Lecture Notes
These notes are my own preparations for lectures and explorations of the topics.
The motion of a
mass on a spring
.
Notes on complex analysis (optional!)
Complex Analysis
Coupled oscillations
Coupled Oscillations
The wave equation for
Waves on a string
The wave equation as the continuum limit of coupled spring systems
The continuum limit
Solutions to the wave equation
Solutions to the wave equation
Vector spaces
Vector spaces
Fourier series
Fourier Series
Fourier analysis
Fourier analysis
Waves in 3 dimensions
Waves in 3 dimensions
Separation of variables in cylindrical coordinates. Bessel functions.
Cylindrical
The Laplace and Helmholz equations in spherical coordinates.
Spherical
Continuity equation, conservation laws, electromagnetism.
Continuity E&M
You may find these notes (from my graduate E&M class) on complex analysis helpful. This is optional reading, but is slightly more complete than the lecture notes above.
Exam Study Guides
Study guide for Midterm Exam 1
Study guide for Midterm Exam 2
Study guide for Midterm Exam 3
Study guide for Final Exam
Check this periodically in case I add questions.
Extras
A bit of biographical history
A bit more detail on complex differentiation and integration