In your first three semesters at Harvey Mudd College, you have taken (at least) three mathematics courses that seek to solidify your understanding of differential and integral calculus and lay foundations in linear algebra and ordinary differential equations. You have also taken an introductory course in computer science, in which you learned some of the basics of computation using Python. You have also taken Engineering 79, in which Laplace transforms were used to solve (systems of) ordinary differential equations.
This course aims to extend your understanding of a range of important mathematical topics and to develop your ability to use Python and standard numerical and graphics libraries to solve physical problems and to visualize solutions.
| Syllabus | Course syllabus |
| Installing Software | Instructions for installing Python, NumPy, SciPy, Matplotlib, and jupyter, as well as hints for efficient configuration |
| Introduction to Jupyter Notebooks | We will use Jupyter Notebooks to run Python code and to visualize results |
| Introduction to NumPy | NumPy and SciPy are the standard packages for numerical computation in Python |
| Introduction to Matplotlib | Matplotlib is the standard package for generating publication-quality graphics in Python |
| Linear Algebra | We will review key results and discuss numerical approaches to solving problems in linear algebra |
| Fourier Series and Transforms | Fourier series represent arbitrary periodic functions as series of sines and cosines. Fourier transforms generalize to the infinite interval. |
| Pseudorandom Numbers | Many simulations rely on random numbers to approximate stochastic processes |
| Stochastic Processes | Stochastic processes involve random steps |
| Ordinary Differential Equations | A quick review of Math 82 with a slant towards the ODEs of physics |
| Partial Differential Equations | Lots of things vary in both space and time, so partial differential equations are central to physics |
| Projects | Information about projects |