# 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.

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.

### 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
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
11 Nov 19, 21

### PDE's, cont'd.

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

• Convex hull
• Tesselation