W1 D1: Math Bits

Introduction to the Static Fields (Math Bits)

Course Lecture Notes
Key Request Form
Research Consent Form

Densities

Acting Out Charge Densities

GSF: Densities
GEM 2.1.4

Non-uniform Densities

Modeling Nonuniform Density

Review Algebra/Calculus Basics
Do this on you own.
See HW 1 Practice.

Unit: (Math Bits) Integration and Differentiation in Curvilinear Coordinates

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Integration and Differentiation in Curvilinear Coordinates

W1 D2: Math Bits

Review Curvilinear Coordinates

GSF: Curvilinear Coordinates
GSF: Change of Coordinates

Scalar Line, Surface, Volume Elements

Total Charge of a Rod
Pineapples and Pumpkins
Scalar Surface and Volume Elements
Curvilinear Volume Elements

GSF: Scalar Surface Elements
GSF: Triple Integrals in Cylindrical and Spherical Coordinates
GEM 1.3.1, 1.4

Total Charge

Total Charge: Spheres \& Cylinders

GSF: Total Charge

W1 D3: Math Bits

Vector Differential

Vector Differential--Rectangular
Vector Differential--Polar
Vector Differential--Curvilinear

GSF: The Vector Differential
GSF: Finding $d\vec{r}$ on Rectangular Paths
GSF: Other Coordinate Systems
GSF: Calculating $d\vec{r}$ in Curvilinear Coordinates

HW 01 Practice w/Solution
HW 01 w/Solution

Use What You Know

Introduction to Use What You Know
Charge on a Parabola
Surface Area of a Paraboloid

GSF: Using $d\vec{r}$ on More General Paths
GSF: Use What You Know

W1 D4: Math Bits

Vector Fields

Draw Vector Fields

GVC: Vector Fields for Mathematicians
GSF: Vector Fields for Physicists

Work and Vector Line Integrals

Vector Line Integrals (Contour Map)

Curvilinear Basis Vectors

Representations for Finding Components
Curvilinear Basis Vectors

GSF: Orthonormal Basis Vectors
GEM 1.4

Review of Derivatives

GSF: Leibniz vs. Newton

Partial Derivatives

Generalized Leibniz Notation
Partial Derivatives from a Contour Map

GEM 1.2.1

W1 D5: Math Bits

Review The Multivariable Differential

GMM: The Multivariable Differential

HW 02 Practice w/Solution
HW 02 w/Solution

Definition of Gradient

GSF: The Geometry of the Gradient
GSF: The Gradient in Rectangular Coordinates
GEM 1.2.2-1.2.3

Properties of Gradient

GSF: Properties of the Gradient

Visualizing Gradient

Acting Out the Gradient
Visualising the Gradient

GSF: Visualizing the Geometry of the Gradient
GSF: Using Technology to Visualize the Gradient
GEM 1.2.2-1.2.3
Taylor 4.3, 4.8

Gradient in Curvilinear Coordinates

GSF: The Gradient in Curvilinear Coordinates
GSF: Formulas for Div, Grad, Curl

Unit: Potentials Due to Discrete Charges

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Potentials Due to Discrete Charges

W2 D1

Introduction to Static Fields (Physics)

Introduction to Static Fields

Electrostatic & Gravitational Potential

Electrostatic Potential Due to a Point Charge

GSF: Electrostatic and Gravitational Potentials and Potential Energies
GEM 2.3.4
GSF: Dimensions

Review Distance Formula

Visualizing Potentials I

Drawing Equipotential Surfaces

Read After Class:
GSF: Visualization of Potentials

W2 D2

Veterans Day (No Class)

W2 D3

Superposition of Discrete Charges

Electrostatic Potential Due to a Pair of Charges (without Series)

Read After Class:
GSF: Superpositions from Discrete Sources
GSF: Two Point Charges
GEM 2.3.4

HW 03 Practice w/Solution
HW 03 w/Solution

Potential Due to a Pair of Charges: Limiting Cases

Electrostatic Potential Due to a Pair of Charges (with Series)

