# Math 703: Methods of Applied Mathematics I: Fall 2013

 Lecture Room: B119 Van Vleck Hall Lecture Time: 9:30–10:45 TuTh Lecturer: Jean-Luc Thiffeault Office: 503 Van Vleck Phone: (608)263-4089 Email: Office Hours: Tues 1:00–2:00, Fri 1:20–2:20, or catch me after class

# FAQ

• Is the final exam simply based on the material from the midterm exam (i.e., is it a cumulative final exam)?

Just the material since the midterm.

• Can we use your notes, or do we simply have to use our own notes? I have my notes in my notebook. I just want to make sure I can use them. Ideally, I would like to have access to both sets of notes.

You can use whaterver notes you want, as long as they are not photocopies or printouts of "other" documents. You can use a printout of notes you typed yourself.

• Can I write some additional notes by hand on separate pieces of paper?

Yes.

• Did you say we can use our homework assignment solutions too?

Yes.

## Description

The course introduces methods to solve mathematical problems that arise in areas of application such as physics, engineering and statistics.

See the official syllabus.

## Textbooks

There two textbooks for the class:

• G. Strang, Introduction to Applied Mathematics (Wellesley-Cambridge Press). ISBN: 0961408804.
• C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (Springer). ISBN: 1441931872 or 0387989315.

## Prerequisites

Math 319 (ODEs), Math 321 (Vector and complex analysis), Math 322 (Sturm-Liouville, Fourier Series, intro to PDEs), Math 340 (Linear Algebra) or equivalent.

## Homework

Every two weeks or so I will assign homework from the textbooks or otherwise and post it here.

Homework 1 (Due Sept. 26 in class): Show that a symmetric matrix is positive-definite if and only if its leading principal minors (determinants of upper-leftmost k by k submatrices along the diagonal) are positive. Problems from Strang: 1.2: 7,8,11; 1.3: 2,6,7,8,11,17; 1.4: 5,7,10,11,12; 1.5: 6,7,11,12,13,23,24.

Homework 2 (Due Oct. 10 in class): Problems from Strang: 1.6: 2,3,5,6; 2.1: 2,3,6,12; 2.2: 2,4; 2.4: 1,4,10,11,12,17.

Homework 3 (Due Oct. 24 in class): Problems from Strang: 3.1: 1,2,4,5,6; 3.2: 2,3,10,12; 3.3: 3,4,5; 3.6: 1,2,9,11,14. [Note for 3.6.9: M refers to the multiplier you use for the question, and m to the one on page 245. In part (c), he means for what values of the length constraint is there no solution.]

Homework 4 (Due Nov. 7 in class): Problems from Strang: 4.1: 10,11,18,19,20,26,30. 4.3: 5,6,7,10,21,27. 4.4: 10,15,17,21,22,23. 4.5: 2,3,5,8,9.

Homework 5 (Due Nov. 26 in class): Problems from Strang: 6.1: 18,20,21,22. 6.2: 2,3,5,6,8,11,12,13,14,19. Bender&Orszag: 4.4 (p. 201) 43,49,51,59.

Homework 6 (Due Dec. 12 in class): Problems from Bender&Orszag: 7 (p. 361) 1,4,9,10,12,18,28,36(a),36(d). 9 (p. 479) 1,3,4,6,17,19,29(a),31. 10 (p. 539) 2,5,8,23.