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

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

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