Math 4457      Methods of Applied Mathematics       Fall, 2003

Professor Peter J. Olver School of Mathematics Institute of Technology University of Minnesota Minneapolis, MN 55455	540 Vincent Hall Phone: 612-624-5534 Fax: 612-626-2017 e-mail: olver@math.umn.edu http://www.math.umn.edu/~olver
Lectures:    MWF 11:15 - 12:05, Vincent Hall 301
Office Hours:   M 1:30-3:30, F 12:15-1:15, or by appointment

• Homework #1:
  Exercises: 1.2.11a,b, 1.2.28, 1.3.1c, 1.3.3f, 1.3.17, 1.3.21, 1.3.22c, 1.3.26, 1.3.27c, 1.4.2a-c, 1.4.9b, 1.4.18c, 1.4.20, 1.5.3b,d,f, 1.5.4, 1.5.24e, 1.5.32c,d.
      Due: Wednesday, September 17
• Homework #2:
  Exercises: 1.6.6, 1.6.13, 1.6.18, 1.6.21, 1.6.22a,c, 1.7.1b, 1.7.2, 1.7.18, 1.8.2a,c, 1.8.6, 1.8.8a,c,i, 1.8.13, 1.8.20c,d.
      Due: Wednesday, September 24
• Homework #3:
  Exercises: 2.1.7, 2.1.11k, 2.2.2a,c,e,f,h, 2.2.5a, 2.2.9, 2.2.13a,b,d,f,h, 2.3.1, 2.3.7, 2.3.12b,c, 2.3.19b,c,d, 2.3.24, 2.3.25, 2.3.31, 2.3.34a,b.
      Due: Wednesday, October 1
• Solutions #1-3     ps      pdf
• Homework #4:
  Exercises: 2.4.2, 2.4.7,b,c, 2.4.12a, 2.5.6b, 2.5.14, 2.5.16, 2.5.19, 2.5.24a,c, 2.5.26iv, 2.5.27c, 2.5.33.
      Due: Wednesday, October 8
• Homework #5:
  Exercises: 3.1.1, 3.1.3, 3.1.10, 3.1.15, 3.1.18b, 3.1.23, 3.1.27a, 3.2.2, 3.2.6, 3.2.15, 3.2.23, 3.2.34, 3.4.1b-e, 3.4.5a-b, 3.4.8a, 3.4.9, 3.4.19i-iii, 3.4.20iii, 3.4.23a, 3.5.1a,c,d, 3.5.4.
      Due: Wednesday, October 22
• Homework #6:
  Exercises: 4.2.1a,b,c,d, 4.2.4ii, 4.2.6, 4.3.1, 4.3.2, 4.3.3, 4.3.8 -- just do (i,iv) in part (b), 4.3.12d, 4.3.13a,c, 4.3.16.
      Due: Wednesday, October 29
• Homework #7:
  Exercises: 4.4.4, 4.4.7, 4.4.10a, 4.4.14b, 4.4.15d, 4.4.20, 4.4.29, 4.4.34a, 4.4.41, 5.1.1a-d, 5.1.3a-d, 5.1.5, 5.1.17, 5.1.20, 5.1.23.
      Due: Wednesday, November 12
• Solutions #4-7     ps      pdf
• Homework #8:
  Exercises: 5.2.1a, 5.2.4a, 5.2.7c, 5.2.8a, 5.2.10a, 5.3.1, 5.3.5a,b-ii,c, 5.3.8, 5.3.14, 5.3.18, 5.3.23a,c, 5.4.2a,b, 5.4.10b, 5.5.2a,c, 5.5.5a,c, 5.5.14b, 5.5.18a, 5.5.31a, 5.6.1a,d, 5.6.9, 5.6.16a,e, 5.6.19b, 5.6.21
      Due: Wednesday, November 26
• Homework #9:
  Exercises: 8.2.1a,d,i, 8.2.9, 8.2.14, 8.2.15, 8.2.18, 8.2.19, 8.2.36, 8.2.39, 8.2.40, 8.3.1a,d, 8.3.3b,c, 8.3.4b,c, 8.3.8
      Due: Friday, December 5
• Homework #10:
  Exercises: 8.4.1a,c, 8.4.3c, 8.4.13a,c, 8.4.23a,b(i), 8.4.31, 8.4.34b, 8.4.35, 9.1.11b,e, 9.1.13, 9.2.1a,b,e, 9.2.3c, 9.2.8, 9.2.9
      Due: Friday, December 12
• Solutions #8-10     ps      pdf
• Homework #11:
  Exercises: 9.3.1, 9.3.3, 9.5.1c,d,f, 9.5.3, 9.5.5a,d,e, 9.5.9, 9.5.16a,c,d, 9.6.1a,c, 9.6.2a-c, 9.6.3a-c

Hour Exams

• Midterm #1: Wednesday, October 15. Will cover chapters 1 - 3.
• Midterm #2: Friday, November 21. Will cover chapters 4 - 5.

Course Description:   The year course Math 4457-8 is designed to introduce the basic tools used in applications of mathematics. Topics include linear algebra, differential equations, boundary value problems, numerical approximations, Fourier analysis, complex variables, dynamical systems, etc. Many applications will be discussed, including mechanical structures, electrical circuits, fluid mechanics, continuum mechanics, geometry, signal and image processing, and many more.

Text:   The course will be based on the professor's typed lecture notes, which will be available at Alpha Print, 1407 4th St. SE, in Dinkytown, 612-379-8535.

Homework:   Each assignment will consist of problems from the text, together with one or more computer projects. Assignments handed out on a Wednesday will be due the following Wednesday.

Computer Projects:   I will be introducing and using the numerical and graphing package Matlab to illustrate many of the concepts and calculations. Students will be expected to learn the basics of Matlab. Some class sessions will meet in the computer lab; dates and place will be announced in advance. The computer projects are expected to be programmed in Matlab. However, neither the professor nor the grader will be expected to read computer code or be responsible for debugging! The final output must be in easily readable form, and the grade will depend on presentation and neatness as well as mathematical correctness. Unintelligible outputs will receive no credit.

Hour Exams:   There will be two midterm exams; the date and chapters covered will be announced in due course. Make-up exams will only be given in exceptional circumstances, and then only when notice is given to me before hand and a suitable written excuse forthcoming.

Final Exam:     Thursday, December 18, 8:00 - 10:00 am

Grading:

• Homework and Computer Projects 30%
• Hour Exams 20% each
• Final Exam 30%

Incompletes:   Only given in extreme circumstances, and only when the student has satisfactorily completed all but a small portion of the work in the course. Students must make prior arrangements with the professor well before the end of the quarter.

Grading Standards and Student Conduct:   Students are expected to be familiar with University of Minnesota policies on grading standards and student conduct, including the consequences for students who violate standards of academic honesty.