### Math 1070 Fall Semester 2021

### Numerical Mathematical Analysis

MWF 12:00-12:50,
G27 Benedum Hall

or virtually via Zoom
(meeting ID info on Canvas Announcements)

#### Aug 27, 2021 - December 10, 2021

### Office Hours

###
MW
3:00 - 4:00, and by appointment (also via zoom)

Office: Thackeray 606

Phone: (412) 624 5681

E-mail: trenchea@pitt.edu

This course is an introduction to modern numerical methods.
Topics include polynomial and spline interpolation, numerical
integration and differentiation, numerical solution of nonlinear
equations and ordinary differential equations. Our goal will be to
understand how and when the methods work. The concept of numerical error
will be used to quantify the accuracy of approximation. We will also
study the stability and the efficiency of the algorithms.

Computer assignments will use Matlab, software produced
by The MathWorks. The Matlab language provides extensive library of
mathematical and
scientific function calls entirely built-in.
Matlab
is available on Unix and Windows in the university computing labs.
The full set of manuals is on the web in
html
and also in
Adobe PDF format. The "Getting Started" manual is a good
place to begin and is available both in html
format and in Adobe
PDF format. The full reference manual as well as manuals for each
of the many toolboxes are all available.

#### Course Delivery

During the first 2 weeks of August 17 to September 10 2021, all instruction will be conducted remotely.
Typically this means your instructor will hold virtual class meetings through Zoom at the scheduled class time, and the links to join these synchronous meetings will be posted in Canvas. The class meetings will be recorded, uploaded to Panopto, and made available for viewing through Canvas.

**Tutoring**: The Mathematics Department offers a free tutoring service.
The
Math Assistance Center (MAC) is located on the second floor of the O’Hara Student Center.
Tutoring services and tutoring hours will be posted outside the MAC as well as on the web at MAC.

## Course materials

**Textbook**:
Elementary Numerical Analysis,
3rd edition by
Kendall Atkinson
and Weimin Han.

Syllabus
Matlab Primer
Matlab Tutorial:
Postscript;
HTML
MATLAB computer lab
exercises by Dr. John Burkardt.
Introduction to Matlab
by Dr. Mike Sussman:
Preliminaries;
Beginning Matlab

For useful material related to this course go to
Kendall Atkinson's class web page

## Software

A collection of matlab codes accompanying the text
Some graphical user interfaces

**Additional references
:
**
*Numerical Mathematics*, second edition, by A. Quarteroni, R. Sacco, F. Faleri.
Book's Programs
Numerical Methods in Scientific Computing, volume I, by G. Dahlquist, A. Bjorck. SIAM.
Numerical Methods, by G. Dahlquist, A. Bjorck. Dover.

## Homework Assignments

Homework 1, Due
September 6, 2021:
**Section 1.1** # 9, **Section 1.2** #6, 9c, 15, 17
Homework 2, Due
September 17, 2021:
**Section 2.2** #1b,d, 5b,c, 6f,h;
**Section 2.3** #9
Homework 3, Due
September 24, 2021: **Section 4.1** #7, 8a, 12-bonus,
23a, 25
Homework 4, Due
October 4, 2021: **Section 4.2** #1, 4;
**Section 4.3** #1, 11;
Hermite interpolation problem
Homework 5, Due
October 11, 2021: **Section 5.1** #1, 11b,c, 16
Homework 6, Due
October 25, 2021: **Section 5.2** #1a, 7, 15, 19
Homework 7, Due
November 1, 2021: **Section 5.3** #2 - only do I-2,
I-3 for 2a,b,c; #9; **Section 5.4** #1a, #3 - only do a), #8, #9 - only do a)
Homework 8, Due
November 8, 2019: **Section 3.1** #1d, 9;
**Section 3.2** #2d, 3, 13 (extra credit); **Section 3.3** #1d, 4
Homework 9, Due
November 15, 2021: **Section 3.4** #1, 5, 8, 11, 13a
Homework 10, Due
November 22, 2021: **Section 3.5** #1 (use the code from
newton.m, error_bd = 1e-8, x0 = -1 and 1), 8
Homework 11, Due
December 2, 2021
## Matlab Assignments

Matlab Exercise 1. Due
September 6, 2021.
Matlab Exercise 2. Due
October 20, 2021.
Matlab Exercise 3. Due
November 15, 2021.
Matlab Exercise 4. Due
December 6, 2021.

## Exams

Exam 1:
October 8, 2021.
Exam 2:
November 8, 2021.
Final Exam: