Differential Forms and Connections

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Cambridge University Press, Sep 22, 1994 - Mathematics - 256 pages
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This book introduces the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--and covers both classical surface theory, the modern theory of connections, and curvature. Also included is a chapter on applications to theoretical physics. The author uses the powerful and concise calculus of differential forms throughout. Through the use of numerous concrete examples, the author develops computational skills in the familiar Euclidean context before exposing the reader to the more abstract setting of manifolds. The only prerequisites are multivariate calculus and linear algebra; no knowledge of topology is assumed. Nearly 200 exercises make the book ideal for both classroom use and self-study for advanced undergraduate and beginning graduate students in mathematics, physics, and engineering.
  

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Excellent book, clear and precise with a careful build-up of material throughout the book, has questions and workings out for you to do for a solid mathematical notational understanding.

Contents

II
ix
IV
3
V
5
VII
6
VIII
10
IX
11
X
15
XI
18
LXXIII
114
LXXIV
115
LXXV
117
LXXVI
118
LXXVII
120
LXXVIII
123
LXXX
128
LXXXII
130

XII
19
XIII
21
XIV
22
XVI
26
XVII
29
XIX
31
XX
33
XXI
37
XXII
39
XXIII
41
XXIV
45
XXV
47
XXVI
48
XXVIII
51
XXX
53
XXXII
58
XXXIII
59
XXXIV
62
XXXVI
67
XXXVII
69
XXXVIII
70
XXXIX
73
XL
74
XLIII
76
XLV
77
XLVII
79
XLIX
83
L
85
LII
86
LIII
89
LV
92
LVII
93
LIX
95
LXI
96
LXIV
98
LXV
100
LXVI
102
LXVII
103
LXIX
105
LXX
108
LXXI
109
LXXII
112
LXXXIII
132
LXXXV
137
LXXXVI
139
LXXXVII
142
LXXXVIII
145
LXXXIX
146
XC
149
XCI
150
XCII
151
XCIII
154
XCIV
158
XCVI
159
XCVII
161
XCVIII
162
C
165
CII
167
CIII
170
CIV
172
CV
176
CVII
179
CVIII
181
CIX
182
CX
185
CXI
187
CXII
192
CXIII
195
CXIV
200
CXV
204
CXVII
210
CXVIII
214
CXIX
217
CXX
220
CXXI
221
CXXIII
223
CXXV
229
CXXVI
231
CXXVII
236
CXXVIII
240
CXXIX
242
CXXX
245
CXXXI
247
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