**COMPUTATIONAL PHYSICS**

Mondays 11:00-12:15 (Meyer 433)

Wednesdays 10:50-12:05 (Meyer 433)

Instructor: Roman Scoccimarro

This is a *physics* course, in which we will use computational techniques to solve problems in physics.

Analytic approximation techniques will also be an important part of the course.

There will be no exams, grades will be based on homework.

You will need to (or learn how to) program (e.g. C, Fortran, Mathematica, MATLAB), use LaTeX and plotting software.

Please return a brief summary of your work (including figures) as a printout generated by LaTeX (see below for a template).

You should also hand in analytic calculations in standard (handwritten) form, and send me the code you use to generate results by email.

Hwk1[Sep29], Hwk2[Oct15], Hwk3[Nov5], Hwk4[Nov24], Hwk5[Dec15]

Lec01, Lec02, Lec03, Lec04, Lec05, Lec06, Lec07, Lec08, Lec09, Lec10, Lec11, Lec12, Lec13,

Lec14, Lec15, Lec16, Lec17, Lec18, Lec19, Lec20, Lec21, Lec22, Lec23, Lec24, Lec25, Lec26,

Lec27

Preparing these notes I found (apart from the textbooks mentioned below) the following material useful,

There is no formal textbook that I will follow, although Numerical Recipes can be very useful.

Other general books that you may want to check are,

For analytic methods, see e.g.

You can find a sample latex file to present your homework here.

There are many tutorials on LaTeX on the web, see e.g.

There is a lot of useful material on the web, see e.g.

You can use Mathematica or MATLAB (see above) or the freely available GNUPLOT, see

Or if you want a graphics subroutine callable from C or Fortran, see e.g.

- Numerical Math: Roundoff error, representation of numbers, etc

- Interpolations and Approximations

- Computing Derivatives and Integrals

- Random Number Generators

- Basic Methods: Euler, Runge-Kutta

- Perturbation Theory: Regular, Singular

- Applications: Perihelion of Mercury, Resonances and Planetary Rings, Trajectory of Spinning Balls, Internal Structure of Stars

- Random Gaussian Fields, Power Spectrum, Correlation Functions, Cumulants

- Fast Fourier Transform

- Windowed Fourier Transforms, Wavelets

- Applications: Filters, Eigenmodes, Non-Linear Oscillators

- Separation of Variables, Sturm-Liouville, WKB

- Method of Characteristics

- Galerkin Method

- Grid Methods: Relaxation, FFT

- Applications: Water Waves, KdV and Sine-Gordon Solitons, Ocean Modes, Earth Cooling

- Basic Ideas of RG: Real Space and Momentum Shell

- RG and Differential Equations

- Random Walks, Monte Carlo, Markov Chains

- Applications: Ising Model, Phase Transitions

- How Computers Work

- Memory, Cache, Compilers, Profiling, Parallelism