E19: Numerical Methods for Engineering

Fall 2012

Mon, Wed, Fri 11:30-12:20, Hicks 211
Instructor: Matt Zucker

Course Description

This course is geared towards students who want to know how to transform a set of equations on a page into a working computer program. No particular programming experience is assumed, and no math courses beyond calculus. Techniques learned will be applied in a series of projects focused on engineering applications.

Look over the course syllabus for more information.

The topics below are subject to change. As we move through the course, I will update the list to reflect the new schedule, readings, and assignments.

Textbook

Steven C. Chapra and Raymond P. Canale, Numerical Methods for Engineers, 6th edition, McGraw Hill 2010.

Useful Links

Class Schedule

Week Dates Topics Readings Labs & HW
1 Sep 3, 5, 7

Introduction

  • Modeling
  • Computation
  • Floating-point representation
  • Error analysis
Syllabus
Part One intro
Ch. 1, 3, 4
Optional:
Nomography Floating point
Homework 1
guess1.m
guess2.m
Project 1: estimating π
2 Sep 10, 12, 14

Roots of equations

  • Bracketing methods
  • Open methods
Part Two intro
Ch. 5, 6, 8
Homework 2
bisect.m
rfmethod.m
3 Sep 17, 19, 21

Linear Algebra

  • Gaussian elimination
  • LU decomposition
  • Matrix inverse
Part Three intro
Ch. 9, 10
Homework 3
gausselim.m
Project 2: traffic / resistors
starter code
4 Sep 24, 26, 28

Linear Algebra, cont'd.

  • Special matrices and Gauss-Siedel
  • Least-Squares regression
  • Singular Value Decomposition
Ch. 11, 17, 12 Homework 4
compass data
P12.38 example
5 Oct 1, 3, 5

Optimization

  • One-dimensional unconstrained
  • Multidimensional unconstrained
  • Exam 1: date and time TBA
Part Four intro
Ch. 13, 14
6 Oct 8, 10, 12

Optimization, cont'd.

  • Constrained optimization
  • Simulated annealing
  • Genetic algorithms
Ch. 15
Supplemental reading
MATLAB examples
Homework 5
FALL BREAK
7 Oct 22, 24, 26

Numerical Differentiation and Integration

  • Newton-Cotes formulas
  • Integration of equations
Part Six intro
Ch. 21, 22, 24
Project 3: applied optimization
traj.m
8 Oct 29, 31, Nov 2

Ordinary Differential Equations

  • Runge-Kutta methods
  • Stiffness and multistep methods
Part Seven intro
Ch. 25, 26
golf.m
test_golf.m
9 Nov 5, 7, 9

ODE's, cont'd.

  • Boundary-Value problems
  • Eigenvalue problems
Ch. 27, 28 Project 4: roller coaster
10 Nov 12, 14, 16

Partial Differential Equations

  • Elliptic Equations
  • Parabolic Equations
  • Exam 2: date and time TBA
Part Eight intro
Ch. 29, 30
Stam fluids paper
Homework 6
quintic.m
Advection/diffusion code
11 Nov 19, 21

PDE's, cont'd.

  • Finite element method
Ch. 31, 32 Projection code
Final Projects
12 Nov 26, 28, 30

Computational Geometry

  • Convex hull
  • Tesselation
Supplemental reading Final fluid code
Convex hull code
13 Dec 3, 5, 7

Student presentations

14 Dec 10

Student presentations

FINAL EXAM - date and time TBA