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)

Thursday, 2 February (Structure, Sequences)
 extended to Tuesday, 7 February
 Cooper, Section 9.1: 2, 3, 4, 5, 7, 9.

Thursday, 9 February (Topology)
 Cooper, Section 9.2: 1, 2, 3, 5, 6, 7.

Thursday, 16 February (Continuity)
 Cooper, Section 9.3: 1, 2, 3, 4, 5.

Thursday, 23 February (RealValued Differentiability)
 Cooper, Section 10.1: 1, 2, 3, 4, 7

Thursday, 1 March (Linear Mappings and Differentiability)
 Cooper, Section 10.2: 1, 2, 3, 4
 Cooper, Section 10.3: 1, 2

Thursday, 8 March (RealValued Differentiability)
 Cooper, Section 10.3: 3, 4, 5, 6, 7, 8

Thursday, 15 March (Round Two)
 Click on the date above to download.
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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)
 Click on the date above to download.
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Assignments on Additional Topics Covered on the Final Exam
(Wednesday, 16 May)

Thursday, 3 May (Constrained Optimization)
 Cooper, Section 13.1: 1, 2, 3, 4, 9.

Thursday, 10 May
(More Constrained Optimization)
 Cooper, Section 13.2: 2, 3.
 Cooper, Section 13.3: 1, 2, 3.
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