Mathematics 616 Download Page (Fall 2000)

As of May 3, 2004, large sections of this site are offline.

• Textbooks:

 

Required:

• Logan, J. David. Applied Mathematics, 2nd ed. New York: Wiley, 1996.
• Weinberger, Hans F. A First Course in Partial Differential Equations With Complex Variables and Transform Methods. New York: Dover, 1995.
  
 

Recommended:

• Guenther, Ronald B., and Lee, John W. Partial Differential Equations of Mathematical Physics and Integral Equations. New York: Dover, 1996.

 
• Suggestion Box

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• Course Syllabus (size: 12K)

• Writing Assignment (size: 10K)

• Handouts

ODE Review (size: 41K)

Fourier Series (size: 45K)

Sine and Cosine Series (size: 51K)

The Gibbs Phenomenon (size: 36K)

The Error Function (size: 38K)

Fourier and Laplace Series revised version posted 10/19/00 (size: 42K)

Single-Species Evolution Equations (size: 31K)

The Phase Plane (size: 55K)

The Hopf Bifurcation (size: 104K)

Hamiltonian Systems (size: 358K)

Action-Angle Coordinates (size: 215K)

Predator-Prey Systems (size: 53K)

Singularly Perturbed ODEs (size: 30K)

Integration by Parts (size: 39K)

Stationary Phase (size: 39K)


 

Homework Sets

Homework Set 1 (size: 39K) revised version posted 9/1/00, Solution Set (size: 57K)

Dimensional analysis (chapter L1).

Homework Set 2 (size: 45K), Solution Set (size: 75K)

The diffusion equation, general Fourier series (sections L4.2, L4.4, W13-16, G1.3-1.5, G3.1, G5.1).

Homework Set 3 (size: 41K) revised version posted 9/14/00, Solution Set (size: 60K)

Trigonometric Fourier series (sections L4.4, W18-21, G3.1-3.3).

Homework Set 4 (size: 43K) revised version posted 9/22/00, Solution Set (size: 72K)

The maximum principle, Sturm-Liouville theory (sections L4.2, L4.4, W13, W22, W28, W36, G1.3, G5.1, G5.2, G7.1, G7.6, and G7.8-7.10).

Homework Set 5 (size: 25K), Solution Set (size: 70K)

Sturm-Liouville theory, inhomogeneous ODEs (sections L4.4, L5.2, L5.3, W28-30, G7.2, and G7.6-7.10).

Homework Set 6 (size: 37K), Solution Set (size: 59K)

The Fredholm alternative, Fourier, sine, cosine, and Laplace transforms (sections L4.5, W63, W66-70, W74, W75, G3.4, and G3.5).

Homework Set 7 (size: 40K) revised version posted 10/19/00, Solution Set (size: 69K)

The heat equation, single-species population dynamics, the phase plane (sections L4.5, L7.1-3, and W74-76).

Homework Set 8 (size: 32K), Solution Set (size: 180K)

Advanced phase plane techniques, polar coordinates (sections L7.1-3).

Homework Set 9 (size: 49K) revised version posted 11/16/00, Solution Set (size: 71K)

Predator-prey models, order estimates, perturbed algebraic equations (sections L2.1, L2.2, and L7.3).

Homework Set 10 (size: 51K) revised version posted 11/30/00, Solution Set (size: 70K)

Perturbed ODEs, integration by parts, Watson's Lemma (sections L2.1, L2.2, and L2.6).

Supplemental Study Material (size: 48K), Solution Set (size: 52K)

Laplace's method, stationary phase, Volterra equations (sections L2.6, L5.1, and G7.3).

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