Vector Calculus

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Springer Science & Business Media, Jan 14, 2000 - Mathematics - 182 pages
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Vector calculus is the fundamental language of mathematical physics. It pro vides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. These top ics include fluid dynamics, solid mechanics and electromagnetism, all of which involve a description of vector and scalar quantities in three dimensions. This book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants. The book is designed to be self-contained, so that it is suitable for a pro gramme of individual study. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications. The physical nature of the subject is clarified with over sixty diagrams, which provide an important aid to the comprehension of the new concepts. Following the introduction of each new topic, worked examples are provided. It is essential that these are studied carefully, so that a full un derstanding is developed before moving ahead. Like much of mathematics, each section of the book is built on the foundations laid in the earlier sections and chapters.
 

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Contents

I
1
II
2
III
3
IV
4
V
7
VI
9
VII
11
VIII
14
XL
76
XLI
78
XLII
83
XLIII
85
XLIV
87
XLV
88
XLVI
91
XLVII
93

IX
16
X
17
XI
21
XII
22
XIII
23
XIV
25
XV
26
XVI
28
XVII
30
XVIII
31
XIX
33
XX
38
XXI
39
XXII
40
XXIII
45
XXIV
47
XXV
48
XXVI
51
XXVII
52
XXVIII
53
XXIX
56
XXXI
58
XXXII
60
XXXIII
61
XXXV
65
XXXVI
68
XXXVII
70
XXXVIII
72
XXXIX
74
XLVIII
95
XLIX
99
L
104
LII
106
LIII
107
LIV
110
LV
115
LVI
117
LVII
119
LVIII
120
LIX
122
LX
123
LXI
126
LXIII
127
LXIV
131
LXV
132
LXVI
134
LXVII
135
LXVIII
137
LXIX
140
LXX
143
LXXI
145
LXXII
146
LXXIII
147
LXXIV
149
LXXV
153
LXXVI
181
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About the author (2000)

Matthews-University of Nottingham, England

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