Science and Computers -- PHY307/607

Syllabus

• Introduction to Python/VPython Elementary ideas about modeling and computer simulation. Visualization: graphs and animation.
• Solving simple differential equations using a computer: Euler algorithm, Newton's laws as difference equations. Motion of falling objects. Simple loops, conditionals and examples of simple simulation.
• Two dimensional motion. Better integration algorithms: Runge-Kutta. Oscillations -- harmonic and nonlinear. Chaos.
• Simple nonlinear maps. Event driven animations. Bacteria in a jar. Attractors and the period doubling route to chaos. Fractals.
• Gravity and orbits. Orbits and trajectories around black holes. General dynamiacal systems: the Solar system.
• Random processes. Random walks. Simple Monte Carlo algorithms. Error analysis.
• Percolation. Cellular automata, self-organized critical phenomena.
• Statistical mechanics -- Monte Carlo simulation of the canonical ensemble. Ising model and phase transitions.
• Quantum mechanics on a computer -- solving time independent Schroedinger equation using shooting method. Matrix representation of simple problems -- eigenvalues and eigenvectors. Simple algorithms for linear algebra.

Course Mechanics

• A short homework assignment will be set every week. This will be given out on Thursday and will be due back by the following Thursday. This homework may be associated closely with a lab and may involve computer work.
• Each week we will meet on the Thursday for a lab. This may take the form of a tutorial on a specific programming topic or more frequently the application of computational techniques to explore some particular topic in science. Many of these labs will spread out over two or more weeks. The writeup for a lab will be due one week after completion.
• There will be a final. In addition there will be a final project -- details to be given later in the semester

Final Grades

• Homeworks : 20%
• Final : 15%
• Total labs : 45%
• Final project: 20%

Office hours

Necessary background