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 discuss the dot or scalar product which is an essential quantity for simplifying mathematical expressions.

1. Vector Components
2. Scalar Dot Product
3. Vector Cross Product (1/2)
4. Vector Cross Product (2/2)
5. Law of Cosines
6. Separation Vector
7. Nabla Operator (1/2)
8. The Gradient Grad
9. The Normal Vector
10. Why the Gradient is Perpendicular to Functions
11. Directional Derivative
12. The Nabla Operator (2/2)
13. The Divergence
14. The Curl of a Vector Field
15. Product Rules for Grad Div Curl
16. Vector Product Rule 2
17. Vector Product Rule 3
18. Vector Product Rule 4
19. Vector Product Rule 5
20. Vector Product Rule 6
21. Vector Quotient Rule 1
22. Vector Quotient Rule 2
23. Vector Quotient Rule 3
24. The Laplacian
25. Curl of the Gradient
26. Divergence of the Curl
27. Curl of the Curl
28. Fundamental Theorem of Calculus
29. Fundamental Theorem for Gradients
30. Green's Divergence Theorem
31. Stokes' Theorem
32. Integration by Parts Rule 1
33. Integration by Parts Example
34. Integration by Parts Rule 2
35. Integration by Parts Rule 3
36. Integration by Parts Rule 4
37. Spherical Polar Co-ordinates
38. Helmholtz Theorem (No Derivation)
39. Dirac Delta Function (1/2)
40. Dirac Delta Function (2/2)
41. Gradient of One Over the Separation Vector
42. Laplacian of One Over the Separation Vector
43. Helmholtz Theorem Proof (Part 1)
44. Helmholtz Theorem Proof (Part 2)
45. Derivation Biot and Savart Law

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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