**SPRING SEMESTER 2016**

## Introduction

Modeling analysis is a capstone course dedicated to solving real world problems. The course carries an AST designation, but in reality it is a physics course, so brace yourselves. You should be comfortable with all areas of physics, especially mechanics, statistical thermodynamics, optics, E&M and modern physics. A strong background in mathematics is very desirable, especially calculus, vector/matrix algebra, solving differential equations, integration, minimization and optimization. If you haven't already, you *will* become best friends with your computer, as numerical/computational mathematics is the foundation of modeling analysis. Scared yet? No need -- if you aren't all the way there with all of the above, you will be by the time the semester ends!

## Assignments:

Assignment: | Data/information | Due date: |
---|---|---|

The Traveling Salesman | 1/19/2016 | |

The Linear Optimization Problem | groceries.txt, linear programming tutorial | 1/26/2016 |

The Kepler Problem | background (pdf) | 2/2/2016 |

Continuous Population Models | US population data | 2/9/2016 |

Discrete Population Models | Markov matrices video | 2/16/2016 |

Dynamical Chaos | 2/23/2016 | |

Real Pendulum | 3/15/2016 | |

Heat transport and diffusion | Advection equation methods | 3/24/2016 |

Poiseuille's law | Viscous flow through pipes | 3/31/2016 |

Discrete Fourier transforms | associated data | 4/5/2016 |

Fast Fourier transforms | associated data | 4/12/2016 |

Artificial Neural Networks | 4/21/2016 | |

Symmetric and asymmetric data fitting | Compartment models, synthetic spectrum of Vega | 4/26/2016 |

## Course content

The course consists of two parts: lecture (1.5 hours) and discussion (1.5 hours). In lecture I will present common approaches to solving a particular type of problem in physics. Every week I will assign a problem that you will be required to solve in the following week and hand in the typeset results. All problem solutions are due in 1 week. All results, caveats and lessons learned are discussed at length in class. You will all be assigned the same problem but, although interaction and discussion is encouraged, you are required to work on it independently. Reports must be typeset (LaTeX is strongly encouraged), figures and tables properly formatted and equipped with captions. I will put all interesting results in a presentation and we will discuss them jointly in class.

## Solving problems and writing reports

For solving problems you can use whatever programming/computing environment that you feel most comfortable in. If you have no preference or have not been exposed to scientific computing before, I would suggest python, a high-level programming language that comes with the optional scipy module. Matlab, Octave, Mathematica, Maple, IDL and other environments might also be very useful.

Reports must be typeset. I strongly suggest that you use LaTeX, the de-facto standard for typesetting in mathematical sciences. You may submit your reports either printed or electronically, via email, in pdf form. You should include any pertinent figures and tables, properly captioned and referenced in the text, as well as all used literature. You should *never* include any program listings -- only discuss the results. If you want to discuss implementation details, make sure you avoid any technical details that would pertain to any given environment and give only general comments on the method and/or intermediate results. **The reports must be in my mailbox (physical or electronic) by 9am on the due date.**

## Grading

Good news first: there are no quizzes, tests, or the final. Modeling analysis is a project-based course.

Every assignment is graded on a scale from 1 to 5 points. Minimal effort will earn you 2 points. 4 points constitute 100%. I will award full 5 points for exceptional work. If you are late submitting the homework, you will get a single point, irrespective of the quality of the work -- this is because everyone has ample opportunity to harvest other people's ideas during discussion. Thus, **it is of utmost importance that you submit your reports in time**. If you are unable to submit your report because of an illness or any other serious situation, you must notify me *before* the submission deadline and I will either extend the deadline for you or drop that problem from your grade-sheet. If you notify me of your absence after the fact, it will not be excused unless you were demonstrably unable to contact me.

The grading will be done according to the following breakdown:

0-56% | F | 68-72% | C- | 84-88% | B |

56-60% | D- | 72-76% | C | 88-92% | B+ |

60-64% | D | 76-80% | C+ | 92-96% | A- |

64-68% | D+ | 80-84% | B- | 96-100% | A |

## Useful links:

Download the Numerical Recipes Book here; code and examples ("free").