18.085  Computational Science & Eng I

Dear class,

Welcome to 18.085, the course on mathematical and computational methods in engineering. You can look at the course content in the syllabus under Materials section. That section will also contain much of the current information on the lectures, homework assignments, exams, solutions, Matlab codes, etc.

The general outline of the course is as follows.

It consists of three parts: 1. Applications of linear algebra: Finite-difference equations and linear systems, matrix factorizations (LU, QR, SVD, SDS^-1) and their applications, systems of linear differential equations, mechanical oscillations, least-square approximation, networks and mechanical structures. 2. Boundary value problems: Wave equation, heat/diffusion equation, Laplace's equation, separation of variables, finite-difference and finite-element methods. 3. Fourier methods: Fourier series and Fourier integral transform, orthogonal functions, discrete Fourier transform and FFT, wavelet transform, signal processing.

The required text for the course is Computational Science and Engineering by G. Strang. We will cover most of the first four chapters. The book description and many useful Matlab codes to go with it are available at http://www-math.mit.edu/cse/. The final grade will be based on three open-book mid-term exams (70%) and six problem sets due in class on the day indicated on the class website (30%). There will be no final exam. Matlab will be used for numerical computations throughout the course. A good book on Matlab is Matlab Guide by D. Higham and N. Higham. Short introductions to Matlab are also posted on the class website.

Aslan