# Numerical Methods

MATH 428 / ENGR 428 / PHYS 428 and PHYS 528

#### Fall 2019: Engineering Outreach

Engineering Outreach at the University of Idaho

#### Instructor:

Lyudmyla Barannyk
317 Brink Hall
tel:  (208) 885-6719
fax: (208) 885-5843
barannyk@uidaho.edu

 Exam Proctoring

## Course Description

This is a survey course of the basic numerical methods which are used to solve practical scientific problems. Important concepts such as accuracy, stability, efficiency and convergence are discussed. The course provides an introduction to MATLAB, an interactive program for numerical linear algebra.

## Textbook

A Friendly Introduction to Numerical Analysis
ISBN: 0-13-013054-0
Publisher: Prentice Hall
Published: 04/26/2005

Numerical Computing with MATLAB
By: Cleve B. Moler
ISBN: 0898715601
Publisher: Society for Industrial & Applied (06/01/2004)

Available electronically at http://www.mathworks.com/moler/

Numerical Methods Using Matlab (Fourth Edition).
By: John H. Mathews and Kurtis D. Fink

Errata for 4th Edition: Numerical Methods Using MATLAB, John H. Mathews and Kurtis D. Fink

An introduction to numerical analysis
By: Kendall E. Atkinson QA 297.A841

Numerical Analysis
By: Richard L. Burden and J. Douglas Faires

Elementary Numerical Analysis (3rd Edition)
By: Kendall Atkinson and Weimin Han

MATLAB guide
By: Desmond J. Higham & Nicholas J. Higham. QA297 .H5217 2000

## Objectives of the course

• Develop numerical methods for approximately solving problems from continuous mathematics on the computer
• Examine the accuracy of these methods
• Examine the stability of these methods
• Examine the failure modes of these methods
• Implement these methods in a computer language (MATLAB)

## Computer language

In this course, we will make extensive use of Matlab, a technical computing environment for numerical computation and visualization produced by The MathWorks, Inc. This will take a little learning, but will pay off in the long run, since programming numerical methods is much easier (and quicker) in Matlab than in virtually any other language.

Matlab is available through VLAB at https://vlab.uidaho.edu/vpn/index.html

Phone: 208-885-4357 (HELP)
Email: helpdesk@uidaho.edu

Teaching Learning Center Room 128

Matlab tutorial by Dr. Mayank Aggarwal

Also available is a MATLAB tutorial written by Peter Blossey: (.pdf)

Another standard one is Kermit Sigmon's Matlab Primer: (.html)

http://web.cecs.pdx.edu/~gerry/MATLAB/programming/basics.html

Here is another Matlab resource available on the net:

In addition, there are many textbooks about Matlab. One of them is

MATLAB guide
By: Desmond J. Higham & Nicholas J. Higham. QA297 .H5217 2000

## Handouts

in format
• Cancellation of Significant Digits Example pdf
• Comparison of Rootfinding Methods (Bisection, False Position, Newton, and Secant) by J. Tropp pdf
• Newton's method pdf
• Numerically determining the order of convergence of the iterative rootfinding scheme pdf
• Elementary Matrices pdf
• LU factorization of a tridiagonal matrix pdf
• Example of LU decompotion with partial pivoting pdf
• Analysis of the SOR iteration matrix pdf
• Romberg Integration and Simpson's 1/3 error term explanation pdf
• Numerical Integration and Richardson's Extrapolation pdf

• Polynomial Interpolation pdf
• Chebyshev and uniform points pdf
• Extra notes on Chebyshev interpolation pdf
• Lecture notes on spline interpolation pdf
• Global error for Euler's method pdf
• Lecture notes on Multistep Methods pdf
• Derivation of Adams-Bashforth 2nd order method pdf

Video lectures are available through Engineering Outreach at https://eo.uidaho.edu/portal.

## Lecture Notes

Lecture 1          Lecture 10           Lecture 19 (midterm review)    Lecture 28         Lecture 37
Lecture 2          Lecture 11           Lecture 20                                 Lecture 29         Lecture 38
Lecture 3          Lecture 12           Lecture 21                                 Lecture 30         Lecture 39
Lecture 4          Lecture 13           Lecture 22                                 Lecture 31         Lecture 40
Lecture 5          Lecture 14           Lecture 23                                 Lecture 32         Lecture 41
Lecture 6          Lecture 15           Lecture 24                                 Lecture 33         Lecture 42
Lecture 7          Lecture 16           Lecture 25                                 Lecture 34         Lecture 43
Lecture 8          Lecture 17           Lecture 26                                 Lecture 35         Lecture 44  (last lecture and final review)
Lecture 9          Lecture 18           Lecture 27                                 Lecture 36

## Schedule, Homework and Exams

Follow links in the table below to obtain a copy of the homework in Adobe Acrobat(.pdf) format.
Homework assignments include assigned and suggested problems. Assigned problems will be graded. Students are responsible for material covered in suggested problems as well. The order of some homework problems is different from that used in lectures.

Homework assignments should submitted by email
barannyk@uidaho.edu by the end of the due day. Please scan your assignments and attach m.files of your programs.
There is a 5 business day grace period. After that late homework will not be accepted.

 Homework Sets Due Date hw1 September 6 hw2 September 20 hw3 October 4 hw4 October 18 hw5 November 1 hw6 December 6

Midterm:

due Friday, October 4, 2019.  Students may bring a one sided page of their notes to the exam. It is recommended to complete the first three homework assignments before the midterm is taken.
Review
Lecture 19   midterm crib sheet
Midterm crib sheet will be included in the test.

Final:       due Thursday, December 19, 2019.  Students may bring a two sided page of their notes to the exam.
Review: see Lecture 44     final exam crib sheet
Final exam crib sheet will be included in the test.

40%- 6 Homework assignments
25%- Midterm Exam
35%- Final Exam

## Exam Proctoring

Please visit the proctor/exam information page on the website. https://eo.uidaho.edu/proctor

Students living outside of the United States will be required to use approved testing centers as their proctors. A testing center is a university, business, or military department with the primary purpose of proctoring tests and exams under direct observation. Students are required to provide a name of a person who will be the primary contact at the testing center. EO reserves the right to require students to take exams at specific pre-approved testing centers in locations outside of the United States.

You can view our proctor approved map to see if there is an approved testing center at the location you will be this summer.https://eo.uidaho.edu/map-international-proctors

If you know of a University Testing Center in the area you will be visiting that is not on our map you can submit that proctor to our office and we can begin the approval process before the semester starts: https://eo.uidaho.edu/proctorform