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This book is primarily about the principles that one uses to solve
problems in applied mathematics. It is written for beginning
graduate students in applied mathematics, science, and engineering,
and is appropriate as a one-year course in applied mathematical
techniques.
This book is written for beginning graduate students in applied
mathematics, science, and engineering, and is appropriate as a
one-year course in applied mathematical techniques (although I have
never been able to cover all of this material in one year). We
assume that the students have studied at an introductory
undergraduate level material on linear algebra, ordinary and
partial differential equations, and complex variables. The emphasis
of the book is a working, systematic understanding of classical
techniques in a modern context. Along the way, students are exposed
to models from a variety of disciplines. It is hoped that this
course will prepare students for further study of modern techniques
and in-depth modeling in their own specific discipline.
"Principles of Applied Mathematics" provides a comprehensive look
at how classical methods are used in many fields and contexts.
Updated to reflect developments of the last twenty years, it shows
how two areas of classical applied mathematics--spectral theory of
operators and asymptotic analysis--are useful for solving a wide
range of applied science problems. Topics such as asymptotic
expansions, inverse scattering theory, and perturbation methods are
combined in a unified way with classical theory of linear
operators. Several new topics, including wavelength analysis,
multigrid methods, and homogenization theory, are blended into this
mix to amplify this theme.This book is ideal as a survey course for
graduate students in applied mathematics and theoretically oriented
engineering and science students. This most recent edition, for the
first time, now includes extensive corrections collated and
collected by the author.
How do biological objects communicate, make structures, make
measurements and decisions, search for food, i.e., do all the
things necessary for survival? Designed for an advanced
undergraduate audience, this book uses mathematics to begin to tell
that story. It builds on a background in multivariable calculus,
ordinary differential equations, and basic stochastic processes and
uses partial differential equations as the framework within which
to explore these questions.
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