# Spring 2017: MTH 285

## MTH285: Applied Mathematics Spring 2017

• Meets: TR 9:40 - 10:55pm, Hylan 203
• Textbook:
Computational Science and Engineering,
by Gilbert Strang
• Instructor: Mike Gage
• Office: Hylan 1010
• Office hours: T 11am-noon, T 4pm-5pm, F 9:30am-11
• E-mail: gage@math.rochester.edu

Grades

• Midterm: 20%
• Final: 20%
• Homework: 60%

Exams

1. There will be a take home midterm.
2. The will be an in-class final (3 hours)
3. The exams are given on the honor system. They are open book, that is, you may consult your notes and the textbook. You may not, however, discuss the examination with each other. You may ask me questions, but depending on the nature of the question I may or may not be able to answer. Please put the anser to each question on a separate piece of paper.

### Syllabus

We will cover roughly the first four chapters of the book and chapter 8. The over arching topics are:

1. Applied linear algebra
2. Discrete differential equations (ODE and PDE)
3. Fourier series (we touch on this)
4. Optimization

### Assignments

Complete list of assignments

1. Due Tue. Jan 24: Read section 1.1 Read “linear algebra in a nutshell”, p685 Read/skim Section 1.2 for class on Monday. Due Tue. Jan 24 in class: 1.1/ 2, 16, 18, 19,(cancel 27 –it’s not there) Look at 1.1/20 – particularly the last example

2. Due Thur. Feb 2 1.2/ 3, 4, 8(Read), 9, 10, 18, 20 1.3/ 2, 8, 11, 14, 15, 16, 17 (linear algebra review) skim sections 1.4 and 1.5 for next week. Answers: sec1.2 sec1.3

3. Due Thur. Feb 9 1.4/ 1, 4, 5 ,6, 9, 11, 13(read) Answers 1.5/ 10, 12, 14, 18, 24, 25

### Lectures

We will follow closely but not exactly the pattern of Strang’s lectures on the web

It may prove helpful to listen to those before hand since it could generate questions and make for a more interactive and productive class. (link is coming)

You should definitely listen to one lecture all the way through. After listening you will understand the writing in the text book MUCH better. You’ll be able to hear Strang’s voice as you read. :-)

1. Thur Jan 19 1.1 Four matrices,linear algebra review (when Ax=b uniquely is possible and when it’s not)
2. Tue Jan 24 1.2 Discrete ODE –Finite differences where those matrices come from.
3. Thur Jan 26 1.3 Linear algebra: LU decomposition – emphasis on symmetric matrices: K = LD transpose(L)
4. Tue Jan 31 1.4 Delta functions.
5. Thur Feb 2 1.5 Eigenvectors/Eigenvalues
6. Tue Feb 7 1.6 Positive definite matrices
7. Thur Feb 9 1.7 Factoring matrices
• $LU$ (Gauss elimination),
• $QR$ (Grahm-Schmidt),
• $S\Lambda S^{-1}$ (eigenvalues),
• $U\Sigma V$ (Singular value decomposition SVD)

### Video resources

MIT has made Strang’s lectures available over the web. http://ocw.mit.edu/courses/mathematics/18-085-computational-science-and-engineering-i-fall-2008/video-lectures/

### Computer language resources

A few problems can be done more quickly using a computer and computer language. I will avoid over emphasizing computer use, but if you are serious about doing applied mathematics you will be using computers. The computer language is your choice – use the languages you are familiar with – they are all equally capable for the problems in this course.

Strang uses MatLab for illustrations in his book. MatLab is available on most UR computers. I’ll get more details on this.

I would also like to use the open source languages supplied through Sage – which is open source, and has a web interface. I’ll let you know how that goes as well.