MTHSC 208, Spring 2009
MTHSC 208, Spring 2009
"You see this little hole? This moth's just about to emerge. It's in
there right now, struggling. It's digging it's way through the thick
hide of the cocoon. Now, I could help it - take my knife, gently widen
the opening, and the moth would be free - but it would be too weak to
survive. Struggle is nature's way of strengthening it."
--Locke (Lost, 2004)
Instructor: Dr. Matthew
Macauley
Class: Introduction to Ordinary Differential Equations
Course Syllabus
Homework
Homework 1: Section 2.1: #6, 7, 17, 20. Section 2.2: #1-3, 13-15, 25,
26, 33, 34. [scanned
copy]. Due Wednesday, January 14th 2009 at 4pm.
Homework 2: Due Tuesday, January 20th at 4:00 pm. Section 2.1:
#31. Section 2.2: #16-20, 35. Section 2.3: #3, 4, 8, 10, 18, 19. For
#31, use the isoclines method to plot the curves (not in the book; see
in-class notes).
Homework 3: Section 2.4: #1, 2, 4, 6, 14-16, 18-21, 29. Additionally, use the
isocline method to sketch the slope fields for #1, 2, and 4. Due
Friday, January 23rd at 4pm.
Homework 4: Section 2.4: #36-44. Section 2.5: #1-4. Due Tuesday,
January 27th at 4pm.
Homework 5. Due
Friday, January 30th at 4pm.
Homework 6: Section 3.3: #1, 2. Section 6.1: #1, 2, 6, 7. Section 4.1:
#1-8. For #6-7 in 6.1, use ONLY step-size h=0.2. Due Monday, February
2nd at 4pm.
Homework 7: Section 2.2: #27, 34. Section 2.3: #4. Section 2.4: #17,
33, 34 (Also, sketch the slope field using isoclines for 33 & 34).
Section 2.5: #5. Section 2.9: #18, 31 (For 31, ``qualitative analysis''
means ``don't actually do the math!''). Section 3.1: #10. Section 6.1:
#3. Due Thursday, February 5th at 4pm.
Homework 8: Section 4.1 #17-18, 26, 28, 30. Section 4.2 #1-4. Section
4.3 #1, 2, 9, 10, 17, 18. Due Monday, February 9th at 4pm.
Homework 9: Section 4.3 #25, 26, 29, 30, 33, 34. Section 4.4: #1, 2, 7, 8.
Section 4.5: #9, 18, 22, 23. Due Friday February 13th at 4pm.
Homework 10: Section 4.5: #20, 24, 31, 32, 38, 39, 41, 44. Section
4.7: #2, 4, 6, 7. Due Monday, February 16th at 4pm.
Homework 11: Section 5.1. #2, 4, 6, 8, 10 (compute the integrals on these)
#15, 17, 19, 21, 23 (use the table to compute these)
#26, 28, 29. Due Friday, February 20th at 4pm.
Homework 12: Section 5.2 #22, 24, 34, 36, 38, 40. Section 5.3 #2-5, 8,
16, 22, 36. Section 5.4 #10, 12. Due Tuesday February 24th at 4pm.
Homework 13: Section 5.4 #2, 6, 28. Section 5.5 #1-3, 10-12. Due
Friday 27th at 4pm.
Homework 14: Section 5.4 #20. Section 5.5 #4-6, 9, 13, 16,
18, 20. Section 5.6 #4, 6, 9-11. Due Monday, March 2nd at 4pm.
Homework 15. Due
Wednesday, March 11th at 4pm.
Homework 16. Due
Monday, March 23rd at 4pm.
Homework 17. Due
Friday, March 27th at 4pm.
Homework 18. Due
Monday, March 30th at 4pm.
Homework 19. Due
Friday, April 3rd at 4pm.
Homework 20. Due
Monday, April 6th at 4pm.
Homework 21. Due
Friday, April 10th at 4pm.
Homework 22. Due
Wednesday, April 15th at 4pm.
Homework 23. Due
Monday, April 20th at 4pm.
Homework 24. Due
Friday, April 24th at 4pm.
Class lecture notes
Week 1:
Exponential growth and decay problems. Heating a cooling
problems. Solving 1st order ODEs by separation of varibles. (Sections
2.1, 2.2, 3.3).
Week 2:
Falling objects, with & without air resistance. Solving linear
equations by integrating factor. Plotting direction fields using
isoclines. (Sections 2.3, 2.4 & supplemental material).
Week
3: Solving linear equations by variation of
parameters. Connections between solutions of 1st order linear ODEs and
parametrized lines (homogeneous and particular solutions). Mixing
problems. Plotting autonomous ODEs. (Sections 2.3, 2.4, 2.9, &
supplemenetal material).
Week 4:
Logistic equation. Autonomous equations. Euler's method. Intro to 2nd
order ODEs. (Sections 2.9, 3.1, 4.1, 6.1).
Week 5:
Solving basic 2nd order ODEs (homogeneous, constant
coefficients). Euler's equation. Writing higher-order ODEs as a system
of 1st order ODEs. [Midterm 1] (Sections 4.1, 4.2, 4.3, 4.4).
Week 6:
Harmonic motion. Solving 2nd order linear inhomogeneous ODEs using the
method of undetermined coefficients. Forced harmonic motion. (Sections
4.4, 4.5, 4.7).
Week 7:
Laplace and inverse Laplace transforms. Using them to solve
ODEs. (Sections 5.1, 5.2, 5.3, 5.4).
Week 8:
Using the Heavyside function to express piecewise
continuous functions, and solving ODEs with discontinuous forcing
terms. Delta functions. Summary of Chapter 9 -- systems of linear
ODEs. (Sections 5.4, 5.5, 5.6).
Week 9:
Cauchy-Euler equations. Basic power series. Radius of
convergence. Solving ODEs using power series. (Sections 11.1, 11.2,
supplemental material).
Week 10:
Power series. Radius of convergence. Ratio test and comparison test
for convergence. [Midterm 2]
Week 11:
Ordinary and singular points of ODEs. Generalized power series and the
method of Frobenius. Basic linear algebra -- vector spaces, bases, and
connections to homogeneous ODEs. (Sections 11.3, 11.4, 11.5, and
supplemental material).
Week
12: Inner products on vector spaces. Fourier series --
derivation and computation (Sections 12.1, 12.3, 12.4, and
supplemental material).
Week
13: Complex Fourier series. Introduction to Partial
Differential equations (PDEs). Solving the heat equation. (Sections
12.4, 13.1, 13.2).
Week
14: Analysis of boundary and initial conditions for the heat
equation. The wave equation. Introduction to PDEs in higher
dimensions. Harmonic functions and Laplace's equation. (Sections 13.2,
13.3, 13.4).
Week
15: Solving the 2D Laplace's equation, heat equation, and wave
equation. Special topics: (1) How Laplace transforms can be used to
solve PDEs, (2) Fourier transforms - an extension of Fourier series,
and how they can be used to solve PDEs, (3) Wavelets - a sometimes
better alternative to Fourier series. (Sections 13.4, 13.9).