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Mathematical Methods for Engineers (10.539/24.539)
Course Description and Requirements

Course Description
This course highlights several important analytical and computational techniques from the field of applied engineering mathematics. The primary focus is on the solution of ordinary and partial differential equations using both analytical and numerical methods. Selected topics from introductory differential equations and linear algebra are reviewed briefly. General solution methods for IVPs and BVPs are then treated with both analytical methods (where possible) and numerical techniques. Power series solution methods, special functions, orthogonality, the Sturm-Liouville problem, and generalized Fourier series are then discussed as tools for advanced analysis. Analytical solution of PDEs via the separation of variables method and with the use of integral transforms is also treated. Finally, the numerical solution of PDEs via the finite difference method with actual implementation within several Matlab programs is discussed in some detail, along with a brief introduction to finite element methods and the use of COMSOL Multiphysics as a general modeling tool for a variety of applications. The emphasis throughout this course is on the development and application of a variety of mathematical tools for solving practical engineering problems. Considerable computer work -- using the Matlab and COMSOL Multiphysics packages -- is required.

J. R. White, Math Methods Lecture Notes (Fall 2007). This collection of notes, which has evolved from teaching this course over the last several years, contains the primary material for this class. The Lecture Notes are available via the Blackboard Vista course management system at UMass-Lowell. Additional information, however, in the form of a good text on Advanced Engineering Mathematics, is also highly recommended. There are a number of such texts to choose from, such as (any book similar to these will be sufficient):

E. Kreyszig, Advanced Engineering Mathematics, 8th Edition, John Wiley & Sons (1999).

A. Jeffery, Advanced Engineering Mathematics, Harcourt/Academic Press (2002).

M. D. Greenberg, Advanced Engineering Mathematics, 2nd Edition, Prentice Hall (1998).

D. G. Zill and M. R. Cullen, Advanced Engineering Mathematics, 2nd Edition, Jones and Bartlett Publishers (2000).

M. R. Spiegel, Schaum's Outline -Theory and Problems of Advanced Mathematics for Engineers and Scientists, McGraw-Hill (1971).

In addition to a good mathematics reference book, it is also highly recommended as a good investment that you purchase a personal version of Matlab (see below), if you have your own computer! Note that this is not an absolute requirement since Matlab is available in the Department Computer Lab. Note also that FEMLAB will be available in the computer lab.

Matlab & Simulink Student Version , The Mathworks, Inc..

Course Website

Course Requirements
Exams for this course include a mid-term and a comprehensive final. The midterm exam (2 hours) will occur around week 7 or 8 of the semester. A specific date for the midterm exam will be announced a minimum of one week before the exam. The comprehensive final exam (3 hours) will occur during Finals Week as formally scheduled by the Registrar. There will be no makeup exams.

Homework and projects are also assigned and collected on a regular basis. The HWs usually involve a combination of analytical and numerical work. These require neat hand written solutions and a brief informal discussion of the results. There will also be 2 or 3 projects over the course of the semester, and these require a more formal, typed report with appropriate sections for introductory material, mathematical modeling, solution methodology, and the results and conclusions of your analyses. These are expected to be professional documents! The Matlab package will be used in most of these assignments and the use of COMSOL Multiphysics may be required for selected projects. The homework exercises and projects are an important part of this course, and they represent a significant part of the overall course evaluation (see below)!

Grading Policy
The final grade for this course will be determined as follows:

Midterm Exam (2 hrs)
Final Exam (3 hrs)

Course Coordinator
Dr. John R. White
Office: EB302
Phone: 978-934-3165
Fax: 978-934-3047

Note: My office hours for this semester will be posted outside my office during the first week of the semester -- as soon as my schedule becomes finalized.

Last updated by Prof. John R. White (Sept. 2007)

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