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Mathematical physics: applied mathematics for scientists and engineers
- Date_TXT
- Allemagne: WILEY-VCH Verlag GmbH & Co. KGaA, 2006
- Auteur
- Kusse, Bruce R., Westwig Erik A
- Type de document
- Livre
Description :
This book is the result of a sequence of two courses given in the School of Applied
and Engineering Physics at Cornell University. The intent of these courses has been
to cover a number of intermediate and advanced topics in applied mathematics that
are needed by science and engineering majors. The courses were originally designed
for junior level undergraduates enrolled in Applied Physics, but over the years they
have attracted students from the other engineering departments, as well as physics,
chemistry, astronomy and biophysics students. Course enrollment has also expanded
to include freshman and sophomores with advanced placement and graduate students
whose math background has needed some reinforcement.While teaching this course,
we discovered a gap in the available textbooks we felt
appropriate for Applied Physics undergraduates. There are many good introductory
calculus books. One such example is Calculus andAnalytic Geometry by Thomas and
Finney, which we consider to be a prerequisite for our book. There are also many good
textbooks covering advanced topics in mathematical physics such as Mathematical
Methods for Physicists by Arfken. Unfortunately, these advanced books are generally
aimed at graduate students and do not work well for junior level undergraduates. It
appeared that there was no intermediate book which could help the typical student
make the transition between these two levels. Our goal was to create a book to fill
this need.The material we cover includes intermediate topics in linear algebra, tensors,
curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace
transforms, differential equations, Dirac delta-functions, and solutions to Laplace’s
equation. In addition, we introduce the more advanced topics of contravariance and
covariance in nonorthogonal systems, multi-valued complex functions described with
branch cuts and Riemann sheets, the method of steepest descent, and group theory.
These topics are presented in a unique way, with a generous use of illustrations