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Teaching Differential Equations

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

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Teaching Differential Equations

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  1. Teaching Differential Equations Roger D. Demaree

  2. 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

  3. 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 The book

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

  5. 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: Resources

  6. 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

  7. 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

  8. 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.

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