CATALOG DATA:
Multidimensional calculus, linear analysis, linear operators, vector algebra, ordinary differential equations.

TEXTBOOKS:
M. Sen and J.M. Powers, 2004, Lecture Notes on Mathematical Methods. (required)
W. Kaplan, 2003, Advanced Calculus, Addison-Wesley (required)
E. J. Hinch, 1991, Peturbation Methods, Cambridge (recommended)
B. Friedman, 1990, Principles and Techniques of Applied Mathematics, Dover (recommended)
P.G. Drazin, 1992, Nonlinear Systems, Cambridge (recommended)

GOALS:
This entry-level graduate course provides the advanced undergraduate with foundational tools necessary for the mathematical characterization of a wide variety of physical systems. Such tools are often necessary in order to understand the key scientific first principles of engineering in areas as disparate as optimization, control, continuum mechanics, kinematics, fluid and solid mechanics, and a host of other subjects. In addition, core mathematics which lie at the heart of modern computational techniques is exposed; the successful student gains experience with software tools for symbolic manipulation, solution of ordinary differential equations, and for generating a variety of plots. Written communication skills are nurtured through the assignment of short assignments which may involve a review of the applied mathematics literature.

PREREQUISITES:
Formally none, knowledge of undergraduate calculus through differential equations.

Topics:

• Mulit-variable calculus
• First-order differential equations
• Linear differential equations
• Series solution methods
• Special functions
• Vectors and tensors
• Linear analysis
• Linear algebra
• Dynamical systems

ABET category content as estimated by faculty member who prepared the course description:
Engineering Science: 3 credits or 100%
Engineering Design: 0 credits

Prepared by: Professor Joseph Powers
Last Update: May 19, 2004

 

Direct comments, questions, and corrections to amedept@nd.edu