Read After Class:
GSF: Power Series for Two Point Charges

Unit: Fields from Continuous Sources

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Fields from Continuous Sources

W2 D4

Visualizing Potentials (with Technology)

Using Technology to Visualize Potentials

Read After Class:
GSF: Using Technology to Visualize Potentials

Series for Multipoles

Multipole Expansions

Read After Class:
GSF: Using Technology to Visualize Power Series

$1/r$ vs. $1/r^2$

$1/r/$ vs. $1/r^2$

Series Approximations

Using Technology to Explore Power Series Approximations

Read After Class:
GMM: Discussion of Approximations Using Power Series
GMM: Using Technology to Explore Power Series Approximations

Power Series Sensemaking

Sensemaking from Graphs of Power Series I
Sensemaking from Graphs of Power Series II

Electrostatic Potential in Curvilinear Coordinates

Electrostatic Potential Due to a Ring of Charge
Ring Sequence Electric Potential

Read After Class:
GSF: Potentials from Continuous Charge Distributions
GSF: Potential Due to a Uniformly Charged Ring
GEM 2.3.4

W2 D5

Multipole Expansion

Linear Quadrupole Follow-up

HW 04 Practice w/Solution
HW 04 w/Solution

Other Continuous Sources

Read After Class:
GSF: Potential Due to a Finite Line of Charge
GSF: Potential Due to an Infinite Line of Charge
GEM 2.3.2

Limiting Cases (V Ring)

Unit: Electric Fields

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Electric Fields, $\vec{E}(\vec{r})$

W3 D1

Constants, Variables, and Parameters

Electric Field Due to a Point Charge

Electric Field of a Point Charge

GSF: Electric Field of a Point Charge

Superposition for Electric Fields

Drawing Electric Field Vectors for Discrete Charges

Read After Class:
GSF: Superposition for the Electric Field
GSF: The Geometry of Electric Fields
GEM 2.2.1

Electric Field for Two Point Charges

Electric Field Due to a Pair of Charges (without Series)

Electric Field Lines

GSF: Electric Field Lines
GEM 2.2.1

W3 D2

Electric Field Due to a Point Charge as a Gradient

GSF: Electric Field
GEM 2.1.1-2.1.2

Electric Fields from Continuous Charge Distributions

Electric Field Due to a Ring of Charge
Ring Sequence Electric Field

Read After Class:
GSF: Electric Field from Continuous Charge Distributions
GSF: Electric Field Due to a Uniformly Charged Ring
GSF: The Electric Field of a Uniform Disk
GEM 2.1

Unit: Gauss's Law (Integral)

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Gauss's Law (Integral Form)

W3 D3

Products of Vectors: Cross Product
Triple Product

Cross Product Review

GMM: Cross Product
GEM 1.1.1-1.1.3

HW 05 Practice w/Solution
HW 05 w/Solution

Vector Surface Elements

Vector Surface and Volume Elements

Read After Class:
GSF: Vector Surface Elements
GEM 1.3.1

Flux Definition

Acting Out Flux

Read After Class:
GSF: Flux
GSF: Flux of the Electric Field
GEM 1.3.1, 2.2.1

W3 D4

Flux Calculation

Flux through a Paraboloid

Read After Class:
GSF: Highly Symmetric Surfaces
GSF: Less Symmetric Surfaces

Visualizing Flux

Visualizing Flux through a Cube

Read After Class:
GSF: Flux through a Cube

Gauss's Law in Integral Form

Gauss's Law in Symmetric Situations

Read After Class:
GSF: Gauss's Law
GSF: Gauss's Law and Symmetry
GSF: Gauss's Law for High Symmetry
GEM 2.2.3

W3 D5

Step Functions

Read After Class:
GMM: Step Functions
GEM 1.5.2
Video:
Step & Delta Functions

HW 06 Practice w/Solution
HW 06 w/Solution

Delta Functions

Read After Class:
GMM: The Dirac Delta Function
GMM: Properties of the Dirac Delta Function
GMM: Representations of the Dirac Delta Function
GEM 1.5

