Engineering Sciences 100 / Physics 100 |
Methods in Applied Mathematics I
Overview
Concepts and methods used in the treatment of linear equations with emphasis on matrix operations, differential equations, and eigenvalue problems will be developed following a brief review of analytic function theory. Topics include the Fourier integral, finite and infinite dimensional vector spaces, boundary value problems, eigenfunction expansions, Green's functions, transform techniques for partial differential equations, and series solution of ordinary differential equations. Properties and uses of orthogonal polynomials and special functions such as the hypergeometric, Bessel, Legendre, and gamma functions are included. Applications in engineering and physics are emphasized.
Prerequisite: Either ENGS 92 or MATH 33 or MATH 43 with permission of instructor, or equivalent .
Instructor
| |
| ||||||||||||||||
Classes
MWF at 11:15-12:20, plus Tuesday (X-hour) from 12:00-12:50. The x-hour will be used occasionally.
Textbook
Mathematical Methods for Physics and Engineering, Third Edition Set
Authors: K.F. Riley, M.P. Hobson and S.J. Bence
ISBN-13: 9780521683395 | ISBN-10: 0521683394
Published by Cambridge University Press, 2006
The set includes a Textbook and a Student Solutions Manual. It is
Available in both print and pdf (ebook) forms.
Evaluation
The course grade is based on performance on homework and examinations with the following weights:
|
Weekly Homework |
50% |
|
Midterm Exam |
25% |
|
Final Exam |
25% |
Additional information about the course objectives can be found in the circular "ENGS/PHYS 100: Objectives and Expectations".
Blackboard
More information about this course, including lecture notes, handouts, and links to useful information, is available at the ENGS/PHYS 100 Blackboard site. You can login to Blackboard using your DND username and password. If you have registered for ENGS 100 or PHYS 100, you will see a link in your "My Courses" list.
References
Many excellent books have been written on the various aspects of applied mathematics you will study in the course. A few of my favorites are listed below. You will find these and many others at the Dartmouth library.
 |
Arfken and Weber, "Mathematical Methods for Physicists, 6th ed.", 2005 | A commonly used alternative to the textbook for this course and the textbook used for the Fall 2007 course. |
 |
Greenberg, "Foundations of Applied Mathematics", 1978 |
Very readable, at the same level as the textbook. "Teaches rather than preaches." Out of print but available in the library. |
 |
Hildebrand, "Methods of Applied Mathematics", 1992 | Hildebrand's classic textbook, "targeted to engineers and physicists." The first chapter is an excellent development of linear vector spaces. Available at the library and from Dover Books. |
 |
Dennery and Krzywicki, "Mathematics for Physicists", 1967 | "Seamless, wonderfully consistent." Available as a Dover book or at the library. |
 |
Brown and Churchill, "Complex Variables and Applications", 2009 | Probably the most commonly used textbook on the subject, to be released as the 8th edition. Previous editions can be found in library. |
 |
Carrier, Krook and Carson, "Functions of a Complex Variable: Theory and Technique", 2005 | A classic text on the subject, now rereleased by SIAM. |
 |
Hochstadt, "Differential Equations: A Modern Approach", 1964 | Key aspects of linear vector spaces and the theory of differential equations are developed. Out of print but available in the library. |
 |
Byron and Fuller, Mathematics of Classical and Quantum Physics", 1992 | Will appeal to the theoretical physicists among you. The basic mathematical structures of theoretical physics are introduced: mainly Quantum Mechanics, Electromagnetic Theory, And Classical Mechanics. |
 |
Abramowitz and Stegun, "AMS55: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables", 1965 | Still the most comprehensive reference for mathematical functions, now available as a Dover book and free online. |
|
|
||
