Mathematical physics: the basics
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hyderabad
Universities Press
2007
Boca Raton, Fl. [u.a.] CRC Press |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltstext Inhaltsverzeichnis |
| Physical Description: | VIII, 247 S. graph. Darst. |
| ISBN: | 1420053027 9781420053029 |
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Record in the Search Index
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| adam_text | IMAGE 1
MATHEMATICAL
PHYSICS T HE B A S I CS
SUB GOTTINGEN 7
221 979 859
III
2008 A 7752
S D JOGLEKAR
PROFESSOR, DEPARTMENT OF PHYSICS INDIAN INSTITUTE OF TECHNOLOGY KANPUR
INDIA
F
UNIVERSITIES PRESS CRC PRESS TAYLOR & FRANCIS GROUP BOCA RATON LONDON
NEW YORK
CRC IS AN IMPRINT OF THE TAYLOR & FRANCIS CROUP, AN INFORMA BUSINESS
IMAGE 2
CONTENTS
PREFACE VII
1 COORDINATE TRANSFORMATIONS, VECTORS AND CARTESIAN TENSORS 1
1.1 COORDINATE TRANSFORMATIONS 1
1.1.1 COORDINATE TRANSFORMATIONS IN 3-DIMENSIONS 4
1.2 EULER ANGLES 7
1.3 DEFINITION OF VECTORS 9
1.3.1 ALGEBRAIC DEFINITION OF A VECTOR 11
1.3.2 PSEUDOSCALARS AND PSEUDOVECTORS 13
1.4 CARTESIAN TENSORS 15
1.4.1 SYMMETRIC AND ANTISYMMETRIC TENSORS OF RANK TWO 16
1.4.2 CARTESIAN TENSOR OF RANK N 18
1.4.3 SPECIAL TENSORS 18
1.4.4 CONSTRUCTION OF NEW TENSORS OUT OF GIVEN TENSORS 20
1.4.5 ALGEBRA OF LEVI-CIVITA TENSOR AND KRONECKER DELTA 21
1.4.6 APPLICATIONS OF THE USE OF SIJ AND E^ TO VECTOR ALGEBRA/CALCULUS
23 PROBLEMS 26
2 LORENTZ TRANSFORMATION, 4-VECTORS AND 4-TENSORS 29
2.1 GENERAL LORENTZ TRANSFORMATIONS AND THE METRIC 29
2.2 COVARIANT AND CONTRAVARIANT 4-VECTORS 32
2.2.1 RAISING AND LOWERING INDICES 32
2.2.2 CLASSIFICATION OF 4-VECTORS 34
2.3 LORENTZ TENSORS 35
2.3.1 CONSTRUCTION OF NEW TENSORS 36
PROBLEMS 38
3 CURVILINEAR COORDINATES 41
3.1 COORDINATE CURVES 41
3.2 SCALE FACTORS 43
IMAGE 3
IV CONTENTS
3.3 GRADIENT, DIVERGENCE AND CURL IN CURVILINEAR COORDINATES 48
3.3.1 GRADIENT 48
3.3.2 DIVERGENCE 48
3.3.3 CURL 50
PROBLEMS 51
4 LINEAR VECTOR SPACES -1 55
4.1 DEFINITION AND EXAMPLES 55
4.2 REAL LINEAR VECTOR SPACE 57
4.3 UNIQUENESS OF NULL AND REVERSED VECTORS 57
4.4 SCALAR PRODUCT OF VECTORS 60
4.4.1 DEFINITION OF SCALAR PRODUCT OF TWO VECTORS 61
4.4.2 SCALAR PRODUCT FOR REAL LINEAR VECTOR SPACES 62
4.4.3 CAUCHY-SCHWARTZ INEQUALITY 62
4.5 METRIC SPACES 66
4.6 LINEAR INDEPENDENCE OF VECTORS AND BASIS FOR A VECTOR SPACE 69 4.7
DIMENSION OF A VECTOR SPACE 70
4.8 ORTHONORMAL BASIS 73
4.9 VECTOR SUBSPACES 75
4.10 DIRECT SUM DECOMPOSITION 77
PROBLEMS 80
5 LINEAR VECTOR SPACES - II: LINEAR OPERATORS 85
5.1 DEFINITION 85
5.1.1 ALGEBRA OF LINEAR OPERATORS 86
, 5.1.2 MINIMAL DEFINITION OF A LINEAR OPERATOR 88
5.1.3 ACTION OF AN ARBITRARY LO ON THE NULL VECTOR 88
5.1.4 SPECIAL OPERATORS 88
5.2 INVERSE OF AN OPERATOR 89
5.3 DUAL SPACES AND ADJOINT OPERATORS 91
5.3.1 DUAL VECTOR SPACE 91
5.3.2 ADJOINT OF AN OPERATOR 91
5.3.3 OPERATORS EXPRESSIBLE AS X){Y , 92
5.4 SPECIAL LINEAR OPERATORS 93
5.5 PROJECTION OPERATORS 94
5.6 EIGENVALUES AND EIGENVECTORS 95
5.7 RESULTS ON THE EIGENVALUES AND EIGENVECTORS OF SPECIAL OPERATORS 97
5.7.1 HERMITIAN AND UNITARY OPERATORS 97
5.7.2 NORMAL OPERATORS 99
5.8 SIMILARITY AND UNITARY TRANSFORMATIONS 101
IMAGE 4
CONTENTS
5.9 MATRIX REPRESENTATIONS 102
5.9.1 CONSTRUCTION OF A REPRESENTATION 103
5.10 RESULTS ON THE EIGENVALUES AND EIGENVECTORS OF MATRICES 106
5.10.1 CHARACTERISTIC (SECULAR) EQUATION 109
5.11 TRANSFORMATION OF BASIS IN A VECTOR SPACE 113
5.11.1 TRANSFORMATION MATRIX 113
5.11.2 TRANSFORMATION OF MATRIX REPRESENTATIONS 114
5.11.3 TRANSFORMATION BETWEEN ORTHONORMAL BASES 115
