Vector Calculus II | 2021-Summer

Course Name
Vector Calculus II
Course Number
mth255
Year/Term
Summer-2021
Course Credits
4
Class meeting times
3 hours of lecture per week
Prerequisites
Course description
Topic/Day
Activities
Resources
Homework Due
1: M 6/21
Vector Addition
Magnitude
Which Way is North?
Vector addition
Bases
2: W 6/23
Curvilinear basis vectors in two dimensions
Acceleration
Position Vector
Curvilinear Position Vector
3: F 6/25
Vector differential in two dimensions
Finding $d\boldsymbol{\vec{r}}$
The Vector Differential
4: M 6/28
Vector representation
Shipwreck
Distance Formula
Dot Product
Curvilinear Coordinates
Curves and differentials
5: W 6/30
Gradient
The Hill
Gradient Definition
Gradient Properties
6: F 7/2
The Valley
Line Integrals on Parametric Curves
Directional Derivatives
01
01 (pdf)
7: W 7/7
Gradients, curves and line integrals
8: F 7/9
Integrals around closed curves, question of conservative vector fields, real application
The Wire
Path Independence
Conservative Vector Fields
Visualizing Conservative Vector Fields
9: M 7/12
Murder Mystery Method
Potential Functions
Vector Fields in MATLAB
10 :W 7/14
The Pretzel
Scalar Line Integrals
Densities
11: F 7/16
Midterm
12: M 7/19
The Grid
02
02 (pdf)
Vector Differential--Curvilinear
Curvilinear Differential
Gradient in Curvilinear Coordinates
Vector differential in three dimensions
Vector Differential--Rectangular
13: W 7/21
Up a dimension
Cross Product
Surface Element
Vector Surface Element
14: F 7/23
The Cone
Mass
15: M 7/26
Surface Integrals
Flux Integrals
Visualization of Divergence
Divergence Definition
Interactive Divergence
Seeing Divergence Divergence in Curvilinear Coordinates
16: W 7/28
The Fishing Net
Divergence Theorem
Highly Symmetric Surfaces
Less Symmetric Surfaces
17: F 7/30
Connecting surface integrals and the next dimension
18: M 8/2
Paddlewheels and Curl
Visualization of Curl
Circulation
Curl in Curvilinear Bases
Definition of Curl
Geometry of Curl
Interactive Curl
Seeing Curl
19: W 8/4
Stokes' Theorem
Stokes' Theorem
20: F 8/6
Divergence and Curl
Visualizing Divergence and Curl
Product Rules for Vector Fields
21: M 8/9
Change of Variables
Change of Variables
03
03 (pdf)
22: W 8/11
review
23: F 8/13
Final