## Mathematics 266B: Elementary Differential Equations

Instructor: Jonathan Smith, 496 Carver, 4-8172 (voice mail)

e-mail: jdhsmithATmathDOTiastateDOTedu (substitute punctuation)

Office Hours: Mon. 11 am, 3.10 pm, 5.30 pm; Wed., Fri. 11am, (subject to change)

Finals Week Office Hours: Tue. 1 - 2pm, Wed. 11am - noon

Grading: based on graded homework assignments and quizzes (45%), 2 in-class tests (15% each), and the final (25%, Wed. 12/17, 2.15-4.15pm). Click here for information about special accommodations.

Textbook: W.E. Boyce and R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 8th ed., Wiley, ISBN 0-471-43338-1

Study plan: reserve 1 - 2 hours for (graded and ungraded) homework between each pair of classes. Successful performance in the class depends critically on completion of the homework assignments.

Although attendance will not be taken, there will be no opportunity to recover credit for quizzes and in-class tests missed through unexcused absence.

Communication devices must remain switched off during the class periods and final.

Syllabus:

• Chapter 1: Introduction (examples, classification of differential equations)
• Chapter 2: First order differential equations
• Chapter 3: Second order differential equations
• Chapter 7: Systems of differential equations

### Assignments

12/1 for 12/3: Do 7.6 (p. 410), Exx. 1, 3, 7 (just solve).

11/14 for 11/17: Do 7.5 (p. 399), Exx. 15, 17; 7.8 (p. 428), Ex. 7 (just solve).

11/12 for 11/14: Do 7.8 (p. 428), Exx. 1, 2, 5 (just solve).

11/7 for 11/10: Do 7.5 (p. 399), Exx. 11, 12.

11/5 for 11/7: Do 7.5 (p. 398), Exx. 1, 2, 3, 5 (general solution only).

11/3 for 11/5: Do 7.3 (p. 384), Exx. 15, 17.

10/31 for 11/3: Do 7.2 (p. 373), Exx. 22, 24. Also, compute the determinants of the matrices from Exx. 14, 16.

10/29 for 10/31: Do 7.3 (p. 383), Exx. 1 - 5.

10/27 for 10/29: Do 7.2 (p. 373), Exx. 1, 2, 10, 14, 16, 18.

 Third graded homework (due 10/27) For maximal credit, full working must be shown. (3 points.) Write the function u(t) = 4 cos t - 3 sin t in amplitude-phase form. (4 points.) Find a particular solution to the differential equation y'' + y = csc t for initial data at  t = 1. (4 points.) Give the general solution to the differential equation     t2y'' - 3ty' + 4y = 0 in the range  t  >  0. If you wish, you may assume that y1(t) = t2 is one solution. Click here for printable version.

10/20 for 10/22: Read pp. 171-172, do 3.5 (p. 173), Exx. 23, 24.

10/17 for 10/20: Do 3.4 (p. 180), Exx. 39, 40, 42.

10/15 for 10/20: Read pp. 187-189, do 3.7 (p. 190), Exx. 1-3.

10/13 for 10/15: Do 3.2 (p. 151), Exx. 1-5.

10/10 for 10/13: Do 3.8 (p. 203), Exx. 1-4, 7.

10/8 for 10/10: Read pp. 192-195, do 3.8 (p. 203), Ex. 5 (just "determine the position  u  of the mass at any time  t ").

 Second graded homework (due 10/8) For maximal credit, full working must be shown. (6 points.) Solve the initial value problem y'' + y = cos t with  y(0) = 1 and  y'(0) = 0. (6 points.) Give the general solution to the differential equation     y'' + 5y' + 6y = et + t2 Click here for printable version.

10/3 for 10/6: Read pp. 179-181, do 3.6 (p. 184), Exx. 6, 7, 10, 17.

10/1 for 10/3: Read pp. 177-179, do 3.6 (p. 184), Exx. 1, 2, 9, 13.

9/24 for 9/26: Read pp. 159-161, do 3.4 (p. 164), Exx. 7, 9, 11, 13.

9/22 for 9/24: Do 3.5 (p. 172), Exx. 1, 2, 3, 12.

9/19 for 9/22: Read pp. 137-141, do 3.1 (p. 142), Exx. 2-12, even numbers.

9/15 for 9/17: P. 131, Exx. 1, 3, 5, 20.

9/12 for 9/15: Read pp. 95, 97, do 2.6 (p. 99), Exx. 1, 2, 3, 4.

9/8 for 9/10: Do 2.1 (p. 41), Ex. 39.

 First graded homework (due 9/8) For maximal credit, full working must be shown. (3 points.) At time  t  (in years), the price of a gallon of gas is \$y(t) . If 10y' = y , how long does it take for the price to double? Give your answer rounded to the nearest whole number of years. (4 points.) Solve the initial value problem y' + y = et with  y(0) = 1 . (3 points.) Give an implicit solution to the initial value problem y'(x) = ( 1 + 4x3) / ( 1 + 4y) with  y(1) = 3 . Click here for printable version.

9/3 for 9/5: Read pp. 44-46, do 2.2 (pp. 47-8), Exx. 5, 13, 15 (solution only, no graph).

8/29 for 9/3: Read pp. 36-37, do 2.1 (p. 39), Exx. 17, 15.

8/27 for 8/29: Read pp. 10-14, do 1.2 (pp. 15-7), Exx. 1 (a)(c) -- "solve" only, 8, 13.

8/25 for 8/27: Read pp. 19-22, do 1.3 (pp. 24-5), Exx. 1-4, 8, 9, 15, 17.