MATH/MAPL 472/698B: Methods and Models in Applied Mathematics

Administrative

Lecture: TuTh 11:00-12:15pm, JMP 1109


Instructor: J.H. Maddocks, jhm@ipst.umd.edu


Assistant: O. Gonzalez, gonzalez@ipst.umd.edu


Matlab: The matrix computation package Matlab will be used in this course. For information on using this program in the WAM and GLUE Computer Labs at UMCP see the Matlab Fact Sheet.

Course Materials

Texts

J.D. Logan (1987) Applied Mathematics: A Contemporary Approach, John Wiley & Sons, New York.


C.C. Lin & L.A. Segel (1988) Mathematics Applied to Deterministic Problems in the Natural Sciences, SIAM Publishing, Philadelphia.


Supplement

J.J. Stoker (1950) Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience Publishers, New York.

Topics

This course is the first in a two semester introduction to the derivation, solution and interpretation of the classic differential equations of applied mathematics. The first semester is primarily concerned with problems involving ordinary differential equations. The second semester is primarily concerned with partial differential equations. The basic topics to be covered in the first semester include
What is Applied Mathematics?

Philosophy and goals
The four stages of modelling


Dimensional Analysis & Scaling

Nondimensionalization and scaling
The Pi-Buckingham theorem and elementary applications
Examples and pitfalls in approximation


Finite-Dimensional Mechanics

Ordinary differential equations in mechanics
Derivation of planar pendulum equations
Regular perturbation and the Poincare-Lindstedt method
Phase-plane techniques
Stability of equilibria and Lyapunov techniques
Parametric resonance and forced mechanical systems


The Calculus of Variations

Elements of the 1-D calculus of variations
Static equations of rods as Euler-Lagrange equations
The principle of least action in dynamics
Isoperimetric Problems


Eigenvalue Problems and Buckling


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