Math 170 - Mathematical Methods for Optimization - Spring 2009

Lectures: TuTh 3:30-5 pm, 85 Evans

Prof: J Strain, email strain@math.berkeley.edu , WWW http://math.berkeley.edu/~strain/

Office hours: Tu 12:30-2, W 1-2:30 in 1099 Evans

Course web page: http://math.berkeley.edu/~strain/170.S09/

Prerequisites: Math 53 and 54 or equivalent.

Required Text: J. Franklin, Methods of Mathematical Economics, Classics in Applied Mathematics no. 37, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2002 (ISBN 0898715091, 9780898715095).

Grading: Grades will be based on the best 6 problem sets (60%), a midterm exam (20%) on March 5 in class, and a take-home final exam (20%) due in 1099 Evans on May 21 by 3:30. The problem sets will be due every Thursday in class; late submissions cannot be accepted after solutions have been distributed.

Problem Sets

  • Problem Set 1: Due February 5, 2009. Solve the following problems from Franklin: Page 19, problems 1, 2, 5 and 6. Page 20, problem 16. Page 26, problem 3. Page 27, problems 6 and 7. Page 32, problems 11 and 12. Solutions PDF
  • Problem Set 2: Due February 12, 2009. Solve the following problems from Franklin: Page 43, problems 1, 2, 3, 4 and 5. Page 44, problems 9 and 10. Page 50, problems 5 and 6. Page 51, problems 8, 14, 15 and 16. Solutions PDF
  • Problem Set 3: Due February 19, 2009. Solve the following problems from Franklin: Page 60, problems 2, 4, 9. Page 61, problems 12, 16, 18, 20. Page 62, problem 23. Page 67, problems 1, 3 and 7. Solutions PDF
  • Problem Set 4: Due February 26, 2009. Solve the following problems from Franklin: Page 77, problem 1. Page 78, problems 2, 4, 6, 7, 8. Page 92, problems 1, 4, 7, 8, 9. Solutions PDF
  • Problem Set 5: Due March 19, 2009. Solve the following problems from Franklin: Page 111, problems 1 and 7. Page 124, problems 1, 2, 3, and 4. Page 125, problems 5, 6, 7, 10 and 11. Page 126, problems 12 and 15.
  • Problem Set 6: Due April 2, 2009. Solve the following problems from Franklin: Page 140, problems 1, 2, 3, 5 and 7. Page 141, problems 9 and 10. Page 154, problem 3. Page 155, problems 9, 11 and 12.
  • Problem Set 7: Due April 16, 2009. Solve the following problems from Franklin: Page 230, problems 1, 2 and 9. Page 249, problems 1 and 5. Page 250, problems 6, 9 and 10. Page 271, problems 1, 2, 3 and 9.
  • Problem Set 8: Due April 23, 2009. Solve the following problems from the first handout on calculus of variations below: Page 491, problem 1. Page 494, problems 14, 15 and 16. Page 496, problems 20 and 21.
  • Midterm problems PDF and solutions PDF from March 5.
  • Take-home final exam problems PDF . These problems are worth 2 points each; please solve as many as you feel necessary to get 20 points and hand in by 3 pm on May 21.

    • Useful Links:

  • A simple proof of the Pontryagin Maximum Principle PDF.
  • References on calculus of variations PDF, optimal control PDF, and the handbook article on calculus of variations PDF.
  • Midterm problems PDF from Fall 2003.
  • Final exam problems PDF from Fall 2003.