### Lecture Description

In this video I continue with my tutorials which cover the necessary vector calculus for classical electromagnetism which is pitched at university undergraduate level. Specifically I introduce arguably the most important operator in vector calculus.

### Course Index

- Vector Components
- Scalar Dot Product
- Vector Cross Product (1/2)
- Vector Cross Product (2/2)
- Law of Cosines
- Separation Vector
- Nabla Operator (1/2)
- The Gradient Grad
- The Normal Vector
- Why the Gradient is Perpendicular to Functions
- Directional Derivative
- The Nabla Operator (2/2)
- The Divergence
- The Curl of a Vector Field
- Product Rules for Grad Div Curl
- Vector Product Rule 2
- Vector Product Rule 3
- Vector Product Rule 4
- Vector Product Rule 5
- Vector Product Rule 6
- Vector Quotient Rule 1
- Vector Quotient Rule 2
- Vector Quotient Rule 3
- The Laplacian
- Curl of the Gradient
- Divergence of the Curl
- Curl of the Curl
- Fundamental Theorem of Calculus
- Fundamental Theorem for Gradients
- Green's Divergence Theorem
- Stokes' Theorem
- Integration by Parts Rule 1
- Integration by Parts Example
- Integration by Parts Rule 2
- Integration by Parts Rule 3
- Integration by Parts Rule 4
- Spherical Polar Co-ordinates
- Helmholtz Theorem (No Derivation)
- Dirac Delta Function (1/2)
- Dirac Delta Function (2/2)
- Gradient of One Over the Separation Vector
- Laplacian of One Over the Separation Vector
- Helmholtz Theorem Proof (Part 1)
- Helmholtz Theorem Proof (Part 2)
- Derivation Biot and Savart Law

### Course Description

This video tutorial series covers a range of vector calculus topics such as grad, div, curl, the fundamental theorems, integration by parts, the Dirac Delta Function, the Helmholtz Theorem, spherical polar co-ordinates etc.

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