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, what would our Standard Model look like?
Index of Topics and Problems
- 2000-Level Course Content
- Finite Area Under Infinite Parameter
- Particle Position in Quantum Mechanics
- Dimensional Analysis in Classical Mechanics
- Atoms for Peace
- 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