2.993J | Spring 2005 | Undergraduate

# Introduction to Numerical Analysis for Engineering (13.002J)

## Lecture Notes

A list of lecture topics and supporting files for the lecture notes are included in the table below.

LEC # TOPICS LECTURE NOTES SUPPORTING FILES

1

Introduction

Computer Architecture

Number Representations

Recursion

horner.m (M)
recur.m (M)
sqr.m (M)

2

Error Propagation

Error Estimation

Condition Numbers

euler.m (M)
sbfj.m (M)
sbfj_3.m (M)
sbfj_f.m (M)
sbfj_f_3.m (M)
sbfy.m (M)
tsbfj.m (M)

3

Linear Systems of Equations: Cramer’s Rule

Gaussian Elimination

tbt2.m (M)
tbt3.m (M)
tbt4.m (M)
tbt5.m (M)
tbt.m (M)

4

Linear Systems: Gaussian Elimination

Pivoting

LU Factorization

Error Analysis

tbt6.m (M)
tbt7.m (M)

5

Linear Systems: Tri-diagonal Systems

Special Matrices

(PDF)

6

Linear Systems: Iterative Methods

Convergence of Iterative Schemes

(PDF)

vib_string.m (M)

7

Roots of Non-linear Equations: Bisection

Newton-Ralphson Iteration

bisect.m (M)
cube.m (M)
div.m (M)
heron.m (M)
sqr.m (M)

8

Interpolation of Functions by Polynomials

Lagrange Interpolation

Triangular Family

langrange.m (M)
newton.m (M)
newton_coef.m (M)
newton_test.m (M)

9

Numerical Differentiation and Integration

Error Estimates

(PDF)

10

Ordinary Differential Equations

Initial Value Problems: Euler and Runge-Kutta Methods

euler.m (M)
rk.m (M)
rkg.m (M)

11

Ordinary Differential Equations (cont.)

Boundary Value Problems: Finite Difference Methods

12

Minimization Problems

Least Square Approximation

Optimization

(PDF)

cost.m (M)
curve.m (M)
lstsq.m (M)
salesman.m (M)

## Course Info

Spring 2005
##### Learning Resource Types
Exams with Solutions
Lecture Notes
Programming Assignments with Examples