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Principles of Applied Mathematics >> Content Detail



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Readings

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Readings are assigned in the following textbooks:



Required


[H1] Amazon logo Haberman, Richard. Applied Partial Differential Equations. 4th ed. Upper Saddle River, NJ: Prentice Hall, March 24, 2003. ISBN: 0130652431.

[H2] Amazon logo ———. Mathematical Models: Mechanical Vibrations, Population Dynamics and Traffic Flow: An Introduction to Applied Mathematics. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1998. ISBN: 0898714087.



For Further Reading


[D] Amazon logo Debnath, Lokenath. Nonlinear Partial Differential Equations for Scientists and Engineers. Boston, MA: Birkhäuser, 1997. ISBN: 0817639020.

[W] Whitham, Gerald Beresford. Linear and Nonlinear Waves. New York, NY: Wiley, 1974.

[B] Amazon logo Barenblatt, Grigory Isaakovich. Scaling, Self-Similarity, and Intermediate Asymptotics. New York, NY: Cambridge University Press, 1996. ISBN: 0521435161 (hardcover), 0521435226 (pbk).

[LS] Amazon logo Lin, Chia-Ch'iao, and L. A. Segel. Mathematics Applied to Deterministic Problems in the Natural Sciences. Material on elasticity by G. H. Handelman. Philadelphia, PA: Society for Industrial and Applied Mathematics, 1988. ISBN: 0898712297.

[C] Amazon logo Crank, John. The Mathematics of Diffusion. 2nd ed. Oxford, UK: Clarendon Press, 1979, c1975, (1986 printing). ISBN: 0198534116. On reserve at the Science Library and math reading room.



Readings by Session



LEC #TOPICSREADINGS
1Introduction: Dense Granular Flow in a Silo.LS, Sections 1.1 and 3.3.
2-3Linear Waves: PDE for Waves in an Elastic Medium, Characteristics, d'Alembert's SolutionH1, Sections 4.2 and 12.2-12.5.
4-13Nonlinear Kinematic Waves: Lighthill-Whitham Theory of Traffic Flow, Density Waves, General Method of Characteristics, Hodograph Method, Expansion Fans, Wave Breaking, Shocks

River Waves, Gas Compression Waves, Shallow Water Waves
H1, Section 12.6.

H2, pp. 56-86.
14-16Dispersive Waves: Fourier transform, group velocity and caustics

Envelope Equations, KdV Equation, Solitons
H1, Sections 14.2 and 14.6.

H1, Sections 14.7.1-3.
17-18Linear Diffusion: Green function for the Diffusion Equation, Some Fourier Analysis

Similarity Solutions
H1, Section 10.4.
19-25Nonlinear Diffusion: Burgers Equation and Shock Structure, Cole-Hopf Transformation

Porous Medium Equation, Similarity Solution

Regular and Singular Perturbations, Boundary Layers, Matched Asymptotic Expansions

Nernst-Planck Equations
LS, Section 9.

 








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