W4 D1

Big Quiz

Static Fields Equation Sheet

Gravity w/Solution

Unit: Maxwell's Equations in Differential Form

Introduction to the Unit
Learning Outcomes

Unit Learning Outcomes: Divergence and Curl

W4 D2

More Gauss's Law

Derivatives of Vector Fields

W4 D3

Definition of Divergence

Read After Class:
GSF: The Definition of Divergence
GEM 1.2.4

HW 07 Practice w/Solution
HW 07 w/Solution

Visualization of Divergence

Read After Class:
GSF: Exploring the Divergence
GSF: Visualizing the Divergence

Divergence Theorem

GSF: The Divergence Theorem
GEM 1.3.4
Taylor 13.7

W4 D4

Thanksgiving (No Class)

W4 D5

Thanksgiving Break (No Class)

HW 08 Practice
HW 08

Unit: Magnetic Fields

Introduction to the Unit
Learning Outcomes Learning Outcomes

Unit Learning Outcomes: Magnetostatic Fields

W5 D1

Divergence in Curvilinear Coordinates

Read After Class:
GSF: The Divergence in Curvilinear Coordinates
GSF: Exploring the Divergence in Polar Coordinates

Differential Form of Gauss's Law

GSF: Differential Form of Gauss's Law
GSF: The Divergence of a Coulomb Field
GEM 2.2.1-2.2.2

Current Density

Acting Out Current Density

Read After Class:
GSF: Current
GEM 5.1.3, 5.2.2

W5 D2

Big Quiz Redux

Total Current

Current from a Spinning Cylinder

Ampère's Law in Integral Form

Amp\`ere's Law in Symmetric Situations

Read After Class:
GSF: Ampère's Law
GSF: Current in a Wire
GSF: Ampère's Law and Symmetry
GSF: Ampère's Law on Cylinders
GEM 5.3.3

W5 D3

Curl

Visualization of Curl

Read After Class:
GSF: The Geometry of Curl
GSF: The Definition of Curl
GSF: The Curl in Curvilinear Coordinates
GSF: Exploring the Curl II
GSF: Visualizing the Curl
GEM 1.2.5

HW 09 Practice w/Solution
HW 09 w/Solution
Proportional Reasoning Practice w/Solution

W5 D4

Stokes' Theorem

GSF: Stokes' Theorem
GEM 1.3.5

Differential Form of Ampère's Law

GSF: Differential Form of Ampère's Law
GEM 5.3.3

Introduction to the Lorentz Force Law

Lorentz Force Law to Words

GSF: The Lorentz Force Law
GEM 5.1, 5.3.4
Taylor 2.5

Relationship of Fields

V, $\vec{E}$, U, $\vec{F}$

Read After Class:
GSF: The Relationship between $V$, $\vec{E}$, $U$, and $\vec{F}$
GEM 2.3.1-2.3.2
Taylor 4.2

Work

Read After Class:
GSF: Conservative Vector Fields
GSF: Independence of Path
GSF: Visualizing Conservative Vector Fields
GSF: Finding Potential Functions
GSF: Finding the Potential from the Electric Field
GEM 1.3.2-1.3.3
GEM 2.4.1
Taylor 4.2

Lorentz Force Law

Lorentz Force and Work Done on a Rectangular Loop

Curl-Free Vector Fields

Read After Class:
GSF: Curl-Free Vector Fields
GEM 1.6.2
Taylor 4.4

Electrostatic Energy Due to Discrete Charges

Electrostatic Energy of Discrete Charges

Read After Class:
GSF: Electrostatic Energy from Discrete Charges
GEM 2.4.1-2.4.2

Electrostatic Energy from a Continuous Charge Distributions

Read After Class:
GSF: Electrostatic Energy from Continuous Sources
GEM 2.4.3-2.4.4

