Surfaces/Bridge Workshop | 2023-Summer

Course Name
Surfaces/Bridge Workshop
Course Number
MTH 923
Year/Term
2023
Display other available years here.
Course Credits
0
Class meeting times
3 1/2 days
Prerequisites
Differential and Integral Calculus
Course description
(none)

Topic/Day

Activities

Resources

Homework Due

6/25 Sun
Arrival
6-8 pm
Welcome Dinner
(Grimm Hall South 002)
Boxed Sandwiches and Salads
Welcome Activity
Surfaces Intro
7:30-8:30 am
Breakfast
8:30-10:00 am
Introduction to Raising Calculus
The Park
Multivariable Pictionary
Introduction to the Geometry of Vectors
Which Way is North?
Representations of Vectors
Introduction to the Workshop
10-10:30 am
Snack Break
(outside classroom)
10:30 am-noon
Derivatives SWBQ
Derivatives SWBQ
Partial Derivatives
The Hot Plate
Partial Derivatives from a Contour Map
Leibniz Notation
Generalized Leibniz Notation
The Anatomy of a Small Group Activity
12-1:30 pm
Lunch Break
(Cafeteria line closes at 1)
1:30-3 pm
Differentials mini lecture (before activity)
Differentials
Differentials Activities
The Resistors
Video:
Rules for Differentials
Product Rule
Chain Rule
Read:
GVC: Leibniz vs. Newton
GVC: Differentials
GVC: Rules for Differentials
GVC: Properties of Differentials
GVC: The Multivariable Differential
GVC: Differentials: Summary
Differentials Version of the Chain Rule
Finding a Chain Rule
Vector Derivatives
The Hillside (Updated)
Multivariable differentials and partial derivatives
Multivariable Differentials
Dot product SWBQ
Dot Product Review
3-3:30 pm
Snack Break
(outside classroom)
3:30-5 pm
\(d\vec{r}\)
GVC: The Vector Differential \(d\vec{r}\)
Gradient Properties (mini-lecture)
GVC: Gradient
GVC: Geometry of Gradient
GVC: Properties of Gradient
GVC: Directional Derivatives
Geometry of the Gradient
The Hill
Acting Out the Gradient
Visualising the Gradient
(resources moved earlier to go with minilecture.)
Choosing Pedagogical Strategies
5-6:30 pm
Dinner
7-8 pm (optional)
Participants Share Their Own Curricular Innovations
7:30-8:30 am
Breakfast
8:30-10 am
Densities
Acting Out Charge Densities
Forming Groups/Furniture
Group Roles
Total Amount
The Boysenberry Patch
Chop, Multiply, Add
Pedagogical Moves
10-10:30 am
Snack Break
(outside classroom)
10:30 am-noon
Curvilinear Coordinates
Curvilinear Coordinates Introduction
Curvilinear Basis Vectors
GVC: Curvilinear Coordinates
Use What You Know
Introduction to Use What You Know
Charge on a Parabola
Charge on a Spiral
Modeling Nonuniform Density
Generating Discussion
Misconceptions
12-1:30 pm
Lunch Break
(Cafeteria line closes at 1)
1:30-3 pm
Cross Product
Cross Product Review
GVC: Cross Product
Vector Fields
Draw Vector Fields
\(d\vec{r}\) in Curvilinear Coordinates
Vector Differential--Rectangular
Vector Differential--Curvilinear
Pineapples and Pumpkins
Vector Surface Elements
Vector Surface and Volume Elements
GVC: Surface Elements
GVC: Vector Surface Elements
3-3:30 pm
Snack Break
(outside classroom)
3:30-5 pm
Groups Prepare Presentations
5-6:30 pm
Dinner
7-8 pm (optional)
Using Vector Calculus in the Physical Sciences
Partial Derivatives from a Contour Map--Thermo Version
7:30-8:30 am
Breakfast
8:30 am-noon
Optimization
The Roller Coaster
The Water Table
GVC: Optimization
Conservative Vector Fields
The Valley
GVC: Path Independence
GVC: Conservative Vector Fields
GVC: Visualizing Conservative Vector Fields
GVC: Potential Functions
Surface and Volume Integrals
The Cake
Linear Approximation
The Gold Mine
Directional Derivatives (Figure 8)
Area (Putting Green)
Gradient (Hillside 2 versions)
Line Integrals (The Wire)
The Wire
Divergence (Fishing Net)
The Fishing Net
Stokes' Theorem
Stokes' Theorem
Surface Integrals (The Cone)
The Cone
10-10:30 am ish
Snack Break
(outside classroom)
12-1:30 pm
Lunch Break
(Cafeteria line closes at 1)
1:30-3 pm
Flux
Acting Out Flux
Flux through a Paraboloid
Visualizing Flux through a Cube
GVC: Flux
GVC: Highly Symmetric Surfaces
GVC: Less Symmetric Surfaces
3-3:30 pm
Snack Break
(outside classroom)
3:30-5 pm
Discussion: Leading Activities.
Workshop Evaluation Focus Group
5:30-6:30 pm
Banquet
7:30-8:30 am
Breakfast
8:30-10 am
Curl (and Divergence) Mini Lecture
GVC: Circulation
GVC: Definition of Curl
GVC: Definition of Divergence
Curl (and Divergence) Visualization
Visualization of Curl
Visualization of Divergence
GVC: Geometry of Curl
GVC: Interactive Curl
GVC: Seeing Curl
GVC: Interactive Divergence
GVC: Seeing Divergence
Divergence and Curl in Curvilinear Coordinates
GVC: The Curl in Curvilinear Coordinates
GVC: The Divergence in Curvilinear Coordinates
Stokes' Theorem (and the Divergence Theorem)
Stokes' Theorem
GVC: Stokes' Theorem
GVC: The Divergence Theorem
10-10:30 am
Snack Break
(outside classroom)
10:30 am-noon
Make Your Own Syllabus
12-1:30 pm
Lunch Break
(Cafeteria line closes at 1)
1:30 pm
Departure
Types of Active Engagement
Effective Wrap-Up
Leading Activities
Constructing a Formula
Anatomy of an Activity