Math 412 Homework, Spring 2012

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.

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

• Assignments on Topics Covered on the First Exam
• Assignments on Topics Covered on the Second Exam
• Assignments on Additional Topics Covered on the Final Exam

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 (Real-Valued 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 (Real-Valued 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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