W5 D5

Product Rule
Integration by Parts
Second Derivatives
Laplace's Equation

GSF: Product Rules
GSF: Integration by Parts
GSF: Second Derivatives
GSF: Second Derivatives and Maxwell's Equations
GSF: The Laplacian
GEM 1.2.6-1.2.7, 1.3.6
GEM 2.3.3

HW 10 Practice w/Solution
HW 10 w/Solution

Magnetic Vector Potential

Magnetic Vector Potential Due to a Spinning Charged Ring
Ring Sequence Magnetic Vector Potential

Read After Class:
GSF: Magnetic Vector Potential
GEM 5.4.1

Magnetic Field $\vec{B}$ from Magnetic Vector Potential $\vec{A}$

GEM 5.4.1

Biot Savart Law

Magnetic Field Due to a Spinning Ring of Charge
Ring Sequence Magnetic Field

Read After Class:
GSF: The Biot-Savart Law
GSF: The Magnetic Field of a Straight Wire
GSF: The Magnetic Field of a Spinning Ring
GSF: Comparing $\vec{B}$ and $\vec{A}$ for a Spinning Ring
GEM 5.2.2

Conductors

Read After Class:
GSF: Conductors
GEM 2.5

Boundary Conditions

GSF: Dot Products and Components
GSF: Boundary Conditions on Electric Fields
GSF: Boundary Conditions on Magnetic Fields
GEM 2.3.5, 5.4.2

Review

Introduction to Static Fields
Static Fields Review

GSF: Learning Outcomes
GSF: The Relationship between $\vec{E}$, $V$, and $\rho$
GSF: The Relationship between $\vec{B}$, $\vec{A}$, and $\vec{J}$
GEM 2.3.5, 5.4.2
GEM 5.3.4

More Paraboloids

12/10, noon

FINAL EXAM

Static Fields Equation Sheet

335 Prereqs: Power Series

Definition of Power Series
Derive Power Series Coefficients

Adding Functions Pointwise
The Functions $1/r$ and $1/r^2$

Review Reading:
Read Before Class:
GMM: Definition of Power Series
GMM: Calculating Power Series Coefficients

Calculating Coefficients of Power Series

Calculating Coefficients for a Power Series

Read After Class:
GMM: Calculating Power Series Coefficients

Guessing Power Series

Read After Class:
GMM: Guessing Power Series from Graphs

Power Series Approximations (Sine Example)

Visualization of Power Series Approximations

Read After Class:
GMM: Visualization of Power Series Approximations

More Power Series Information

Read After Class:
GMM: Common Power Series
GMM: Dimensions in Power Series
GMM: Convergence of Power Series
GMM: Theorems about Power Series

335 Prereqs: Derivatives

Zapping with d

Differentials

Review how to find total differentials
Watch some short video:
Rules for Differentials
Product Rule
Chain Rule
and/or Read:
GSF: Leibniz vs. Newton
GSF: Differentials
GSF: Rules for Differentials
GSF: Properties of Differentials
GSF: The Multivariable Differential
GSF: Differentials: Summary

335 Prereqs: Coordinates and Vectors

Review on your own(as needed):Basic Calculus, Exponentials & Logarithms, Vectors

Review Reading
GSF: Review of Single Variable Differentiation
GSF: Vectors
GSF: Bases
GSF: Unit Vectors
GEM 1.1.1-1.1.2
Taylor 1.2
Rules for Differentials

Representations of Vectors

Dot Product

Dot Product Review

Read After Class:
GSF: The Dot Product
GEM 1.1.1

Position Vector

Read After Class:
GSF: The Position Vector
GEM 1.1.4

Calculating the Distance Between Two Points

The Distance Formula (Star Trek)

Read After Class:
GSF: The Distance Formula
GEM 1.1.2, 1.1.4

Curvilinear Coordinates

Curvilinear Coordinates Introduction

GSF: Curvilinear Coordinates
GSF: Change of Coordinates
GEM 1.4

Topic/Day

Activities

Resources

Homework Due