fourier and Laplace Transforms
Rating: 4.6 out of 5(126 ratings)
1,651 students

Fourier and Laplace Transforms

The Mathematics of the Fourier and Laplace Transforms
Created byRoss McGowan
Last updated 3/2022
English

What you'll learn

  • Gain an Intuitive Understanding of the Fourier and Laplace Transforms.
  • Understand the Core Mathematics of Transforms.
  • Build Intuition using a Unique 3D Graphical Approach.
  • Matlab Simulation Files.
  • A Deeper Mathematical Understanding.
  • 196 Course Slides in Colour and Black and White for Printing.
  • Subtitles Manually Updated in English and Converted to 78 Different Languages.

Explore related topics

Course content

6 sections • 53 lectures • 9h 53m total length

  • Introduction2:26

    Introductory video to say hello and let you put a face to the voice. Also see the original course hand written notes in black and white and colour in the resources section. Note these have been superseded by the course slides which are in the resources section of the next video.

  • Course Slides13:16

    This video shows the entire 196 course slides. They are available in the resource section for download as colour and black and white for printing.

  • Derivation of Taylor Series26:33

    In this video I derive the Taylor series and also take a look at the approximation of the sin function on a graphical calculator. (New course video)

  • Euler's Identity and the Complex Exponential11:29

    From the Taylor polynomial I derive the complex exponential. (New course video)

  • Derivation of the Fourier Series Part 111:16

    Errata - At 1.42 I say a vector is defined as a directed line segment. This a very limited view of a vector. In fact a vector has a very precise mathematical definition and is any mathematical entity that adheres to a well defined set of axioms.

    This is the first of three videos deriving the Fourier Series.(New course video).

  • Derivation of the Fourier Series Part 216:05

    This is the second of three videos deriving the Fourier Series. (New course video).

  • Derivation of the Fourier Series Part 311:49

    This is the final of three videos deriving the Fourier Series. (New course video).

  • Fourier Series Approximation to a Square Wave15:24

    In this lecture we derive the Fourier series approximation to a square wave and look at it in the graphical calculator.(New course video).

  • Time and the Complex Exponential15:48

    We introduce time to the Fourier series and the complex exponential.

  • Phase Shift7:26

    A look at different ways of writing Fourier Series and why we choose this particular realisation.

  • Course Book4:31

    This video shows the complete course book, in order to give you a flavour of what is to come. You can download this pdf in colour or black and white for easy printing. The course book has been superseded by the new course slides but I have left it in as you may find it useful.

Requirements

  • Basic calculus (differentiation and integration) and some imagination and enthusiasm.

Description

This course is an introduction to the Fourier and Laplace Transforms. I introduce this subject both geometrically to give a good intuition using Matlab simulations and an online graphical calculator and also in a more formal mathematical way. The equations are broken down into small elements and an intuitive 3 dimensional graphical method is used in order to build intuition and finally understanding of the mathematics. This 3D intuitive learning approach is also backed up by some solid mathematics. This course has been created in order to give you a core understanding of the methods of mathematical transforms. Some sections are quite advanced and some real thinking is required. Your time and dedication will be rewarded with a deeper understanding of this beautiful subject.

Subtitles manually updated in English and converted to 78 different languages.

I can assure you that if you are willing to take the time to comprehend the mathematics then the effort will be rewarded ten fold.  For example , Fourier Transform (FT) , Discrete Time Fourier Transform (DTFT) , Discrete Frequency Fourier Transform (DFFT) , Discrete Time and Frequency Fourier Transform (DTFFT) , the Discrete Fourier Transform (DFT), the Fast Fourier Transform (FFT) , discrete versions of the  Laplace Transform (Z-transform). How are they all related ? By the end of this course you will understand where they all come from and how they are all related to one another. This is not a course about the practical implementation of transforms. This course is about understanding the core subject at a deeper mathematical level. This course is for those who want to truly understand this subject. If you want a new shiny car just to drive then this is not the course for you. If you want to open up the bonnet and take the engine apart to see how it works then this is definitely the course for you.


Who this course is for:

  • This is a course targeted towards those who really want to understand the Fourier and Laplace Transforms at a deeper level.

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