MATH 616 Download Page

• Textbook:

Logan, J. David. Applied Mathematics, 4th ed. New York: Wiley, 2013.

• Suggestion Box

• Course Syllabus (size: 146K) revised 9/1/23
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• Writing Assignment (size: 102K) revised 9/1/23
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• Outline Assignment (size: not yet posted)
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• References

Failure of Radioactive Waste Tanks

Web-Based Tool for Plotting Phase Planes (Cartesian and Polar)

Geogebra Web-Based Tool for Plotting Phase Planes

Flipping a Coin Deterministically

Mathematica Notebook with Useful Commands (size: 17K)

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• Handouts

Review (size: 315K)	Logistic Map (size: not yet posted)
Single-Species Evolution Equations (size: 195K)	Algebraic Discrete Model (size: not yet posted)
Bifurcations (size: 441K)	Exponential Discrete Model (size: not yet posted)
The Phase Plane (size: 470K)	2-D Discrete Systems (size: not yet posted)
The Hopf Bifurcation (size: 300K)	Nicholson-Bailey Model (size: not yet posted)
Action-Angle Coordinates (size: 725K)	Beddington Model (size: not yet posted)
Hamiltonian Systems (size: 2.4M)	The Stefan Problem (size: not yet posted)
Conservative Systems (size: 702K)	Linear 1st Order Equations (size: not yet posted)
Liapunov Functions (size: 1.8M)	Quasilinear Equations (size: not yet posted)
Lotka-Volterra Model (size: 282K)	Envelopes (size: not yet posted)
Other Predator-Prey Models (size: not yet posted)	Shocks (size: not yet posted)
Epidemics (size: not yet posted)	Conservation of Momentum (size: not yet posted)
Traveling Waves (size: not yet posted)	The Navier-Stokes Equations (size: not yet posted)
Fisher’s Equation (size: not yet posted)	Singularly Perturbed ODEs (size: not yet posted)

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• Homework Sets

Homework Set 1 (size: 160K) revised 9/5/23, Solution Set (size: 181K)

Dimensional analysis and scaling (sections 1.1, 1.2).

Homework Set 2 (size: 148K), Solution Set (size: 192K)

Single-species population dynamics, bifurcations (section 1.3).

Homework Set 3 (size: 137K) revised version posted 9/22/23, Solution Set (size: not yet posted)

The phase plane (section 2.1-2.4).

Homework Set 4 (size: 116K), Solution Set (size: not yet posted)

Advanced phase-plane techniques, predator-prey models (section 2.3).

Homework Set 5 (size: not yet posted), Solution Set (size: not yet posted)

Epidemics, the diffusion equation (sections 2.6.3, 6.2.1, 6.2.3, 6.2.4).

Homework Set 6 (size: not yet posted), Solution Set (size: not yet posted)

The diffusion equation, traveling waves, Fisher’s equation, spatial epidemics (sections 6.2.1, 6.2.3, 7.2.2).
The diffusion equation, the Stefan problem, traveling waves, spatial epidemics, linear first-order PDEs (sections 7.1, 7.2.2).

Homework Set 7 (size: not yet posted), Solution Set (size: not yet posted)

Discrete modeling in 1- and 2-D, the Stefan problem (sections 9.1, 9.2).

Homework Set 8 (size: not yet posted), Solution Set (size: not yet posted)

First-order PDEs (sections 7.1–7.3).

Homework Set 9 (size: not yet posted), Solution Set (size: not yet posted)

Shocks, the wave equation, conservation of mass (sections 7.1–7.4.2, 8.1).

Homework Set 10 (size: not yet posted), Solution Set (size: not yet posted)

Conservation of momentum, unidirectional flows, Volterra equations (sections 5.4-5.4.1, 8.4).

Supplemental Study Material (size: not yet posted), Solution Set (size: not yet posted)

Perturbation methods (sections 3.1-3.3).

Return to the syllabi download page.