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1
Parametric curves and arc length
2
Line integrals of functions
3
Example: line integral of a function
4
Introducing vector fields
5
The 'del' operator
6
The gradient vector field
7
Divergence of a vector field
8
Curl of a vector field
9
Some divergence examples
10
Interpreting curl
11
Line integrals of scalar fields, revisited
12
Line integrals of vector fields
13
Line integral example 1
14
Line integral example 2
15
Terminology for curves
16
Properties of line integrals
17
Fundamental Theorem of Calculus
18
FTC example 1
19
FTC example 2
20
FTC example 3
21
FTC example 4
22
Conservative vector fields and independence of path
23
Further terminology for curves in the plane
24
Green's Theorem
25
Verifying Green's Theorem with an example
26
Sketching the proof of Green's Theorem
27
Green's Theorem for multiply-connected domains: an example
28
Using Green's Theorem to find the area under a cycloid
29
Green's Theorem and polygon areas
30
Parametric surfaces
31
Tangent and normal vectors for parametric surfaces; surface area
32
Surface area
33
Surface area of a sphere
34
Surface integral of a scalar field
35
Surface integrals of vector fields
36
Surface integral example
37
Computing flux across a cube (surface with 6 faces!)
38
Some surface integrals over spheres
39
The Divergence Theorem
40
Gauss' Law
41
Stokes' Theorem
42
Using Stokes' Theorem: Example 1
43
Using Stokes' Theorem: Example 2
Description:
Dive into a comprehensive exploration of vector calculus through a series of video lectures designed for advanced calculus students. Learn about parametric curves, line integrals, vector fields, and fundamental theorems in multivariable calculus. Explore concepts such as the gradient, divergence, and curl of vector fields, and master techniques for solving line and surface integrals. Discover important theorems like Green's Theorem, the Divergence Theorem, and Stokes' Theorem, along with their applications. Gain insights into parametric surfaces, surface area calculations, and flux computations. Enhance your understanding of vector calculus through numerous examples and practical applications, preparing you for advanced mathematical analysis in physics and engineering.

APEX Calculus - Vector Calculus

Sean Fitzpatrick
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#Mathematics #Calculus #Vector Calculus #Green's Theorem #Vector Fields #Surface Integrals #Divergence Theorem #Line Integrals #Divergence #Programming #Web Development #cURL
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Parametric curves and arc length