“The circle is now complete. When I left you, I was but the learner. Now I am the master.”

That’s what Darth Vader said when he encountered Obi-Wan Kenobi in Star Wars Episode IV. This is how I feel about our Mathematical Methods course. I remember taking an undergraduate course AND a graduate version. I was clearly “but the learner”. Now, I am ready to be full master. I’m not even going to use a textbook (because none of them really fit the course).

Instead of a textbook, I’m going to list my topics for this course (along with any resources that I have). If you like, you can think of this blog post as my textbook. Oh, but it’s a living textbook. I’m going to modify this throughout the semester to match what’s going on in class. 

OK, let’s get to it. Oh, most of these links are videos.

External Resources

Here are some things that I like to use in class. 

• Intermediate Mechanics Tutorials. Some really great stuff here.
• Paradigms in Physics – Oregon State University

Vectors and Derivatives in Cylindrical and Spherical Coordinates

• Velocity in Polar Coordinates
• Acceleration in Polar Coordinates
• Projectile Motion in Polar Coordinates (Medium)
• Unit vectors in cylindrical and spherical coordinates
• Unit vectors in spherical coordinates in terms of Cartesian coordinates – Part 1
• Velocity and acceleration in spherical coordinates – Part 2
• Velocity and acceleration in spherical coordinates – Part 3
• Newton’s Second Law in spherical coordinates

Numerical Derivatives and Integrals (Python)

Line Integrals and Surface Integrals

Stokes Theorem and Green’s Theorem

Damped Driven Oscillators

The Wave Equation (Including Finite Difference Method)

Matrices and the Eigenvalue Problem