Mathematics 616 Download Page (Fall 2012)

• 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: 126K)

• Writing Assignment (size: 81K)

• Handouts

ODE Review (size: 143K)


Fourier Series (size: 183K)

Sine and Cosine Series (size: 152K)

The Error Function (size: 178K)

Fourier and Laplace Series (size: 138K)

Single-Species Evolution Equations (size: 145K)

The Phase Plane (size: 370K)

The Hopf Bifurcation (size: 211K)

Hamiltonian Systems (size: 2.4M) revised version posted 11/9/12

Conservative Systems (size: 511K)

Liapunov Functions (size: 1.8M)

Action-Angle Coordinates (size: 515K)

Predator-Prey Systems (size: 499K)

Logistic Map (size: 119K)

Singularly Perturbed ODEs (size: 119K)

 

Homework Sets

Homework Set 1 (size: 117K) revised version posted 9/11/12, Solution Set (size: 132K)

Dimensional analysis and scaling (sections L1.1, L1.2).

Homework Set 2 (size: 125K) revised version posted 9/17/12, Solution Set (size: 155K)

The diffusion equation, separation of variables, orthogonality (sections L4.1, L6.2.3-6.2.5, W13-16, G1.3-1.5, G3.1, G5.1, G5.6, and G7.6).

Homework Set 3 (size: 120K) revised version posted 9/25/12, Solution Set (size: 161K) revised version posted 9/28/12

Fourier series (sections L4.1, W16-19, and G3.1-3.3).

Homework Set 4 (size: 125K), Solution Set (size: 146K)

Even/odd functions, the heat equation, Sturm-Liouville theory (sections L4.1, L4.2, L6.1, L6.2, W13, W20-22, G1.3, G5.1, G5.2, and G7.1).

Homework Set 5 (size: 101K) revised version posted 10/9/12, Solution Set (size: 134K)

Sturm-Liouville theory, delta and Green's functions (sections L4.2, L4.4, L4.5, L5.2, L5.3, W28, W36, G7.2, G7.6, and G7.8-G7.10).

Homework Set 6 (size: 119K), Solution Set (size: 144K)

Green's functions, the Fredholm alternative, Fourier transforms (sections L4.4, L6.5.2, W29, W63, W66-70, G3.4, G3.5, G5.4,
G7.2, and G7.7).

Homework Set 7 (size: 131K), Solution Set (size: 156K)

Laplace transforms, the heat equation, single-species population dynamics (sections L1.3, L6.5.1, and W74--76).

Homework Set 8 (size: 91K) revised version posted 11/12/12, Solution Set (size: 2M)

The phase plane, Liapunov functions (section L1.4).  

Homework Set 9 (size: 126K), Solution Set (size: 148K)

Polar coordinates, predator-prey models, discrete modeling (sections L1.4 and L5.1).  

Supplemental Study Material (size: 114K), Solution Set (size: 138K) revised version posted 12/14/12

Order estimates, perturbed algebraic and ordinary differential equations, Volterra equations (sections L2.1-2.3, L4.3.2, and G7.3).

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