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]
Grading recipe (no make-ups are given, except in cases of proven medical emergency):
Component |
Time |
Remark |
% of Grade |
---|---|---|---|
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)
WH# | Due Date | Problems |
1 | 09/12/07 | §1.1: 7, 28, 35, 45; §1.2: 7, 15, 23, 44; |
2 | 09/19/07 | §1.3: 16, 30; §1.4: 26, 42; §1.5: 14, 31; §1.6: 25, 54; |
3 | 09/26/07 | §1.7: 7, 11, 32; §1.8: 25, 30; §2.1: 6, 32, 51; |
4 | 10/03/07 | §2.2: 10, 29, 39; §2.3: 21, 35, 49, 52; §2.4: 10, 15, 22; |
5 | 10/17/07 | §2.5: 10, 39, 59; §2.6: 4, 19, 26, 28; §2.7: 7, 17, 23; |
6 | 10/24/07 | §3.1: 7, 23; §3.2: 7, 24; §3.3: 23, 41; §3.4: 16; §3.5: 11; |
7 | 10/31/07 | §3.6: 15; §4.1: 17, 39; §4.2: 10, 27, 36; §4.3: 6, 23; |
8 | 11/07/07 | §4.4: 11, 38; §4.5: 16, 26; §4.6: 11, 18; §5.1: 9, 24; |
9 | 11/14/07 | §5.2: 7, 26; §5.3: 17, 27; §5.4: 26, 38; §5.5: 14, 21; |
10 | 11/21/07 | §5.6: 1, 33; §5.7: 1, 27; §5.8: 5, 17; §6.1: 1, 9; |
11 | 11/28/07 | §6.2: 1, 5, 10; §6.3: 1, 5, 10; §6.4: 1, 4, 8; |
12 | 12/05/07 | §7.1: 1, 10; §7.2: 1, 8; §7.3: 5, 15; §7.4: 1, 11; |
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.
© Tristan Hübsch, 2007