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University of North Carolina

Math 524
Elementary Differential Equations

Fall 2008



The photo above is of Swiss currency featuring L. Euler.  See http://jeff560.tripod.com/


Schedule / Assignments:

Note:  All assignments are due at the beginning of class (8:00am) on the specified day.  The section numbers, page numbers, and problem numbers correspond to those in the 4th edition of the textbook.

Please show all of your work.  A correct answer without proper supporting work is worth zero credit.

[8/19/08]

Euler's method (2.4), Improvement to Euler (2.5), Runge-Kutta method (2.6)
[8/21/08]

Laplace transforms (7.1)

Assignment 1:  Section 2.4 (p. 121-122) #6; Section 2.5 (p. 132-133) # 10; Section 7.1 (p. 450-451) #6
Solutions
[8/26/08]

Application of Laplace transform to initial value problems (7.2), Review of partial fractions (7.3)

Assignment 2:  Section 7.1 (p. 450-451) #39; Section 7.2 (p. 462-463) #4, 27
Solutions
[8/28/08]

Assignment 1 due

Application of Laplace transform to initial value problems (7.2), Translation (7.3)

Assignment 3:  Section 7.2 (p. 462-463) #34; Section 7.3 (p. 472) #26, 38
Solutions
[9/2/08]

Assignment 2 due

Periodic and Piecewise Continuous Input Functions (7.5), Impulses and Delta Functions (7.6)

Assignment 4:  Section 7.5 (p. 491-492) #18, 29, 34
Solutions
[9/4/08]

Assignment 3 due

Impulses and Delta Functions (7.6),  Derivatives, Integrals, Convolutions (7.4)

Assignment 5:  Section 7.6 (p. 502-503) #7, 15; Section 7.4 (p. 481-482) #24
Solutions
[9/9/08]

Assignment 4 due

Derivatives, Integrals, Convolutions (7.4), Introduction and Review of Power Series (8.1)

Assignment 6:  Section 7.4 (p. 481-482) #26, 31, 39
Solutions
[9/11/08]

Assignment 5 due

Review of Power Series (8.1), Series Solutions Near Ordinary Poitns (8.2)

Assignment 7:  Section 8.1 (p. 516-517)  #14, 16, 24
Solutions
[9/16/08]

Assignment 6 due

Series Solutions Near Ordinary Poitns (8.2)

Assignment 8:  Section 8.1 (p. 516-517)  #25; Section 8.2 (p. 526-528) #14, 29
Solutions
[9/18/08]

Assignment 7 due

Regular Singular Points (8.3), Euler equations

No assignment due to the exam in one week
[9/23/08]

Assignment 8 due

Review, Euler equations, Regular singular points (8.3)

Assignment 9:  Section 3.1 (p. 158-160) #51, Section 3.3 (p. 183-184) # 51, Section 8.3 (p. 543-544) #14
Solutions
[9/25/08]

Exam 1
- No assignment to be collected due to the exam
[9/30/08]

Assignment 9 due

Regular singular points (8.3)

Assignment 10: Section 8.3 (p. 543-544) #20, 24, 34
Solutions
[10/2/08]

No assignment to be collected due to the exam

Regular singular points (8.3), The exceptional cases (8.4)

Assignment 11: 
Section 8.3 (p. 543-544) #31, 39, 41
Solutions
[10/7/08]

Assignment 10 due

The exceptional cases (8.4)

Assignment 12: 
Section 8.4 (p. 559-561) #10, 13, 16
Solutions
[10/9/08]

Assignment 11 due

The exceptional cases (8.4), Legendre equation (8.2)

Assignment 13 (due 10/21): 
Section 8.4 (p. 559-561) #15, Section 8.2 (p. 526-528) #32, 33
Solutions
[10/14/08]

Assignment 12 due

Legendre equation (8.2), Bessel functions (8.5)

Assignment 14 (due 10/23): 
Section 8.5 (p. 570-571) #2, 4, 26 (skip the graph, just look at the graph in the solutions)
Solutions
[10/16/08]

Fall Break - No class
[10/21/08]

Assignment 13 due

First order linear systems (5.2)

Assignment 15:  Section 5.2 (p. 316-317) #6 (solution only), 18, 32 (no graph is needed)
Solutions
[10/23/08]

Assignment 14 due

First order linear systems - complex eigenvalues (5.2)

Assignment 16:  Section 5.2 (p. 316-317) #24, 26, 40
Solutions
[10/28/08]

Assignment 15 due

First order linear systems - repeated eigenvalues (5.4)

Assignment 17: Section 5.4 
(p. 345-347) # 8, 20, 22
Solutions
[10/30/08]

Assignment 16 due

Nonlinear systems, the phase plane, and stability (6.1)

No assignment due to the exam in one week

[11/4/08]

Assignment 17 due

Review for exam, The phase plane and classifying linear system behavior (6.1, 6.2)

Assignment 18:  Section 6.1 (p. 381-383)  18 (you can sketch the graphs by hand), 27, 28
Solutions
[11/6/08]

Exam 2 - No assignment to be collected due to the exam
[11/11/08]

Assignment 18 due

Classifying linear system behavior (6.2)

No assignment due to instructor error - the updated webpage failed to upload
[11/13/08]

No assignment to be collected due to the exam

Classifying linear system behavior and almost linear systems (6.2)

Assignment 19:  Section 6.1 (p. 381-383) 22; Section 6.2 (p. 395-397) # 5, 10 (hand sketches for the graphs)
Solutions
[11/18/08]

No assignment due to instructor error - the updated webpage failed to upload

Euler-like systems, Laplace transform on systems, Fourier series (9.1, 9.3)

Assignment 20:  S
ection 6.2 (p. 395-397): #30,32 (hand sketches for the graphs); Section 9.1 (p. 588) #24
Solutions

[11/20/08]

Assignment 19 due

Fourier series (9.1, 9.2, 9.3), Separation of variables applied to the heat equation (9.5)

No assignment due to Thanksgiving
[11/25/08]

Assignment 20 due

Separation of variables applied to the heat equation (9.5), Laplace's equation in polar coodinates (9.7)

Assignment 21:  Section 9.2 (p. 594-595) #15; Section 9.5 (p. 626-628) #8, 20
[11/27/08]

Thanksgiving  -- no class
[12/2/08]

Assignment 21 due

Last lecture
- Review, Another example of solving a heat equation with separation of variables (9.5)
Saturday [12/6/08]

Final Exam - 8:00-11:00am

Other dates of interest:

10/16-10/17/08    - Fall break (no classes)
11/26-11/28/08    - Thanksgiving recess (no classes)

10/13/08        - Last Day to Drop
12/3/08      - Last day of lectures

9/25/08, 11/6/08 - Midterm exams
12/6/08       -
Final Exam, 8:00-11:00 am

Academic Calendar

Honor code:

The honor code will be strictly enforced on all assignments.   Acceptable collaboration on homework is limited to discussion among peers after which each individual must complete his or her assignment on his or her own.  I.e., when you are writing up your solutions, you should not be looking at any notes developed in discussion of the problems with another student.  Suspiciously similar assignments will be considered in violation of the honor code and treated accordingly.