Math 450---Applied Mathematics I

Fall Semester 2001

• Class Meets: 9-9:50 am, MWF, in Wilson 1-126
• Instructor:
  Curt Vogel
  2-210 Wilson Hall
  ph. 994-5332
  e-mail: vogel@math.montana.edu
  Office Hours: 10:00-10:50, MWF
• Textbook:
  Applied Mathematics, Second Edition, by J. David Logan,
  published by Wiley.
• Course Outline:
  Chapter 1. Dimensional Analysis and Scaling.
  Chapter 2. Perturbation Methods.
  Chapter 3. Calculus of Variations.
• Grading:
  HW & Projects --- 40%
  Midterm Exam --- 30%
  Final Exam ----- 30%

  The final exam is scheduled for 8:00-9:50 am, Monday, Dec. 17, 2001. Students are strongly encouraged to work together on homework assignments. Late homework will be accepted only with the advanced permission of the instructor.

• Homework Assignment 1:
  Exercises 1.1, 2.1, 2.3, 2.7 in Chapter 1. Due Friday, Sept. 14.
  Exercises 1.2, 2.2, 2.4, 2.5 in Chapter 1. Recommended.
• Homework Assignment 2:
  Exercises 3.4, 3.5, 3.7, 3.9 in Chapter 1. Due Monday, Sept. 24.
  Exercises 3.3, 3.6, 3.10 in Chapter 1. Recommended.
• Homework Assignment 3:
  Exercises 1.1, 1.5a, 1.7, 1.9, 1.10 in Chapter 2. Due Friday, Oct. 5.
  Exercises 1.2 (compare with numerical solution only), 1.5b, 1.8, 1.12 in Chapter 2. Recommended.
• Homework Assignment 4:
  Exercises 1.3c, 1.3i, 2.1b, 2.2 in Chapter 2. Due Friday, Oct. 12. Click here for information on graphing solutions.
  Exercise 2.3 in Chapter 2. Recommended.
• Homework Assignment 5:
  Exercises 3.2b, 3.4 in Chapter 2. Due Friday, Oct. 19.
  Exercise 3.7c in Chapter 2. Due Monday, Oct. 22. Hint: Look for bndry layer at t=1.
  Exercise 3.3 in Chapter 2. Recommended.
• Homework Assignment 6:
  Exercises 4.2, 4.3b in Chapter 2. Due Friday, Oct. 26.
  Exercise 4.1 in Chapter 2. Recommended.
• Midterm Exam, Monday, Oct. 29
• Homework Assignment 7:
  Exercises 1.1 and 1.2 in Chapter 3. Due Friday, Nov. 2. Hint on 1.1: Show that J(y) is bounded by cos(pi y(0)) / pi - cos(pi y(1)) / pi.
• Homework Assignment 8:
  Exercises 2.1a-c, 2.3, 2.11, and 2.13 in Chapter 3. Due Friday, Nov. 9. Hint on 2.1: The given sets are subsets of C[0,1], so you only need to verify 2 properties---closure under vector addition and closure under scalar multiplication.
  Exercises 2.2 and 2.4 are recommended.
• Homework Assignment 9:
  Exercises 3.1a, 3.1c, 3.2a, 3.4, 3.7, 3.8b in Chapter 3. Due Monday, Nov. 19. Problem 3.8b is extra credit. Hint on 3.2a: Eqn (2) on p. 124 holds. Follow the reasoning in Lemma 3.1 on p. 124 with h(x) replaced by h'(x).
• Homework Assignment 10:
  Exercises 4.2ab, 4.4a, 4.5b, 4.12a, 4.17 in Chapter 3. Due Friday, Nov. 30. Problem 4.14 is extra credit.
• Homework Assignment 11:
  Exercises 6.1, 6.4, 6.7 in Chapter 3. Also, use the Lagrange multiplier method to find the point on the plane x + y + 2z = 4 which is closest to the origin. Due Monday, Dec. 10.
• Final Exam is 8:00-9:50, Dec. 17.