COURSE DESCRIPTION
The goal of this course is to give you:
- practical experience with common computational methods in engineering, and
- enough theoretical understanding to know when those methods can go wrong
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
Textbook: Computational Science and Engineering by Gilbert Strang
Optional Textbook (for Matrix concepts): Matrix Analysis and Applied Linear Algebra by Carl Meyer
Can be accessed online through MIT Library
Grades: 40% problem sets, 60% two in-class quizzes (30-30).
Problem Sets: Due at start of class on Wednesday, unless otherwise noted. Half of problem set score will be for completion, remaining half will be for one graded problem.
Registration: Registration must be submitted by the end of the first week of the summer session (Friday, June 12). Registration submitted after this deadline is subject to a $50 late fee.
All students attending should be registered either for credit or as listener.
Online lectures: online lectures from Gil Strang are available here. You are encouraged to look at them, either before or after class!
Matlab Resources: Matlab codes from the textbook's website.
Matlab tutorials (see especially matrix-vector operations).
RECENT UPDATE
[07.13.2015] Solutions to Exam 1 are posted below. The mean for the exam was 76, with a standard deviation of 15.
[07.10.2015] Dan's final office hours will be on Tuesday (7/14) 4-5pm in E18-358.
[07.07.2015] Special Exam Office Hours on Thursday (7/9) 4-6pm in E18-466A.
[06.29.2015] PSET 3 is now updated. (Removed problem 6, the rest is the same.)
[06.15.2015] PSET 1 is now updated. (Modified problem 4 and removed problem 5, the rest is the same.)
[06.09.2015] Dan's office hours will be held today from 4-6pm in E18-358.
[05.20.2015] Welcome to 18.085!
SCHEDULE
| Event | Date | Related Documents |
|---|---|---|
| PSET 1 | Due June 17 | Solution PSET 1 |
| PSET 2 | Due June 24 | Solution PSET 2 |
| PSET 3 | Due July 1 | Solution PSET 3 |
| PSET 4 | Due July 8 | Solution PSET 4 |
| EXAM 1 | July 10, 9:30 am | Solution EXAM 1 Past exams with solutions: Spring 2012 - Quiz 1 (Q1,Q2,Q3,Q4,Q5) Summer 2013 - Quiz 1 (Q1,Q2,Q3,Q4,Q5,Q6) Summer 2014 - Quiz 1 (Q1,Q2,Q3,Q4,Q5) Spring 2012 - Quiz 2 (Q1,Q4a,Q5) Summer 2013 - Quiz 2 (Q1,Q2) Summer 2014 - Quiz 2 (Q1,Q3) |
| PSET 5: 3.1, 3.11, 3.11 w/midpoint rule, 3.11 with: c(x)=1/(1+x), f(x)=x^3, n=3, and midpoint rule | Due July 22 |
Syllabus
| Day | Topics (page numbers are approximate) | Related Documents | |
|---|---|---|---|
| June 8 | Linear algebra basics (685-689) | ||
| June 10 | Four fundamental subspaces Fundamental theorem of linear algebra (690) | Useful matrix identities | |
| June 12 | Truss stability problem (186-188, 192-194) | ||
| June 15 | Resistor network problem Solving linear systems Ax=b LU decomposition (26-30) | Solving linear systems in MATLAB | |
| June 17 | LU decomposition (cont.) LU-decomposition operation count (32-33) | luTiming.m More information on pivoting | |
| June 19 | Elastic string problem Boundary value problems (13-22) Finite differences and difference equations | ||
| June 22 | Delta and Green's functions (36-43) | ||
| June 24 | Best fit problem Least squares (128-137) Normal equations | ||
| June 26 | Gram-Schmidt (80-81) QR decomposition (79-81) | Householder example | |
| June 29 | 1st order systems of differential equations Eigenvalues and eigenvectors (46-55) | Calculating determinants | |
| July 1 | Symmetric and positive definite matrices (66-67) SVD (81-83) | ||
| July 3 | No class, holiday. | ||
| July 6 | SVD (81-83) continued Error analysis and condition number (84-87) | ||
| July 8 | Radioactive decay problem Forward and backward Euler, trapezoidal method (113) | ||
| July 10 | EXAM 1 (in class): book and notes allowed, no electronic devices, no calculators. | ||
| July 13 | 3.1 | ||
| July 15 | 3.1 | ||
| July 17 | 3.2 | ||
| July 20 | 3.2 | ||
| July 22 | 3.3, 3.4 | ||
| July 24 | 3.4, 3.5 | ||
| July 27 | 3.5 | ||
| July 29 | 3.6 | ||
| July 31 | 3.6 | ||
| August 3 | 4.1 | ||
| August 5 | 4.3 | ||
| August 7 | 4.3 | ||
| August 10 | 4.4 | ||
| August 12 | 4.4 | ||
| August 14 | EXAM 2 (in class): book and notes allowed, no electronic devices, no calculators. |