Vector Calculus II | 2023-Winter

Course Name
Vector Calculus II
Course Number
mth255
Year/Term
Winter-2023
Course Credits
4
Class meeting times
3 hours of lecture per week
Prerequisites
Course description
Topic/Day
Activities
Resources
Homework Due
1: M 3 Jan
Parametrization
Position vector
Parametric curves
2: T 4 Jan
Vector Addition
Magnitude
Which Way is North?
Vector addition
Bases
Vector representation
Distance Formula
Dot Product
Curvilinear Coordinates
3: W 5 Jan
Curvilinear basis vectors in two dimensions
Acceleration
Position Vector
Curvilinear Position Vector
4: F 7 Jan
5: M 10 Jan
6: T 11 Jan
Vector differential in two dimensions
Finding $d\boldsymbol{\vec{r}}$
The Vector Differential
7: W 12 Jan
Vector differential in three dimensions
Curvilinear Differential
Gradient in Curvilinear Coordinates
Vector Fields in MATLAB
8: F 14 Jan
The Pretzel
Scalar Line Integrals
Densities
9: T 18 Jan
Gradient
The Hill
Gradient Definition
Gradient Properties
10 : W 19 Jan
11: F 21 Jan
Quiz 1
12: M 24 Jan
Murder Mystery Method
Potential Functions
13: T 25 Jan
Integrals around closed curves, question of conservative vector fields, real application
The Wire
Path Independence
Conservative Vector Fields
Visualizing Conservative Vector Fields
14: W 26 Jan
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Line Integrals
Vector Line Integrals
Use what you know
vector differential
15: F 28 Jan
16: M 31 Jan
17: T 1 Feb
The Valley
Diagonal Differential
Line Integrals on Parametric Curves
Directional Derivatives
The Cone
Mass
18: W 2 Feb
19: F 4 Feb
Cross Product
Surface Element
Vector Surface Element
Visualization of Divergence
Divergence Definition
Interactive Divergence
Seeing Divergence
Divergence in Curvilinear Coordinates
20: M 7 Feb
21: T 8 Feb
Flux Integrals
The Fishing Net
Divergence Theorem
Highly Symmetric Surfaces
Less Symmetric Surfaces
22: W 9 Feb
23: F 11 Feb
Quiz 2
24: M 14 Feb
25: T 15 Feb
The Grid
26: W 16 Feb
Visualization of Curl
Circulation
Curl in Curvilinear Bases
Definition of Curl
Geometry of Curl
Interactive Curl
Seeing Curl
27: F 18 Feb
28: M 21 Feb
29: T 22 Feb
Stokes' Theorem
Stokes' Theorem
30: W 23 Feb
31: F 25 Feb
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32: M 28 Feb
33: T 1 Mar
Divergence and Curl
Visualizing Divergence and Curl
Product Rules for Vector Fields
34: W 2 Mar
35: F 4 Mar
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Quiz 3
36: M 7 Mar
37 : T 8 Mar
Change of Variables
38: W 9 Mar
39: F 11 Mar
40: Th 17 Mar
Final 9:30am
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