Instructor: Gil Strang

Email: gilstrang@gmail.com

Office: Room 2-245

Lectures: MWF 1-2, Room 2-190

## 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.