5.12 DIAGONALIZATION OF MATRICES 117
5.13 MAIN THEOREM ON DIAGONALIZATION 120
PROBLEMS 124
6 COMPLEX VARIABLES -1 131
6.1 INTRODUCTION 132
6.1.1 TRIANGLE INEQUALITIES 133
6.2 FUNCTIONS OF A COMPLEX VARIABLE AND DIFFERENTIABILITY. 135
6.2.1 CAUCHY-RIEMANN CONDITIONS 137
6.2.2 CR CONDITIONS IN TERMS OF INDEPENDENT VARIABLES Z AND Z* 139 6.2.3
SUFFICIENT CONDITIONS FOR DIFFERENTIABILITY 140
6.2.4 CR CONDITIONS IN POLAR COORDINATES 142
6.3 ANALYTIC FUNCTIONS 145
6.3.1 HARMONIC FUNCTIONS 147
6.4 SPECIAL ANALYTIC FUNCTIONS 148
6.4.1 THE EXPONENTIAL FUNCTIONS 149
6.4.2 TRIGNOMETRIC FUNCTIONS 150
6.4.3 LOGARITHMIC FUNCTION 153
6.4.4 COMPLEX EXPONENTS 154
PROBLEMS 155
7 COMPLEX VARIABLES - II 158
7.1 CONTOUR INTEGRALS 158
7.1.1 DEFINITION OF A CONTOUR INTEGRAL 159
7.1.2 DARBOUX INEQUALITY 160
7.2 CAUCHY THEOREM 161
7.2.1 GREEN S THEOREM 161
7.2.2 THE CAUCHY THEOREM 163
7.2.3 THE CAUCHY-GOURSAT THEOREM 164
7.2.4 GENERALIZATIONS 165
7.3 CAUCHY S INTEGRAL FORMULA 166
7.4 DERIVATIVES OF AN ANALYTIC FUNCTION 168
IMAGE 5
VL CONTENTS
7.5 TAYLOR SERIES 171
7.6 LAURENT SERIES 176
7.6.1 ALTERNATE FORM FOR THE COEFFICIENTS A N AND B N 178
7.6.2 UNIQUENESS OF LAURENT SERIES 179
7.6.3 NATURE OF AN ISOLATED SINGULARITY 180
7.7 CONVERGENCE 181
7.7.1 UNIFORM AND ABSOLUTE CONVERGENCE OF A COMPLEX POWER SERIES 181
7.7.2 INTERCHANGE OF SUMMATION AND DIFFERENTIATION/INTEGRATION 185 7.8
RESIDUE THEOREM 188
7.8.1 RESIDUES AT POLES 188
7.8.2 RESIDUE THEOREM 194
7.9 EVALUATIONS OF INTEGRALS USING THE RESIDUE THEOREM 195
7.9.1 JORDAN LEMMA 200
7.9.2 FURTHER REAL INTEGRALS USING RESIDUE THEOREM 202
PROBLEMS 206
8 COMPLEX VARIABLES - III 213
8.1 ANALYTIC CONTINUATION 213
8.1.1 UNIQUENESS OF ANALYTIC CONTINUATION 217
8.2 CONFORMAL MAPPING AND ITS APPLICATIONS TO ELECTROSTATICS 220
8.2.1 CONSTRUCTION OF AN ANALYTIC FUNCTION 220
8.2.2 ANALYTIC TRANSFORMATION AND ELECTROSTATIC PROBLEMS 224 8.2.3
CONFORMAL MAPPING 226
8.3 METHOD OF STEEPEST DESCENT 227
8.3.1 AN EXAMPLE 227
8.3.2 GENERAL CONSIDERATIONS IN THE METHOD 231
8.3.3 GENERAL THEORY OF THE METHOD OF STEEPEST DESCENT 235
8.4 MULTIVALUED FUNCTIONS AND RIEMANN SURFACES 237
PROBLEMS 239
INDEX 244
|
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| spelling | Joglekar, Satish D. Verfasser aut Mathematical physics the basics S. D. Joglekar Hyderabad Universities Press 2007 Boca Raton, Fl. [u.a.] CRC Press VIII, 247 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algèbre linéaire Espaces vectoriels Nombres complexes Physique mathématique Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Physik (DE-588)4037952-8 s DE-604 http://www.gbv.de/dms/goettingen/557552842.pdf kostenfrei Inhaltsverzeichnis DE-601 pdf/application http://www.zentralblatt-math.org/zmath/en/search/?an=1144.00002 Zentralblatt MATH kostenfrei Inhaltstext GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017537274&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Mathematical physics the basics |
| title_auth | Mathematical physics the basics |
| title_exact_search | Mathematical physics the basics |
| title_full | Mathematical physics the basics S. D. Joglekar |
| title_fullStr | Mathematical physics the basics S. D. Joglekar |
| title_full_unstemmed | Mathematical physics the basics S. D. Joglekar |
| title_short | Mathematical physics |
| title_sort | mathematical physics the basics |
| title_sub | the basics |
| topic | Algèbre linéaire Espaces vectoriels Nombres complexes Physique mathématique Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd |
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