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Calculus of Variations (Udemy.com)

The First Variation

4.5
108 reviews

Created by: Ross McGowan

Last updated August 2023

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What you will 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

How it compares

Against the other 127 rated Udemy courses in Math on CourseDuck:

  • Rating4.5 out of 5higher than 25% of them
  • Reviews108#102 of 128 by number of reviews
  • Length6 hoursshorter than 66% of them
  • Last updatedAugust 2023earlier than 62% of them

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Course 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.

Read More Intermediate Intermediate Level product length iconTime: 6h

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Instructor Details

Ross McGowan

Hi, I'm Ross. I currently teach mathematics and statistics at Glasgow University International College (GIC). I help students build a strong conceptual foundation in mathematical reasoning, computational thinking, and statistical analysis—skills that are essential in both academia and industry.

Before moving into teaching, I spent 7 years working in the semiconductor industry, specialising in analogue and mixed-signal integrated circuit (IC) design. This work gave me a deep appreciation for the mathematical and physical principles underlying real-world systems, particularly those related to signal processing, data conversion, and precision arithmetic.

After my time in IC design, I transitioned into the mobile telecommunications sector, working on the rollout and optimisation of mobile networks. This gave me a practical understanding of large-scale systems, reliability engineering, and the complexity of real-time digital communication.

Today, my focus is on the fundamentals of computer architecture and the mathematics of algorithm design. I’m especially interested in floating-point number systems—how they work at the hardware level, how algorithms are adapted to their quirks, and how performance can be squeezed out of tight constraints. I’ve written my own assembler, designed a custom 16-bit CPU (the RTM-16), and implemented mathematical algorithms in both high-level languages and assembly.

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Reviews

4.5

108 ratings on Udemy

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By Jakub Kowalczyk on 7/2/2023

Because everything is explained in detail it allows one to focus on the areas that aren't understood well and fast-track through ones that are. Well made and comprehensive

By Adil hafeez on 4/21/2022

Professor is really an expert particularly in these domains of Math.... he always explained the math by taking the analogy in real world which makes it fun to learn.

By Martin Reynolds on 8/28/2021

Well I've just finished Section 1.7 and it seems OK. I think I spotted the need for a delta function which went unmentioned.

By Adam Vile on 8/22/2021

Really well explained, just at the right level (you probably need undergrad level calculus) and very clear. I studied the calculus of variations at university and was clueless, within minutes of this course the penny dropped. Thank you

By Jeffrey Ehme on 6/23/2021

Spent a lot of time talking about a very minor and easy topic.

By Kresimir Duvnjak on 12/22/2020

Finally some course which depicts the smallest details instead of 'generalized conclusion' out of black box. Precise and easy to follow. Videos are filled with manualy transcribing algebra equations. I feel like I am finaly watching TV from the front and not from above. THANK YOU for these courses.

By Mira Sanger on 3/7/2020

This course has been a wonderful introduction to the calculus of variations! Ross has taught it in a very straightforward way with so many examples to help you. I admittedly never expected to get much from an online course but I was totally proven wrong here. I'd recommend this course many times over, especially for fellow physics majors!

By Ka Im on 1/4/2020

Good course but requires familiarity with the topic as the contents are quite difficult and rely heavily on strong mathematical foundation. Section 3 maybe covered earlier for better understanding of the example problems solved in section 2.

By Alex Chilton on 12/8/2019

Excellent... :-) Having studied mathematical physics at the same uni as Ross, I wasn't sure what to expect...but its nicely done, only thing i would change is his pronunciation of derivative ;-) In lecture 10 he mentions he could do a whole course on lagrangians, that would be fun - throw in Hamiltonians too! I'd buy it...

By Jonathan Cooke on 11/30/2019

This course is incredible and a rare find! The instructor begins with physical intuition and builds from there. Like he mentions, you won't find a course about calculus of variations on the web like this. Most of what I've found has been a random assortment of videos compiled into playlists. The instructor generously answers questions and clearly loves the subject. Do yourself a favor and purchase his course.

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Overall Score : 90 / 100

Calculus of Variations
Visit course on Udemy Write a review
  • Video Duration: icon 6h
  • Price: $59.99
  • Provider: icon Udemy
  • Updated: icon August 2023
  • Level: Intermediate Intermediate
  • Language: icon English
  • Certificate: icon Yes
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