Back of the envelope calculations, 2013

What this course is about

The common language of physics grows out of a very small set of tools. A clear understanding of these tools is sufficient to understand most talks. As a result, this is the language in which experimental and theoretical physicists talk to each other. This course is an introduction to this language. About half the course will be devoted to constructing and analyzing non-textbook problems, and checking whether they can lead to interesting research problems.

Course contents

Dimensional analysis: A couple of examples of non-trivial systems treated in dimensional analysis; conversion of units and the meaning of dimensionful "constants of nature"; use of dimensional analysis in converting equations to dimensionless form; the use of dimensional analysis in comparing the importance of different physical effects on a system. (7 hours)
Statistical inference: Random sampling, bias and estimation; Bayes' theorem and inference from observations; the central limit theorem and exceptions; covariance, regression and reduction of variables; fitting; classification. (7 hours)
Approximation methods: Solutions of equations, exploiting approximate symmetries, perturbation; quick estimates of integrals, approximate solutions of ODEs; exploiting linearity, using integral transforms, inverse transformations; highly oscillatory integrals, asymptotic expansions, steepest descent. (7 hours)
Using data bases: Hands-on introduction to major databases, using them for literature surveys, finding most important papers. (3 hours)
Example problems: Several problems where estimates of effects are used to extract dimensional quantities, unnecessary scales are removed, and simple models are written, the model is solved, and perturbations in the remaining small effects are set up. (16 hours)