# Math 412 Homework, Spring 2012

(24 April version)

There will be homework assignments worth 10 points each. These are given below, but are subject to changes announced in class. Only your 10 best homework scores count toward your course grade.

When and Where to Turn in Your Homework. Each Homework assignment should be turned in no later than its due date by either:

• giving it to me in class,
• bringing it to my MTH3313 office before 6:00pm.
If the University cancels class for any reason on the scheduled due date of an assignment then that assignment will be due on the first day that the class subsequently meets. Assignments turned in late will be recorded, but may not be graded for full credit.

How Each Homework Should Look. Your homework should be neat and legible. You should give the number of each problem attempted and the work for each problem should be indicated clearly. (There should be no arrows running around or between pages!) The reasoning behind each answer should be given. Your answers should be presented in the order that the problems are assigned. If you use more than one sheet of paper, they should be stapled together. The top of the first page should include: your name, our course and section number, my name, and the date the assignment is due.

How Each Homework Will Be Graded. Your score for each homework assignment will be the sum of your scores of the graded problems renormalized so that the maximum possible score on each assignment is 10 points.

## Homework Assignments

Return the Math 412 homepage.

Assignments on Topics Covered on the First Exam (Thursday, 8 March)

Assignments on Topics Covered on the Second Exam (Thursday, 19 April)

• Thursday, 29 March (Linear Systems, Contraction Mappings)
• Cooper, Section 11.1: 1, 2.
• Cooper, Section 11.2: 3, 4, 5. (Use MatLab for 5. Print out your code and a plot of the iterates.)
• Thursday, 5 April (Inverse and Implicit Function Theorems)
• Cooper, Section 11.4: 1, 2, 3.
• Cooper, Section 11.5: 4, 5, 6, 7.
• Thursday, 12 April (Newton Method)
• Cooper, Section 11.3: 1, 2, 3, 5, 6, 7.
Problem 1b should read "... following equation (11.15), deduce that || x_{k+1} - x_* || <= ...
Problem 2 should read ... <= r^{2^k - 1} || x_1 - x_0 ||^{2^k} where r = 2 || Df(x_*)^{-1} || L .
• Thursday, 19 April (Quadratic Approximation and Convexity)
• Cooper, Section 12.1: 1, 2, 4, 5.
• Cooper, Section 12.2: 1, 3, 4, 5.
• Thursday, 26 April (Round Two)