Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Prerequisites
Calculus (18.01), Calculus (18.02), and Differential Equations (18.03). Some exposure to linear algebra (matrices) at the level of Linear Algebra (18.06) helps, but is not required. The assignments will involve basic computer programming in the language of your choice (Matlab® recommended; this class encourages you to learn Matlab if you don't already know it).
Summary
Numerical analysis is the story of how functions, derivatives, integrals, and differential equations are handled as strings of numbers in the computer. At the heart of numerical analysis is an understanding of the speed of convergence of Taylor, Fourier, and other series expansions. Most scientists and engineers are sooner or later faced with computing tasks that require some knowledge of numerical analysis.
Topics
- Series expansions: from calculus to computation
- Integrals as sums and derivatives as differences
- Interpolation, splines, and a second look at numerical calculus
- Numerical methods for ODE, initial-value problems
- Root finding, Newton's method, boundary-value problems
- Fourier transform, Fourier series, Shannon sampling theory
- Bandlimited interpolation, spectral methods
- Least-squares approximation
- Principal component analysis
The class will NOT cover Linear Partial Differential Equations (18.303), and will contain much less linear algebra than the course Linear Algebra (18.06SC).
Grading
| ACTIVITIES | PERCENTAGES |
|---|---|
| Homework | 50% |
| In-class midterm exam | 20% |
| In-class final exam | 30% |
The homework problem sets will consist of both theoretical problems and numerical experiments. No late copy will be allowed. The lowest score will be dropped. Collaboration is allowed, but the codes and copies you turn in must be original and written by you.
The midterm and final exams are open-book. No calculators, phones, or computers are allowed.