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Calculus of Variations
Rating: 4.6 out of 5(106 ratings)
933 students

Calculus of Variations

The First Variation
Created byRoss McGowan
Last updated 8/2023
English

What you'll learn

  • A thorough grounding in the Calculus of Variations. Covering the first variation
  • Simulations using a graphical calculator to help your understanding
  • Introduction to the subject using an intuitive geometric approach which you will not see anywhere else
  • Euler Lagrange Equation derived both geometrically and analytically
  • Derivation and simulation of double pendulum

Explore related topics

Course content

5 sections • 40 lectures • 6h 0m total length

  • Introduction2:47

    This is a quick introduction to the course. New course video.

  • Course Slides6:50

    Here are all the course slides. If this looks like the course for you then sign up and let's get started.

  • Motivation8:33

    This is a motivation for the course. Please note that you can easily pick holes in the logic of this video , take it as a very rough introduction and note that much more thorough discussions will follow from it. New course video.

  • Potential Energy of Hanging Rope11:33

    In this video we derive the potential energy of a hanging rope. New course video.

  • Functional4:44

    In this video we derive a general equation for a simple functional.New course video.

  • Road Map to Euler Lagrange5:45

    In this video we look at the bigger picture and create a map of our intended route. New course video.

  • Derivation of Euler Lagrange 15:06

    In this video we derive the first part of the Euler Lagrange equation which looks at a change in position from the equilibrium point. New course video.

  • Derivation of Euler Lagrange 213:14

    In this video we derive the second part of the Euler Lagrange equation which details a change in gradient. New course video.

  • Catenary10:15

    In this video we answer the first question posed in this video series , 'what is the equation of a hanging rope' and then we prove that it is something called a catenary. New course video.

  • Shortest Distance Between 2 Points8:00

    We use the calculus of variations to prove that the shortest distance between 2 points is a straight line. New course video.

  • Simple Pendulum7:57

    In this video we derive the equation of motion of a simple pendulum. New course video.

  • Course Book5:00

    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. If you want to just get started then head onto the next video.

Requirements

  • You will need some basic calculus. Differentiation and integration and some of the rules ,for example, the product rule and chain rule for differentiation and integration by parts. What is more important is a willingness to just think and not to give up at the first hurdle. Also not to fixate on something you do not understand, move on or better still ask me.

Description

This is not your average Udemy course. You will not see the calculus of variations taught as thoroughly and intuitively anywhere on the internet (I know because I looked for such a course and not having found one decided to create this course). You will not see this subject taught in this way anywhere else online. The most important point and value in this course is COMPREHENSION. I want you to understand the subject , I want you to be able to say at the end of this course, 'I OWN THE CALCULUS OF VARIATIONS - IT BELONGS TO ME'.

If you want to understand the calculus of variations as opposed to just applying some random maths equations and wonder what is going on then this is the course for you. What matters is true comprehension. As such I have introduced this subject in a non standard way. I derive the basic building block of calculus of variations namely the Euler-Lagrange equation in  the terms that Euler first derived it and leave the standard derivation to much later in the course. The course has many examples including some of the most famous but also some that you just won't see in any textbook. The derivations are thorough and explained line per line equation to equation. You just won't get this subject taught like this unless you pay to go to university (and even then you will probably get the standard formulaic version).

In this course you will get access to my original derivations , some of which are common derivations you will get in any book but some of the derivations you will not find in any books (I know I looked for them and in the end spent many hours deriving them myself). You can download a PDF copy of each lecture or a PDF of the entire lecture course.

This is NOT AN EASY COURSE and to cover all the maths in depth will take you a lot of time. It will be time well spent as you will learn lots of tips and mathematical tricks that you just won't find anywhere else. I recommend you recreate the derivations and think about them as you walk to work or have coffee at lunch. Don't get put off or dejected - remember I AM HERE if you need help.

Good luck with the course.

Who this course is for:

  • If you have been stuck with your understanding the calculus of variations or you are new to it then this is the course for you.

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