An archive of staple topics in physics and mathematics. The plan is to approach quantitative problems with a varying degree of mathematical rigor, providing motivation for centuries of academic development.
To demonstrate the power of modern computational methods, programming-based approaches are emphasized for each topic. If Einstein and Euler had access to the CPUs of today, would the standard model be any closer to completion?
Index of Topics and Problems
- 2000-Level Course Content
- Finite Area Under an Infinite Length
- Particle Position in Quantum Mechanics
- Dimensional Analysis in Classical Mechanics
- Set Properties of Rational and Real Number Sets
- 3000-Level Course Content
- Real (Damped) Oscillators in 1-D
- Vector Calculus in Newtonian Mechanics
- 4000-Level Course Content
- Vibrating Membrane in $\Bbb{R}^3$
- Two-Level Laser System (unf.)
University Research and Real Problems
- Vibration Characterization of a Noise-Sensitive Laboratory (unf.)
- MATLAB; Fourier transforms; spectral analysis; ISO standards; accelerometers and oscillopscopes.
- Measuring Local Gravitational Acceleration with Kater's Pendulum (unf.)
- Chi-square minimization; error analysis and propogation; standard deviation; matrix operations.
Textbook Problems and Solutions
- Mathematics for Quantum Mechanics, J.D. Jackson (1962)
- 2-1: Eigenfrequencies of a Vibrating Membrane in $\Bbb{R}^3$
- 2-2: Normal Modes for Coupled Oscillators (unf.)
Technology, Programming, etc.
- Baremetal and Embedded Programming for STM32 Microcontrollers
- Embedded C: Blinking an LED to Estimate a Program's Execution Time