Instructor: | Carl McTague | |||

Lectures: |
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Office Hours: | W 2:30–4:30pm in Krieger 212 | |||

Text: | Boyce & DiPrima, Elementary Differential Equations and Boundary Value Problems, 10th Ed., Wiley, 2012 (Amazon). |

12 Dec | Here is the Dear Abby question from the final exam. (There is incidentally the most oblique of references to Buñuel’s Obscure Object of Desire (1977).) |

8 Dec | Where to take the final exam (at 9am on Weds 11 Dec): §§1–2 in Shaffer 101, §§3–5 in Maryland 110, §§6–8 in Hackerman B17. |

15 Nov | Where to take the 2nd Midterm Exam: §§1–2 in Gilman 132, §§3–4 in Maryland 110, §§5–8 in Remsen 101. |

7 Nov | The 2nd Midterm Exam on Fri 15 Nov will not cover §§5.4–6, Power Series Solutions at a Regular Singular Point. |

6 Nov |
Mathematica: Manipulate[With[{v={{a,2},{-2,0}}.{x,y}}, StreamPlot[v,{x,-5,5},{y,-5,5}]],{a,-10,10,Appearance ->"Labeled"}] |

20 Oct | Office hours for Week 8 will be 2:30–4:30pm Mon 21 Oct rather than Weds 23 Oct. |

22 Sept | The schedule now recognizes the existence of Thanksgiving. |

13 Sept | I have changed my office hours to try to accommodate more of you. |

11 Sept | Solutions to the first homework assignment have been posted below. |

2 Sept | Please attend section this week. Your TA will review some calculus. |

8 Aug | The ISBN 978-1-119-92506-4 listed in ISIS is for a special paperback run of the text available exclusively at the JHU bookstore with “Johns Hopkins University” and the course number printed on the cover (here’s a photo of it). The first word of the title has been dropped and the “and” appears to have been accidentally changed to “with” (but a few pages in, the title returns to normal). The color graphs are reproduced in black & white. The content is otherwise identical to the standard 10th edition but the price ($120) is lower. Note though that reluctance by non-JHU students to buy a JHU-branded text is likely to reduce its resale value. The price at Amazon ($150) for the standard 10th edition hardback is significantly lower than the list price the bookstore quoted ($240) when the dept decided to order the special paperbacks. The dept ordered them simply to help you save money. I am presently investigating why the Amazon price is so low (there are Amazon comments about needing to pay Wiley $75 separately for “access codes”—I doubt we’ll be needing them and don’t think the special paperbacks have them either). The Kindle edition ($80) appears to be an exact digital replica of the printed book (essentially a DRM’d PDF). Could you pull off using the 9th edition? Here’s what the author says is new in the 10th: (1st page), (2nd page). I intend to assign problems from the 10th edition and will expect you to hand in solutions to them. If you use the 9th edition then it will be your responsibility to ensure that you hand in solutions to the correct problems. |

Lecture | Date | Topic | Reading | Assignment | Due Date |
---|---|---|---|---|---|

1 | Sept 4 | Introduction | §1.1: §1.2: | 4, 8, 12, 22, 24. 2, 8, 13. | (solutions) (1.1.4), (1.1.12) |

2 | 6 | Geometric Methods | §1.3: | 1, 5, 12, 18, 20. | Sept 9 |

First Order ODE’s: | |||||

3 | 9 | Linear Equations—Integrating Factors | §2.1: | 5, 6, 12, 13, 15, 17, 27. | (solutions) |

4 | 11 | Separable Equations | §2.2: | 3, 4, 8, 12, 21, 23, 28. | (2.1.5), (2.1.6) |

5 | 13 | Substitution Method & Applications | §2.3: §2.4: | 2, 4, 10, 13, 14. 3, 4, 10, 14, 23, 27, 28. | (2.1.12), (2.2.12) Sept 16 |

6 | 16 | Autonomous Equations | §2.5: | 3, 7, 10, 20, 24. | (solutions) |

7 | 18 | Exact Equations | §2.6: | 1, 4, 6, 10, 22, 23, 32. | |

8 | 20 | Existence & Uniqueness | §2.8: | 2, 4, 8. | Sept 23 |

Second Order Linear ODE’s: | |||||

9 | 23 | Constant Coefficients, Real Roots | §3.1: | 3, 5, 10, 12, 17, 22. | (solutions) |

