Methods for Engineers (10.539/24.539)
Course Description and Requirements
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
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,
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)!
The final grade for this course will be determined as follows: