Department of Applied Mathematics & Theoretical Physics -- (302) 857-7516 (main), -7517 (fax)

Differential Equations
Math-351 (18220) : MWT, 2:00–2:50 pm, EH 247
[Topics][Daily Schedule][Assignments][Welcome]

Instructor: Tristan Hübsch, ETV 103, (302) 857-6603, thubsch@mac.com, thubsch@desu.edu
Office hours: MW 3:00–6:00 pm

Textbook (required): C. Henry Edwards & David E. Penney, Elementary Differential Equations (5th ed.)

Additional material: Instructor’s handout notes, Cookbook recipes, Homework solution hints, Midterm Solution 

---

Grading recipe (no make-ups are given, except in cases of proven medical emergency):

Component	Time	Remark	% of Grade
Homework	See in daily schedule	Late HW = 0 credit !!!	30%
Mid-Term Exam	October 10, 2007, in-class	comprehensive (§1–2)	30%
Final Exam	As scheduled in the Catalogue	comprehensive (§1–7)	40%

Differential Equations (Math 351) introduces and develops its subject, differential equations, which turn out to provide the fundamental concept used in modeling phenomena in Nature. Applications occur throughout the sciences, both natural and social, but also in practical daily life and business. The emphasis of the course is then divided between the underlying mathematics and the various applications.

“Success = 1% inspiration + 99% perspiration”--T.A. Edison
But, learning is still 100% learning!

§1: Fist Order Differential Equations
§2: Linear Equations of Higher Order
§3: Power Series Methods
§4: Laplace Transform Methods
§5: Linear Systems of Differential Equations
§6: Numerical Methods
§7. Nonlinear Systems and Phenomena

08/29: Introductory Matters
08/31: Differential vs. Algebraic Equations: conceptual introduction & language
09/03:  Labor Day Recess
09/05: ODE & Modeling: §1.1
09/07: General vs. Particular Solutions: §1.2
09/10: Slope Fields & Solution Curves: §1.3
09/12: Separable Equations: §1.4 [HW.1 due]
09/14: Linear, 1st Order ODE: §1.5
09/17: Substitution Methods: §1.6
09/19: Population and Acceleration-Velocity Models: §1.7–8 [HW.2 due]
09/21: Special Classes of 1st Order ODE: extra
09/24: 2nd Order & Linear ODE: §2.1–2
09/26: Homogeneous ODE w/Constant Coefficients: §2.3
09/28: Mechanical Vibrations: §2.4
10/01: Nonhomogeneous Equations & Undetermined Coefficients: §2.5 [HW.3 due]
10/03: Forced Oscillations, Resonance, Electric Circuits: §2.6–7
10/05: Boundary-Values and Eigenvalues: §2.8 [HW.4 due]
10/08: Review
10/10: Mid-Term Exam (1-hour, in class, open text & class notes; §1–2)
10/12: Power Series: §3.1
10/15: Series Solution: §3.2
10/17: Regular Singular Points: §3.3 [HW.5 due]
10/19: Frobenius' Method—The Exceptional Cases: §3.4
10/22: Bessel's Equation and Its Applications: §3.5–6
10/24: Laplace and Inverse Transforms, Initial Values: §4.1–2 [HW.6 due]
10/26: Translation and Partial Fractions: §4.3
10/29: Algebra and Calculus with Transforms & Special Cases: §4.4–5
10/31: Impulses and Delta-Functions: §4.6 [HW.7 due]
11/02: 1st Order Systems, Application and the Method of Elimination: §5.1–2
11/05: Matrices and Linear Systems: §5.3
11/07: Eigenvalue Methods and Homogeneous Systems: §5.4 [HW.8 due]
11/09: 2nd Order Systems and Mechanics: §5.5
11/12: Multiple Eigenvalue Solutions: §5.6
11/14: Matrix Exponentials and Linear Systems, and Nonhomogeneous Linear Systems: §5.7–8 [HW.9 due]
11/16: Numerical Approximation: Euler's Method: §6.1
11/19: More on Euler's Method: §6.2
11/21: The Runge-Kutta and Other Numerical Methods: §6.3–4 [HW.10 due]
11/23: Thanksgivings Recess
11/26: Equilibrium Solutions and Stability: §7.1
11/28: Stability and Phase Space: §7.2 [HW.11 due]
11/30: Linear and Almost Linear Systems, and Ecological Models: §7.3–4
12/03: Nonlinear Systems and Chaos: §7.5–6
12/05: Review [HW.12 due]
12/10-14: Final Exam (as scheduled in the catalogue; 2-hour, in-class, open text & class notes; comprehensive)

Homework assignments

All homework assignments are due in class on the day indicated. Only in case of no attendence in class on the due day should homework be left in the instructor's mailbox in ETV#116. Late homework will not be accepted, except in cases of proven emergency.

Collaboration policy

Collaboration -- but not blind copying -- on the homework assignments is strongly encouraged; students should use this to learn from each other. All exams and quizzes are open text and open class-notes (including notebooks and class handouts), but no collaboration is allowed; by signing the exams and quizzes, the student implicitly agrees to abide by this policy. Violation of this policy is covered under University regulations on academic dishonesty and cheating.

Presentation and organization

While a neat presentation of home,- quiz- and exam-work is not required for full credit, it certainly makes it easier to assess the quality of the work and give the proper credit due. In all cases, include a simple sketch if it might help conveying the approach or the calculations. Where necessary, include all units and symbols such as the measure of an integral, arrow on a vector, vertical bars for the absolute value of a quantity, for the magnitude of a vector or for the determinant of a matrix, etc.

• Homework: Submitted answer sheets should be stapled (preferably in the top-left corner). The Student's full name (and ID number) should be indicated on the first (cover) page. Solutions should be labeled and ordered consecutively by the problem numbers. Include all calculation/work and give full reference to any result quoted from any source other than the text, and page/equation number for results quoted from the text.
• Quizzes: The Student's full name (and ID number) should be indicated on the first (cover) page, unless otherwise requested at the time of the quiz. Include all calculation/work and give the page/equation number for results quoted from the text. Speed and efficiency is important, but the presentation must be legible.
• Mid-term exam(s): All exam questions are given on a question sheet and include the detailed point distribution and the place to write in the Student's full name and ID number. This question sheet is to be stapled on the top of the answer sheets, in the top-left corner. It will be used to indicate the acquired points, part by part and in total, the average score and the standard deviation.
• Final exam: All exam questions are given on a question sheet and include the detailed point distribution and the place to write in the Student's full name and ID number. This question sheet is to be stapled on the top of the answer sheets, in the top-left corner. It will be used to indicate the acquired points, part by part and in total, the average score and the standard deviation. The final exams are stored by the instructor, but are available to the individual student for review after the exam.

© Tristan Hübsch, 2007