Teaching Differential Equations

Roger D. Demaree

Audience: Which students are ready?

• Students who have finished Calculus BC

• Students taking Calculus BC concurrently, after a 4 or 5 on Calculus AB– Note: Calc BC and Diff Eq should be

coordinated so that Diff Eq does not start series until Calc BC finishes series.

• Generally appropriate for future math, science, or engineering majors

The book

• Elementary Differential Equations and Boundary Value Problems, 9th edition (RHHS uses 8th edition, but 9th has better resources)

– By Boyce and DiPrima

• Chapters:– 1. Introduction

– 2. First Order Linear

– 3. Second Order Linear

– 4. Higher Order Linear

– 5. Series Solutions

– 6. The Laplace Transform

– 7. Systems of First Order

– 8. Numerical Methods

– 9. Nonlinear

– 10. Partial Differential Equations

– 11. Boundary Value Problems

Resources

• Online solutions to ALL problems provide significant detail. Problems from book:– 1. – 2. – 4. – 6. – 8. – 9.

• Online solutions:

032 yyy

023 yyy

032 yyy

094 yy

022 yyy

02 yyy

1)0(,1)0( yywith

Resources

• Tough problems have solutions extending more than a page.

• Extra detail is included for new types of problems.

• Powerpoint explanations for each section, with examples

• All support files are pdf or ppt and can be saved to your computer

• PDE Online solution:

Slide from Online Powerpoint:8.1 Euler’s Method

• We will concentrate on the first order initial value problem

• Recall that if f and f /y are continuous, then this IVP has a unique solution y = (t) in some interval about t0.

• In Chapter 2.7, Euler’s method was formulated as

where fn = f (tn, yn). For a uniform step size h = tn – tn-1, Euler’s method becomes

00 )(),,( ytyytfdt

dy

,2,1,0,11 nttfyy nnnnn

,2,1,0,1 nhfyy nnn

Benefits of offering Diff Eq

• Challenge our top students

• Offer another math class to advanced Collins/Krummel students who will soon need four math credits

• Not yet an AP course but Howard County Differential Equations students have received college credit at numerous schools

Other

• My homework assignments are online http://teacherweb.com/MD/RiverHill/MrDemaree/h2.aspx

• Having students in this class with Calculus BC may raise AP scores

• We have 180 days (slightly less for seniors) to cover what colleges teach in 45 days

• Possible to incorporate MIT’s Open Courseware into homeworkhttp://ocw.mit.edu/OcwWeb/Mathematics/18-03Spring- 2006/VideoLectures/index.htm

• Covering the College Park curriculum in 180 days is quite manageable.