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Vector Calculus (Div Grad Curl)
Rating: 4.5 out of 5(45 ratings)
620 students

Vector Calculus (Div Grad Curl)

Divergence , Gradient , Curl , Laplacian vector operators derived and explained
Created byRoss McGowan
Last updated 3/2019
English

What you'll learn

  • Gain an understanding of divergence, gradient, curl and Laplacian vector calculus operators
  • Matlab Simulations
  • Course pdf book

Explore related topics

Course content

4 sections • 35 lectures • 5h 16m total length

  • Course Book6:18

    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.

  • Introduction1:00

    Short introduction to say hello

  • Vector Functions7:29

    This is an easy introduction to the idea of a vector function.

  • Electrostatics10:06

    An introduction to vector functions

  • Unit Normal23:54

    Derivation of the unit normal vector

  • Surface Integral22:14

    Introduction to the surface integral

  • Flux4:40

    Derivation of the idea of flux

  • Divergence of a Vector Field10:08

    Now we are getting somewhere.

  • Divergence in Cylindrical Coordinates13:08

    Derivation of divergence in cylindrical coordinates

  • Divergence in Spherical Coordinates14:33

    Derivation of divergence in spherical coordinates

  • The Del Operator1:55

    The del operator

  • Divergence Theorem8:52

    Divergence theorem

  • MATLAB Divergence6:49

    In this video I look at a Matlab simulation of divergence.

Requirements

  • Basic Calculus

Description

If you have ever wondered what the vector calculus operators divergence , gradient and curl mean and where they come from then this course is for you. With Matlab  simulations of the vector calculus operators to give you a good graphical intuition.

In this course we derive the vector operators DIV GRAD  CURL and LAPLACIAN in cartesian, cylindrical and spherical coordinates. We also take a look at Stoke's theorem and look at their use in Electromagnetics. The course covers all the mathematics you need to know in order to understand Maxwell's field equations for Electromagnetics and is an ideal mathematical primer for anyone who wants to study Electromagnetics or fluid dynamics.

The mathematics of Divergence , Gradient  , Curl and Laplacian derived from first principles with a graphical intuition in a manner which you will not have seen before. If you really want to understand the core mathematics of Vector Calculus then this  course will provide you with a step by step derivation of the mathematics and also a graphical intuition.

This is a subject that always interested me and I could not find any explanations other than very basic derivations. This is why I generated my own course so that I could teach it the way I thought it should be taught.



Who this course is for:

  • Anyone who wants to understand Divergence , Gradient and Curl of a vector field. This course would also suit anyone who wants to study electromagnetics or maybe fluid dynamics as it provides an introduction to the mathematics required to study these subjects.

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