Course Name
The Geometry of Maxwell's Equations
Course Number
AIMS 21
Year/Term
2021
Display other available years here.
Course Credits
0
Class meeting times
3 hours of lecture per week
Prerequisites
Listed below is the background knowledge you should have for this course. Physics: We do not expect you to know any physics. We will motivate the mathematical techniques using physics examples and terminology, we will teach the necessary physics content as part of the course. For those of you who may have seen some of the physics topics before, there should still be plenty of new material. Mathematics: We expect that you have taken a first course in calculus, covering the basics of single-variable differentiation and integration. (It's OK if you need to refresh your memory.) Previous exposure to multivariable calculus (partial derivative and multiple integrals) would be an advantage, but is not necessary.
Course description
Electromagnetism is beautifully described using vector calculus, yet most treatments of vector calculus emphasize algebraic manipulation, rather than the geometric reasoning that underpins Maxwell's equations. This course attempts to bridge that gap, providing a unified view of both electro- and magneto-statics and the underlying vector calculus.

Topic/Day

Activities

Resources

Homework Due

3 Wed 1 Dec
Position Vector
Electric Field for Two Point Charges
5 Fri 3 Dec
Power Series for the Electric Field Electric Field for Two Point Charges
7 Tues 7 Dec
Scalar Line, Surface, Volume Elements
GEM 1.3.1
Proportional Reasoning
Assignment I
12 Tues 14 Dec
Divergence Theorem
Magnetic Field \(\vec{B}\) from Magnetic Vector Potential \(\vec{A}\)
Current Density
Total Current
Assignment II
13 Wed 15 Dec
Circulation
Stokes' Theorem
Differential Form of Ampère's Law
14 Thurs 16 Dec
Electric Field Due to a Point Charge
Curl-Free Vector Fields
Relationship of Fields
GEM 2.3.1-2.3.2
Work
GEM 1.3.2-1.3.3
16 Tues 21 Dec
Assignment III
OPTIONAL
The material from this point on will be covered if time allows.
Product Rule
Integration by Parts
Second Derivatives
Laplace's Equation
Compare Series and Visualization
Limiting Cases
Electrostatic Energy Due to Discrete Charges
GEM 2.4.1-2.4.2
Boundary Conditions