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Essential Mathematical Methods for Physicists

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This text is designed for the usual introductory physics courses to prepare undergraduate
students for the level of mathematics expected in more advanced
undergraduate physics and engineering courses. One of its goals is to guide
the student in learning the mathematical language physicists use by leading
them through worked examples and then practicing problems. The pedagogy
is that of introducing concepts, designing and refining methods, and practicing
them repeatedly in physics examples and problems. Geometric and algebraic
approaches and methods are included and are more or less emphasized in
a variety of settings to accommodate different learning styles of students.
Sometimes examples are solved in more than one way. Theorems are usually
derived sketching the underlying ideas and describing the relevant mathematical
relations so that one can recognize the assumptions they are based on and
their limitations. These proofs are not rigorous in the sense of the professional
mathematician, and no attempt was made to formulate theorems in their most
general form or under the least restrictive assumptions.

An important objective of this text is to train the student to formulate
physical phenomena in mathematical language, starting from intuitive and
qualitative ideas. The examples in the text have been worked out so as to
develop the mathematical treatment along with the physical intuition.Aprecise
mathematical formulation of physical phenomena and problems is always the
ultimate goal.

equations to determinants and matrix solutions of general systems of linear
equations, eigenvalues and eigenvectors, and linear transformations in real
and complex vector spaces. These chapters are extended to function spaces
of solutions of differential equations in Chapter 9, thereby laying the mathematical
foundations for and formulation of quantum mechanics. Chapter 4
on group theory is an introduction to the important concept of symmetry in
modern physics. Chapter 5 gives a fairly extensive treatment of series that
form the basis for the special functions discussed in Chapters 10–13 and also
complex functions discussed in Chapters 6 and 7. Chapter 17 on probability
and statistics is basic for the experimentally oriented physicist. Some of its
content can be studied immediately after completion of Chapters 1 and 2, but
later sections are based on Chapters 8 and 10. Chapter 19 on nonlinear methods
can be studied immediately after completion of Chapter 8, and it complements
and extends Chapter 8 in many directions. Chapters 10–13 on special functions
contain many examples of physics problems requiring solutions of differential
equations that can also be incorporated in Chapters 8 and 16. Chapters 14
and 15 on Fourier analysis are indispensible for a more advanced treatment of
partial differential equations in Chapter 16.

Historical remarks are included that detail some physicists and mathematicians
who introduced the ideas and methods that later generations perfected
to the tools we now use routinely. We hope they provide motivation for students
and generate some appreciation of the effort, devotion, and courage of
past and present scientists.

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Informasi Detail

Judul Seri

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No. Panggil

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Penerbit

London : ACADEMIC PRESS., 2003

Deskripsi Fisik

xxi, 932 Hlm.

Bahasa

English

ISBN/ISSN

0-12-059877-9

Klasifikasi

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Tipe Isi

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Tipe Media

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Tipe Pembawa

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Edisi

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Subjek

MATEMATIKA

Info Detail Spesifik

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Pernyataan Tanggungjawab

agus

Versi lain/terkait

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