Computational physics
Undergraduate · Physics
Syllabus focus
Topics typically covered
Standard syllabus
Numerical foundations
- Floating-point arithmetic and stability
- Root finding and linear algebra routines
- Numerical differentiation and integration
- ODE solvers: Euler, RK4, and adaptive step
- Interpolation and least-squares fitting
Simulation methods
- Molecular dynamics for particle systems
- Monte Carlo integration and sampling
- Finite-difference PDEs: heat and wave equations
- Eigenvalue problems for quantum wells
- Chaos in logistic and driven oscillators
Data and visualization
- Python/NumPy/Matplotlib workflows
- Error bars and bootstrap resampling
- Animating time evolution of fields
- Version control for scientific code
- Reproducibility and random seeds
STEM / applied
High-performance practice
- Vectorization vs explicit loops
- Parallel computing with multiprocessing or MPI intro
- GPU acceleration overview (CUDA/JAX)
- Profiling and bottleneck identification
- Benchmarking against analytic solutions
Domain applications
- N-body gravity simulations
- Ising model and phase transitions
- Finite-difference Maxwell solvers (1D)
- Quantum time evolution with split-operator
- Parameter sweeps for lab instrument design
Software engineering for science
- Modular code structure and unit tests
- Documenting APIs for lab groups
- Containerization for shared environments
- Continuous integration for research code
- Publishing supplemental simulation data
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Numerical foundations
Floating-point arithmetic and stability
Coming soon - Simulation methods
Molecular dynamics for particle systems
Coming soon - Data and visualization
Python/NumPy/Matplotlib workflows
Coming soon
Notes
Topics reflect common upper-division physics syllabi at US colleges and universities. Prerequisites, lab pairing, and mathematical depth vary by department.