Vector Calculus II | 2021-Fall

Course Name
Vector Calculus II
Course Number
mth255
Year/Term
Fall-2021
Course Credits
4
Class meeting times
3 hours of lecture per week
Prerequisites
Course description
Topic/Day
Activities
Resources
Homework Due
1: W 22 Sept
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Euclid \& Vectors
2: F 24 Sept
Curvilinear basis vectors in two dimensions
Acceleration
Position Vector
Curvilinear Position Vector
Vector representation
Distance Formula
Dot Product
Curvilinear Coordinates
3: M 27 Sept
4: T 28 Sept
Vector Addition
Magnitude
Vector addition
Bases
5: W 29 Sept
6: F 1 Oct
7: M 4 Oct
8: T 5 Oct
Vector differential in three dimensions
Vector differential in two dimensions
The Vector Differential
9: W 6 Oct
Vector Differential--Curvilinear
Curvilinear Differential
Gradient in Curvilinear Coordinates
10 :F 8 Oct
11: M 11 Oct
12: T 12 Oct
Gradient
The Hill
Gradient Definition
Gradient Properties
13: W 13 Oct
Gradients, curves and line integrals
14: F 15 Oct
Quiz 1
15: M 18 Oct
16: T 19 Oct
The Valley
Line Integrals on Parametric Curves
Directional Derivatives
17: W 20 Oct
The Pretzel
Scalar Line Integrals
Densities
18: F 22 Oct
Murder Mystery Method
Potential Functions
19: M 25 Oct
Cross Product
Surface Element
Vector Surface Element
20: T 26 Oct
Integrals around closed curves, question of conservative vector fields, real application
The Wire
Path Independence
Conservative Vector Fields
Visualizing Conservative Vector Fields
21: W 27 Oct
Flux Integrals
22: F 29 Oct
23: M 1 Nov
The Cone
Mass
24: T 2 Nov
The Grid
25: W 3 Nov
26: F 5 Nov
Quiz 2
27: M 8 Nov
Visualization of Divergence
Divergence Definition
Interactive Divergence
Seeing Divergence Divergence in Curvilinear Coordinates
28: T 9 Nov
Divergence Theorem
Highly Symmetric Surfaces
Less Symmetric Surfaces
29: W 10 Nov
30: F 12 Nov
Circulation
Curl in Curvilinear Bases
Definition of Curl
Geometry of Curl
Interactive Curl
Seeing Curl
31: M 15 Nov
-
Paddlewheels and Curl
32: T 16 Nov
Stokes' Theorem
Stokes' Theorem
33: W 17 Nov
34: F 19 Nov
35: M 22 Nov
36: T 23 Nov
Divergence and Curl
Visualizing Divergence and Curl
Product Rules for Vector Fields
37 : W 24 Nov
38: M 29 Nov
39: T 30 Nov
Change of Variables
Change of Variables
40: W 1 Dec
41: F 3 Dec
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Line Integrals
Vector Line Integrals
Use what you know
vector differential