18.085 - Computational Science and Engineering I (Spring 2013)


Instructor: Paul E. Hand

Office: Room 2-390

Email: hand [at] math.mit.edu

Lectures: Tu,Th 2:30 - 4:00 PM 2-190

Office Hours:
  • Amelia Servi: Mondays, 5-7 PM 1-242
  • Paul Hand: Wednesdays, 4-6 PM, 2-390

Webpage: http://math.mit.edu/~hand/teaching/18.085-spring-2013/

Stellar (for grades): https://stellar.mit.edu/S/course/18/sp13/18.085/


The goal of this course is to give you:

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. Frequent use of MATLAB in a wide range of scientific and engineering applications.

This class is suitable for masters students, advanced undergraduates, or anyone interested in building a foundation in computational science.

Prerequisites: Calculus and some linear algebra

Text Book: Computational Science and Engineering by Gilbert Strang

Grades: 50% problem sets, 50% three in-class quizzes. Lowest problem set score will be dropped.

Problem Sets: Will be due in class.




Topics and dates are tentative
Day Topics (page numbers)
Feb 5Truss stability problem (185-188, 192-193)
Linear algebra basics (685-689)
Feb 7Rank-nullity theorem (690)
Feb 12Resistor network problem (142-151)
Linear equations, Ax=b (686-687)
LU decomposition (78, 26-30)
Feb 14LU operation count (32-33)
Feb 21Best fit problems
Least squares
Normal Equations
Feb 26 Gram-Schmidt (80-81)
QR decomposition (79-81)
Feb 28Eigenvalues and eigenvectors
Positive definite matrices
Error analysis in solving Ax=b
Condition number
Singular value decomposition
Mar 5Singular value decomposition (continued)
Mar 7Quiz 1
Mar 12Frequency identification problem
Complex numbers, vectors, and matrices
Fourier basis
Discrete Fourier Transform
Mar 14Discrete Fourier Transform (continued)
Mar 19Radioactive decay problem
Forward Euler
Backward Euler
Trapezoidal Rule
Mar 21Mass spring problem
Leapfrog methods
Apr 2 Elastic membrane problem
Boundary value problems
Dirac Delta
Apr 4 Finite element method in 1d
Apr 9 Finite element method in 2d
Apr 11 Quiz 2
Apr 18 Fourier series
Apr 23 Fourier series and boundary value problems
Apr 25 Potential flow
Apr 30 TBD
May 2 TBD
May 7 Review
May 9 Quiz 3
May 14 TBD
May 16 TBD