## COURSE DESCRIPTION

Review of linear algebra, applications to networks, structures, and estimation, finite difference and finite element solution of differential equations, Laplace's equation and potential flow, boundary-value problems, Fourier series, discrete Fourier transform, convolution.

Use of MATLAB/PYTHON/JULIA in a wide range of scientific and engineering applications.

**Prerequisites:** Calculus and some linear algebra

**Text Book:** *Computational Science and Engineering*, by Gilbert Strang (MIT COOP)(Amazon)(Office)

**Book Website:** http://math.mit.edu/cse/

**OCW Video Lectures site:** http://ocw.mit.edu/courses/mathematics/18-085-computational-science-and-engineering-i-fall-2008/

**Stellar (Grades, Announcements and Homeworks):** http://stellar.mit.edu/

### New Topics

- Deep Learning with Neural Nets
- Architecture and Backpropagation
- Convolutional for Images
- Optimization by Stochastic Gradient Descent

### Established Topics

- Applied Linear Algebra
- Finite Differences and Finite Elements
- Differential Equations and Boundary Conditions
- Stiffness Matrix and Conductance Matrix
- Trusses and Constraints
- Partial Differential Equations: Equilibrium and Flow
- Fourier Transforms, DFT and the FFT
- Filters, Convolutions, and the Convolution Rule
- Graphs and Networks

## EVALUATION

**Grades:** 36% homework, 36% two in-class quizzes, 28% project. No Final Exam.

**Problem Sets:** The homework problem sets will consist of both theoretical and numerical questions. No late copy will be allowed, but the lowest score will be dropped. Please use MATLAB notation to describe algorithms. Use of MATLAB/PYTHON/JULIA for tedious calculations is encouraged, however you need to know how to do the basic algorithms taught in the course by hand (at least for small matrices) for the quizzes.

## COLLABORATION POLICY

Problem sets should represent the student's own work but cooperation with another's is welcome. Cooperation should be noted in writing on the problem set.

## ADD/DROP POLICY

ADD DATE (last day to add a subject): **October 5th**

DROP DATE (last day to drop a subject): **November 21st**

Students may join the class up to ADD DATE using an on-line Add/Drop form: https://studentformsandpetitions.mit.edu/

Students may drop a subject up to DROP DATE. Ceasing to attend a course does not constitute dropping it. The student must officially drop the course with the Registrar by DROP DATE, or receive an 'F' at the end of the term.

## QUOTES FROM PREVIOUS YEARS

http://math.mit.edu/classes/18.085/StrangQuotes.pdf. Students claimed to write them down at the time.