Essential Mathematical Methods for the Physical Sciences
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Essential Mathematical Methods for the Physical Sciences

K. F. Riley, M. P. Hobson

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eBook - PDF

Essential Mathematical Methods for the Physical Sciences

K. F. Riley, M. P. Hobson

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About This Book

The mathematical methods that physical scientists need for solving substantial problems in their fields of study are set out clearly and simply in this tutorial-style textbook. Students will develop problem-solving skills through hundreds of worked examples, self-test questions and homework problems. Each chapter concludes with a summary of the main procedures and results and all assumed prior knowledge is summarized in one of the appendices. Over 300 worked examples show how to use the techniques and around 100 self-test questions in the footnotes act as checkpoints to build student confidence. Nearly 400 end-of-chapter problems combine ideas from the chapter to reinforce the concepts. Hints and outline answers to the odd-numbered problems are given at the end of each chapter, with fully-worked solutions to these problems given in the accompanying Student Solutions Manual. Fully-worked solutions to all problems, password-protected for instructors, are available at www.cambridge.org/essential.

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86
Matrices
and
vector
spaces
1
2
3
m
m
M
2
km
kM
kM
(a)
ω
2
=
c
+
d
m
(b)
ω
2
=
c
(c)
ω
2
=
c
+
2
d
M
+
d
m
Figure
1.7
The
normal
modes,
as
viewed
from
above,
of
the
coupled
pendulums
in
Problem
1.39
.
(a)
I
1
=
0,
I
2
=
I
3
;
no
current
in
P
Q
;
equivalent
to
two
separate
circuits
of
capacitance
C
and
inductance
L
.
(b)
I
1
=
2
I
2
=
2
I
3
;
no
current
in
T
U
;
capacitance
3
C/
2
and
inductance
2
L
.
1.45.
ω
=
(2
.
634
g/l
)
1
/
2
or
(0
.
3661
g/l
)
1
/
2
;
θ
1
=
ξ
+
η
,
θ
2
=
1
.
431
ξ
2
.
097
η
.
1.47.
Estimated,
10
/
17
<
Maω
2
/T
<
58
/
17;
exact,
2
2
Maω
2
/T
2
+
2.

Table of contents