Mathematics 616 Download Page (Fall 2006)

As of October 20, 2009, large sections of this site are offline.

• Textbooks:

 

Required:

• Logan, J. David. Applied Mathematics, 3rd ed. New York: Wiley, 2006.
• 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: 112K)

• Writing Assignment (size: 68K)

• Handouts

ODE Review (size: 52K)

Fourier Series (size: 56K)

Sine and Cosine Series (size: 64K)

The Error Function (size: 52K)

Fourier and Laplace Series (size: 56K)

Single-Species Evolution Equations (size: 44K)

The Phase Plane (size: 284K)

The Hopf Bifurcation (size: 156K)

Hamiltonian Systems (size: 224K)

Conservative Systems (size: 200K)

Action-Angle Coordinates (size: 392K)

Predator-Prey Systems (size: 336K)

Singularly Perturbed ODEs (size: 32K)

Integration by Parts (size: 44K)

Stationary Phase (size: 44K)


 

Homework Sets

Homework Set 1 (size: 60K) revised 9/11/06, Solution Set (size: 76K)

Dimensional analysis (chapter L1).

Homework Set 2 (size: 38K) revised 9/18/06, Solution Set (size: 64K)

The diffusion equation, general Fourier series (sections L4.1, L6.2, W13-16, G1.3-1.5, G3.1-3.3, G5.1, G5.6, and G7.6).

Homework Set 3 (size: 28K) revised 9/27/06, Solution Set (size: 44K)

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

Homework Set 4 (size: 28K), Solution Set (size: 52K)

The heat equation, the maximum principle, Sturm-Liouville theory (sections L4.2, L6.3, W13, W22, W27, W36, G1.3, G5.1, G5.2, G7.1, G7.6, and G7.10).

Homework Set 5 (size: 32K), Solution Set (size: 54K)

Sturm-Liouville theory, delta and Green's functions, inhomogeneous ODEs (sections L4.2, L4.4, L4.5, W28-30, W36-39, and G7.10).

Homework Set 6 (size: 33K), Solution Set (size: 76K)

Green's functions, The Fredholm alternative, Fourier, sine, cosine, and Laplace transforms, the heat equation (sections L6.4, L6.5, W28, W30, W63, W66-70, W74-W76, G3.4, G3.5, G5.4, G7.6, and G7.7).

Homework Set 7 (size: 28K), Solution Set (size: 117K)

Single-species population dynamics, the phase plane (sections L1.3, 1.4).

Homework Set 8 (size: 24K), Solution Set (size: 1.9M)

Advanced phase plane techniques, polar coordinates (section L1.4).

Homework Set 9 (size: 32K), Solution Set (size: 64K)

Predator-prey models, order estimates, perturbed algebraic equations (sections L1.4 and L2.1).

Homework Set 10 (size: 28K), Solution Set (size: 48K)

Perturbed algebraic and ODEs, integration by parts, (sections L2.1-2.3 and L2.6).

Homework Set 11 (size: 55K), Solution Set (size: 72K)

Watson's Lemma, Laplace's method, stationary phase, Volterra equations (sections L2.6 and L4.3).

Supplemental Study Material (size: 20K), Solution Set (size: 28K)

Fredholm integral equations (sections L4.3, and G7.5-7.9).

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