## MA 238: Applied Differential Equations I

Schedule: MW 4:30-5:45 p.m. in ILB 370.

Office hours: MWF 11-noon, TR 1:30-3, or by appointment.

First-day handout, Spring 2014 (pdf file)

ODE Solver: The applet dfield will graph slope fields and numerically computed solution curves. Use it for the homework in Section 1.3. Check the Help menu that appears when you run the applet for tips on syntax. "Bad syntax" warnings may appear as you start to type an expression but disappear when you have finished.

Visusal DE Solver Applet. Among other things, this graphs the response of a mass-spring system to various input functions such as sine waves, square waves, step functions. This is one of Paul Falsted's many fantastic applets for math, physics and engineering. Tryout the 3-D vector fields applet.

MyPhysicsLab applets for mass-spring systems, single and double pendulum, and lots more.

David Harrison's Flash Animations for Physics. These include a chaotic 3-body system and very convincing animations of Hooke's Law and driven simple harmonic motion.

Wheel of Steel: A New York Times interactive graphic on the design of the pendulum apparatus for a Ringling Bros. Circus act.

Inverse Laplace Transform applet. Computes the inverse Laplace transform of a rational function (quotient of polynomials) and graphs it.

### Assignments

Carefully read each section we cover.

M 1/13: Read sections 1.1 and 1.2. Work problems 1.1 #1-17 odd, 23, 27, 33, 35, 43, 44, 47; also, find all solutions to y''=0.

W 1/15: Read 1.3. Work problems 1.2 #1, 2, 3, 5, 6, 8, 9, 11, 14, 15, 17, 18, 27, 28, 29.

W 1/22: Read 1.4. Work problems 1.3 #1-20, 22, 23, 25, 27-31. Also, use the applet dfield (see first link above) to plot some of the slope fields and solutions in these problems.

M 1/27: Work problems 1.4 #1-5, 9, 12, 17.

W 1/29: Work problems 1.4 #29, 36, 39, 44, 45, 46, 49, 65. Start reading 1.5.

M 2/3: Finish reading 1.5. Work problems 1.5 #1-21 odd, 29, 30.

W 2/5: Work problems 1.4 #47 and 1.5 #26, 27, 33, 37, 38, 41 (also 29, 30 if you didn't get them last time.) Read 1.6.

M 2/10: Work problems 1.6 #31-41 odd.

W 2/12: Work 1.6 #1, 3, 7, 8, 10, 13, 17, 19, 21, 23, 57, 58, 66, 67. For 1-23, first determine if the equation is homogeneous, Bernoulli, both or neither.

M 2/17: Work 2.1 #3, 5, 6, 9, 10, 23, 24, 33, 35.

M 2/24: Work 2.2 #1-13 odd, 19, 21, 23. (You may skip the questions regarding bifurcation diagrams.) We will go on to 3.1 next.

W 2/26: Work 3.1 #1, 3, 7, 9, 15, 19, 20, 23, 24, 25.

M 3/10: Work 3.1 #27-47 odd, 48.

W 3/12: Work 3.2 #1, 3, 6, 7, 8, 13, 17-25 odd, 26, 27, 33 and 3.3 #1-15 odd.

M 3/17: Work 3.3 #8, 21-29 odd, 33, 39, 40.

W 3/19 Work 3.4 #1-5, 13, 14, 15, 17, 19

M 3/24: Work 3.5 #1-15 odd, 21-33 odd.

W 3/26: Work 3.6 #1, 3, 5, 6, 11, 15, 18, 19.

M 3/31: Work 4.1 #1-17 odd, 12, 21, 22, 24, 29, 30.

W 4/2: Work 4.2 #1, 2, 3, 5, 7, 8, 9, 38.

M 4/14: Work 7.1 #7, 8, 9, 11, 224, 25, 32, 36, 37, 38.

W 4/16: Work 7.1 #39, 40 and 7.2 #1-11 odd, 25, 27, 28.

M 4/21: Work 7.3 #1-10, 11-17 odd, 27-31, 39, 40 and 7.5 #1-15 odd.

W 4/23: Work 7.5 #17-22, 25, 26, 29, 30-35.

M 4/28: Work 7.6 #1-7odd, 13, 15, 16, 22. Take-home quiz 9 is due on Wednesday.

The final is Monday 5/5, 6-8 p.m. Here is a study guide.