10 | 25 | The Wronskian | §3.2: | 3, 4, 8, 14, 22, 38. | |

11 | 27 | Constant Coefficients, Complex Roots | §3.3: | 2, 5, 10, 18, 22, 25. | Sept 30 |

12 | 30 | Euler Equations, Reduction of Order | §3.4: | 4, 12, 16, 21, 24, 31, 37. | (solutions) |

13 | Oct 2 | Method of Undetermined Coefficients | §3.5: | 2, 10, 18, 29. | |

14 | 4 | Variation of Parameters | §3.6: | 4, 7, 14, 19. | Oct 7 |

15 | 7 | Review | |||

† | Oct 9 | FIRST MIDTERM (lectures 1–14) | |||

16 | 11 | Higher Order Linear ODE’s | §4.1: §4.2: §4.3: | 8, 16. 7, 11, 12. 4. | (solutions) Oct 21 |

— | 14 | Fall Break Day (last day to drop is 13 Oct) | |||

Power Series Methods: | |||||

17 | 15 | Power Series Solutions : Ordinary Point | §5.1: §5.2: §5.3: | 2, 11, 16. 2, 6. 2, 3, 10. | (solutions) |

18 | 16 | Power Series Solutions : Regular Singular Point | §5.4: §5.5: §5.6: | 5, 17, 21. 4, 6, 12. 1, 14, 19. | Oct 21 |

Laplace Transform: | |||||

19 | 18 | Laplace Transform | §6.1: | 5, 15, 19. | Oct 28 |

20 | 21 | Solving Initial Value Problems | §6.2: | 3, 6, 12, 22, 29. | (solutions) |

21 | 23 | Discontinuous Forcing | §6.3: §6.4: | 12, 15, 22, 27. 5, 10, 15. | |

22 | 25 | Impulse Functions, Convolution | §6.5: §6.6: | 1, 5. 4, 9, 15. | Oct 28 |

Systems of Linear ODE’s: | |||||

23 | 28 | Linear Systems | §7.1: §7.4: | 2, 6, 8, 16. 6. | (solutions) |

24 | 30 | Review of Linear Algebra | §7.2: §7.3: | 8, 10, 16, 22, 25. 2, 10, 16, 20, 22, 26. | |

25 | Nov 1 | Constant Coefficient Linear Systems | §7.5: | 2, 7, 14, 18, 25, 27. | Nov 4 |

26 | 4 | Complex Eigenvalues | §7.6: | 2, 8, 9, 14, 18. | (solutions) |

27 | 6 | Fundamental Matrices | §7.7: | 3, 11, 16. | |

28 | 8 | Repeated Eigenvalues | §7.8: | 1, 2, 7, 15. | Nov 13 |

29 | 11 | Nonhomogeneous Linear Systems | §7.9: | 1, 5, 7. | Nov 13 |

30 | 13 | Review | |||

† | Nov 15 | SECOND MIDTERM (lectures 17–29) | |||

Nonlinear ODE’s and Stability: | |||||

31 | 18 | Geometry of Linear Systems | §9.1: | 1, 2, 15. | |

32 | 20 | Geometry of Linear Systems (cont’d) | §9.1: | 20, 21. | |

33 | 22 | Autonomous Systems | §9.2: | 2, 10, 15, 19, 21. | Nov 25 |

34 | 25 | Locally Linear Systems | §9.3: | 1, 5, 14, 20, 27. | Dec 2 (solutions) |

— | 27–29 | Thanksgiving | |||

35 | Dec 2 | Applications | §9.4: §9.5: | 2, 5, 10. 2, 9, 13. | not collected(partial solutions) |

36 | 4 | Periodic Solutions and Limit Cycles | §9.7: | 1, 3, 10, 11. | |

38 | 6 | Euler’s Method | §2.7: §8.2: | 2, 11, 15. 1(a). | |

‡ | Dec 11 | FINAL EXAM (lectures 1–38) |

TA | time | room | office | hours | help room | hours (Krieger 213) | |||
---|---|---|---|---|---|---|---|---|---|

