Mathematics 616 Download Page (Fall 1999)

• 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

As of March 6, 2000, large portions of this site have been taken offline.

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• Course Syllabus (size: 11K)

• Writing Assignment (size: 9K)


• Handouts

Fourier Series (size: 46K)
Sine and Cosine Series (size: 51K)
ODE Review (size: 41K)
The Error Function (size: 38K)
Single-Species Evolution Equations (size: 31K)
The Phase Plane (size: 55K)
The Hopf Bifurcation (size: 104K)
Hamiltonian Systems (size: 359K)
Action-Angle Coordinates (size: 215K)
Predator-Prey Systems (size: 54K)
Singularly Perturbed ODEs (size: 20K)
Integration by Parts (size: 29K)
 

Homework Sets

Homework Set 1 (size: 38K), Solution Set (size: 61K)

Dimensional analysis (chapter L1).

Homework Set 2 (size: 46K) revised version posted 9/18/99, Solution Set (size: 75K)

The diffusion equation, general Fourier series (sections L4.4, W13-16, G1.3-1.5, G3.1-3.3, G5.1).

Homework Set 3 (size: 34K) revised version posted 9/23/99, Solution Set (size: 49K ) revised version posted 10/14/99

Trigonometric Fourier series (sections L4.2, W18-21, G3.1-3.3).

Homework Set 4 (size: 36K) revised version posted 9/30/99, Solution Set (size: 65K)

The maximum principle, Sturm-Liouville theory (sections L4.2, L4.4, W13, W22, W27, W36, G1.3, G5.1, G5.2, G7.1, G7.6, and G7.8-7.10).

Homework Set 5 (size: 34K) revised version posted 10/19/99, Solution Set (size: 58K )

Inhomogeneous ODEs, the Fredholm alternative, Fourier transforms (sections L4.4, L4.5, L5.2, L5.3, W28-30, W63, W66-70, G3.4, G3.5, G7.2, and G7.6-7.10).

Homework Set 6 (size: 42K), Solution Set (size: 62K)

Sine, cosine, and Laplace transforms, especially as applied to the heat equation (sections L4.2, L4.5, W28-30, W68-70, W74-76, G3.4, G3.5, and G5.4).

Homework Set 7 (size: 33K) revised version posted 11/2/99, Solution Set (size: 85K)

Population dynamics, the phase plane (sections L7.1, L7.2).

Homework Set 8 (size: 38K), Solution Set (size: 124K)

Hamiltonian systems, polar coordinates, predator-prey models (sections L7.1, L7.2).

Homework Set 9 (size: 34K) revised version posted 11/15/99, Solution Set (size: 64K) revised version posted 11/22/99

Order estimates, asymptotic root finding, regularly perturbed ODEs (sections L2.1, L2.2).

Homework Set 10 (size: 33K) revised version posted 11/23/99, Solution Set (size: 53K)

Singularly perturbed ODEs, integration by parts, Watson's Lemma (sections L2.2, L2.6).

Homework Set 11 (size: 46K) revised version posted 12/7/99, Solution Set (size: 65K)

Watson's Lemma, Laplace's method, method of stationary phase, Volterra integral equations (sections L2.6, L5.1, G7.3).

Supplemental Study Material (size: 27K) revised version posted 12/14/99, Solution Set (size: 45K) revised version posted 12/14/99

Fredholm integral equations.

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