Course Name
AIMS: Problem Solving
Course Number
aims23
Year/Term
Fall-2024
Course Credits
0
Class meeting times
30 hours total
Prerequisites
TBA
Course description
Physicists and other physical scientists and engineers routinely use algebra and calculus, including vector calculus, in problem-solving. But the hard part of physics problem solving is often at the beginning and end of the problem, namely getting to an algebraic expression from a description of a physical situation in words or other representations, and interpreting an algebraic expression as a statement about what will happen in the real world. This course will use examples from electromagnetism involving scalar and vector fields in the three-dimensional world to explore a variety of problem-solving methods, including using information from experimental data, approximations, idealizations, and visualizations. The emphasis will be on how geometry can help.
Topic/Day
Activities
Resources
Homework Due
W1 D1
Introduction to the Course
Using Gradescope
Densities
Read AFTER class:
GSF: Densities
Student Introductions
Representations of Scalar Fields
Read AFTER class:
GSF: Scalar Fields
W1 D2
Student Introductions
Contour Maps
Visualizing Contour Maps
What is Charge?
More about Density
The Functions \(1/r\) and \(1/r^2\)
Electrostatic & Gravitational Potential and Potential Energy
The Superposition Principle
W1 D3
Power Series Introduction
Power Series Notation
Derivation of Power Series Coefficients
Calculating Coefficients of Power Series
Visualizing the Relationship between Power Series and their Graphs
Guessing Power Series
More Power Series Information
W1 D4
Definition of the Position Vector
Dot Product
Read AFTER class:
GSF: The Dot Product
GEM 1.1.1
The Distance Formula
Read AFTER class:
GSF: The Distance Formula
GEM 1.1.2
Law of Cosines
W1 D4 Tutorial (4 pm)
Making Clear Justifications
W1 D5
Student Introductions
Compare Series and Visualization
Addition Formulas
Read AFTER Class:
GMM: Addition Formulas
W2 D1
Vector Fields in Curvilinear Coordinates
Introduction to the Lorentz Force Law
Read AFTER Class:
GSF: The Lorentz Force Law
The Magnetic Field Due to a Current Carrying Wire
W2 D2
Geometric Introduction to Differentials
W2 D2 Tutorial (2 pm)
More Power Series
W2 D3
Limiting Cases for Potential Due to a Ring
Definitions of Multipoles
W2 D4
Charge on a Cube
Scalar Line, Surface, Volume Elements
GEM 1.3.1
W2 D4 (4-6 pm)
Individual/Group Test
W2 D5
Proportional Reasoning
Review of Derivatives
Use What You Know
The Helix
W3 D1
Vector Surface Elements
Flux Definition
Total Current
Flux Calculation
W3 D2
W3 D2 (Tutorial) 4 pm
More Surface Integrals
W3 D3
Partial Derivatives
GEM 1.2.1
Derivatives of Vector Fields
Visualizing the Gradient 1
Properties of Gradient
Directional Derivatives
The Multivariable Differential
Electric Field Due to a Point Charge
W3 D4
Using Technology to Visualize the Gradient
Divergence Theorem
W3 D4 (4-6 pm)
In-class Individual/Group Test
W3 D5
Stokes' Theorem
Differential Form of Ampère's Law
Review Test Questions
Geometric Reasoning