# Introduction to Ordinary Differential Equations

# Introduction to Ordinary Differential Equations

## Tentative Course Outline

Week |
Section |
Recommended HW |

1 | Introduction | Handout |

1.1 Basic Definitions and Terminology | Page 10:odd 1–33 | |

1.2 Initial Value Problems | Page 16:odd 1–37 | |

2 | MLK Day | No class |

2.2 Separable Variables | Page 54:odd 1–99 | |

2.3 Linear Equations | Page 65:odd 1–37 | |

3 | 2.4 Exact Equations | Page 73:odd 1–39 |

2.5 Solutions by Substitutions | Page 78:odd 1–35 | |

4 | 1.3, 3.1, 3.2 Mathematical Models | Page 98:odd 1–41 |

5 | TEST #1 | Sections 1.1–3.2 |

4.1 Linear Differential Equations: Basic Theory | Page 137:odd 1–41 | |

6 | 4.2 Reduction of Order | Page 141:odd 1–19 |

4.3 Homogeneous Linear Equations with Constant Coefficients | Page 147:odd 1–41 | |

7 | 4.4 Undetermined Coefficients - Superposition Approach | Page 176:odd 1–41 |

4.5 Undetermined Coefficients - Annihilator Approach | Page 166:odd 1–71 | |

8 | 4.6 Variation of Parameters | Page 172:odd 1–25 |

4.7 Cauchy-Euler Equation | Page 178:odd 1–37 | |

5.1 Linear Models: Initial Value Problems | Page 207:odd 1–41 | |

9 | 5.2 Linear Models: Boundary Value Problems | Page 217:odd 1–19 |

Appendix 2: Introduction to Matrices | Page APP-18:odd 1–61 | |

10 | Spring Break | No classes |

11 | 8.1 Preliminary Theory | Page 336:odd 1–25 |

8.2 Homogeneous Linear Systems | Page 351:odd 1–45 | |

12 | TEST #2 | 4.1–4.7, 5.1–5.2, 8.1–8.2 |

7.1 Definition of the Laplace Transform | Page 283:odd 1–39 | |

13 | 7.2 Inverse Transforms and Transforms of the Derivative | Page 322: odd 1–41 |

7.3 Operational Properties I | Page 301:odd 1–73 | |

7.4 Operational Properties II | Page 312:odd 1–49 | |

14 | 7.2–7.4 More Practice | |

7.5 The Dirac Delta Function | Page 354:odd 1–15 | |

15 | Review of Power Series | |

6.1 Solutions about Ordinary Points | Page 248:odd 1–33 | |

6.2 Solutions about Singular Points | Page 257:odd 1–23 | |

17 | COMPREHENSIVE FINAL EXAMINATION |

**Course Policy**

1. You must be on the class roster by January 26, 2009 to
participate in any way (attend class,

submit homework, take quizzes, take tests).

2. Attendance is required by University rules . If you have
to miss a class, you are responsible

for any missed class notes, or assignments.

3. Students are expected to comport themselves as adults,
and to follow all University Rules,

Regulations and Policies, including those on discipline, academic honesty, and
harassment.

Disruptions, including inappropriate language, are unacceptable. Cell phones and
beepers

should be turned off during class.

4. The prerequisite for this course is a grade of C- or
better in 3450:223 Analytic Geometry –

Calculus III, or the equivalent . Students who do not meet the prerequisite are
liable to be

withdrawn from the course.

5. Important Dates :

January 12, 2009 – classes begin

January 19, 2009 – Martin Luther King Day, no classes

January 26, 2009 – last day to withdraw without advisor’ s signature

March 6, 2009 – last day to withdraw without instructor’s signature

March 14 – March 20, 2009 – Spring Break, no classes

April 10, 2009 (5:00pm) – last day to withdraw from courses

May 1, 2009 – last day of class

May 4, 2009 – Final Examination 8:00–9:55am, room to be announced

6. Incompletes will only be given in documentable cases of
long- term illness , or similar problems.

In addition, at least half of the semester’s work must have been completed, with
at

least an average grade of C. College policy also states that a student may not
sit in on the

course the next semester to make up the incomplete, but only to make up the
missed work.

7. There is a recommended list of homework problems given
for each section. You should do as

many as necessary to gain mastery of the material. These homeworks will not be
collected.

There will be additional homeworks assigned, and collected, usually on
Wednesday. Each

homework question will be graded out of 5 points. **No late homework will be
accepted.
All work submitted must be your own. Neatness and and other communication
skills, including spelling, count.** Some homeworks will be dropped to compute
your final

score. There may also be quizzes given.

8. If you are going to miss a test (which will be
announced approximately one week in advance),

you must have a valid, documentable excuse and notify me in advance, or as soon
as

reasonable afterward. The make-up will be as soon as possible, generally within
a week of the

original test date.

9. Final grades will be determined from 450 points, broken
down as follows : 2 exams @ 100

points each, homework/quizzes @ 100 points, comprehensive final exam @ 150
points.

The final scale used will be no higher than A 90-100%, B
80-90%, C 70-80%, D 60-70%, F

0-60%. Plus and minus grades will be given at my discretion.

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