
ENGS/PHYS
100
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2009 Schedule
Thayer
School
of
Engineering
Dartmouth
College 

Methods in Applied
Mathematics I
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 .
MWF at 11:1512:20, plus Tuesday (Xhour) from
12:0012:50. The xhour will be used occasionally.
Mathematical Methods for Physics and Engineering, Third Edition Set
Authors: K.F. Riley, M.P. Hobson and S.J. Bence
ISBN13: 9780521679718  ISBN10:
0521679710
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.
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".
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.
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. 