1 | Kauffman | <kauffman> | Tues | 1:30–2:20pm | Krieger 302 | Fri 2–3pm | in Krieger 200 | Mon | 5–7pm |

2 | Kauffman | <kauffman> | Tues | 3–3:50pm | Krieger 309 | Fri 2–3pm | in Krieger 200 | Mon | 5–7pm |

3 | Xing Wang | <xwang> | Thurs | 3–3:50pm | Ames 234 | Weds 3–5pm | in Krieger 201 | Thurs | 7–9pm |

4 | Xing Wang | <xwang> | Thurs | 4:30–5:20pm | Krieger 302 | Weds 3–5pm | in Krieger 201 | Thurs | 7–9pm |

5 | Biggs | <rbiggs> | Tues | 4:30–5:20pm | Krieger 309 | Tues 3–4pm | in Krieger 411 | Weds | 1–3pm |

6 | Xinyang Wang | <xwang92> | Thurs | 1:30–2:20pm | Krieger 205 | Thurs 2:20–3:30pm | in Krieger 207 | Mon | 7–9pm |

7 | Qian | <yqian6> | Thurs | 3–3:50pm | Krieger 308 | Thurs 4–5pm | in Krieger 207 | Thurs | 9–11am |

8 | Tolliver | <tolliver> | Tues | 3–3:50pm | Krieger 302 | Thurs 2–3pm | in Krieger 201 | Mon | 1–3pm |

We will cover Chapters 1–9 of the text. Key topics will include:

First order ODE’s (linear, separable, autonomous, exact), Second Order Linear ODE’s (with constant & nonconstant coefficients), Higher Order Linear ODE’s (with constant & nonconstant coefficients), Series Methods, The Laplace Transform, Systems of Linear ODE’s, and Stabilitity in Nonlinear ODE’s.

**Grading**: The grading scheme will be:

Homework 15% — First Midterm Exam 25% — Second Midterm Exam 25% — Final Exam 35%

Your 2 lowest homework scores will not count toward your grade.

**Homework**: Your assignments will be posted above. They will be collected in lecture (generally on Mondays) and returned in section. *Late homework will not be accepted.* Your two lowest homework scores will not count toward your grade. You are encouraged to discuss homework problems with one another. However, each of you must write up your solutions independently, in your own words, without supervision or well-meaning influence from anyone else. Disputes regarding homework grading should be discussed with your TA.

**Midterm Exams** will be in class on **Weds 9 Oct** and **Fri 15 Nov**. Books, notes, phones & calculators are forbidden. You must bring your ID to the exam, and may be called upon to show it. If you do not have your ID and your TA cannot attest to your identity then you may not receive a grade for the exam. The first midterm is scheduled so that the grades will be available before the drop deadline (Dec 13). You have the one hour of section time to bring up grading errors or omissions on the midterms, once they have been returned to you. You may not take the exam home and bring it back for corrections.

**The Final Exam** will be 9am–12pm Weds 11 Dec. Further particulars nearer the time.

**Absence**: You are expected to attend class and take exams as scheduled. **There will be no makeup exams.** If you miss a midterm exam then you will get a zero for that exam. If you miss the final exam then you will automatically fail the course. In exceptional circumstances documented by a letter from your doctor or your academic supervisor, the remaining homework and final exam may be given correspondingly more weight to take up the slack.

**Disability**: Any student with a disability who may need accommodations in this class must obtain an accommodation letter from Student Disability Services, 385 Garland, (410) 516-4720, studentdisabilityservices@jhu.edu.

**Ethics**: Don’t get it WRONG, like Kant! Seriously though, cheating & other forms of academic dishonesty are corrosive & harmful to our university:

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.

Report any violations you witness to the instructor. You may consult the associate dean of student affairs and/or the chairman of the Ethics Board beforehand. See the guide on “Academic Ethics for Undergraduates” and the Ethics Board Web site for more information.

Copyright © 2013 by Carl McTague