### 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 in this video I discuss an extremely powerful technique in mathematics known as integration by parts. We shall see in the future that it can be done in many may ways on very many expressions!

### 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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