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Introduction to Mathematical Physics [Kõva köide]

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  • Formaat: Hardback, 458 pages, kõrgus x laius: 240x160 mm, kaal: 788 g
  • Ilmumisaeg: 30-Jan-2013
  • Kirjastus: Alpha Science International Ltd
  • ISBN-10: 1842657836
  • ISBN-13: 9781842657836
Teised raamatud teemal:
Introduction to Mathematical PhysicsSuurem pilt
  • Formaat: Hardback, 458 pages, kõrgus x laius: 240x160 mm, kaal: 788 g
  • Ilmumisaeg: 30-Jan-2013
  • Kirjastus: Alpha Science International Ltd
  • ISBN-10: 1842657836
  • ISBN-13: 9781842657836
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781842657836.html
An accessible and simplified approach to mathematical physics, this book contains a variety of supportive material to aid in the discussion of the elementary of the subject, including areas like the Curvilinear Coordinates, Vector Space, Matrices, Tensors, before moving on to the more complex Differential Equations, different functions, Fourier Series, Fourier Transform and Laplace Transform.

An accessible and simplified approach to mathematical physics, this book contains a variety of supportive material to aid in the discussion of the elementary of the subject, including areas like the Curvilinear Coordinates, Vector Space, Matrices, Tensors, before moving on to the more complex Differential Equations and the many different functions.
Preface vii
I Curvilinear Coordinates 1(20)
1 Relations between some coordinate systems
1(2)
2 Orthogonal curvilinear coordinate system
3(2)
3 Scale factors
5(5)
4 Gradient of a scalar field
10(1)
5 Divergence of a vector field
11(2)
6 Curl of a vector field
13(3)
7 Laplacian operator
16(3)
8 Problems and questions
19(2)
II Vector Space 21(14)
1 Linear independence of vectors
21(2)
2 Dimensionality of a space
23(1)
3 Basis for a space
24(1)
4 Inner product of two vectors
24(6)
5 Linear transformations
30(2)
6 Problems and questions
32(3)
III Matrices 35(38)
1 Inverse of a matrix
35(3)
2 Gauss-Jordan method
38(4)
3 Orthogonal matrix
42(3)
4 Unitary matrix
45(3)
5 Eigenvalues and eigenvectors of a matrix
48(11)
6 Diagonalization of matrix
59(5)
7 Complete orthonormal set of functions
64(1)
8 Cayley-Hamilton theorem
65(3)
9 Problems and questions
68(5)
IV Tensors 73(34)
1 Introduction
73(1)
2 N-dimensional space
74(1)
3 Coordinate transformations
74(1)
4 Summation convention
75(1)
5 Contravariant and covariant vectors
76(2)
6 Contravariant, covariant and mixed tensors of rank two
78(2)
7 Order and rank of a tensor
80(2)
8 Scalars
82(1)
9 Algebraic operations of tensors
82(2)
10 Symmetric and skew-symmetric tensors
84(1)
11 Relative tensors
85(1)
12 Kronecker delta
86(2)
13 Line element and metric tensor
88(2)
14 Conjugate or reciprocal tensor
90(3)
15 Associate tensors
93(1)
16 Christoffel symbols
94(6)
17 Covariant derivative of a tensor
100(1)
18 Curvature tensor
101(3)
19 Problems and questions
104(3)
V Some Functions 107(32)
1 Beta function
107(2)
2 Gamma function
109(3)
3 Evaluation of sonic integrals
112(13)
4 Error function
125(2)
5 Dirac delta function
127(1)
6 Green function method
128(9)
7 Problems and questions
137(2)
VI Complex Analysis 139(80)
1 Complex variables
139(2)
2 Algebraic operations of complex numbers
141(1)
3 Polar form of a complex number
142(3)
4 Function of a complex variable
145(1)
5 Analytic function
146(9)
6 Laplace equation
155(6)
7 Line integral of a complex function
161(1)
8 Some preliminary concepts
162(1)
9 Cauchy integral theorem
163(4)
10 Evaluation of line integrals by indefinite integration
167(1)
11 Cauchy integral formula
168(2)
12 Derivatives of an analytic function
170(4)
13 Taylor series
174(2)
14 Laurent series
176(4)
15 Singularities of a function
180(2)
16 Residues
182(5)
17 Cauchy residue theorem
187(2)
18 Evaluation of definite integrals
189(13)
19 Jordan lemma
202(15)
20 Problems and questions
217(2)
VII Differential Equations 219(13)
1 Introduction
219(2)
2 First order linear differential equation
221(5)
3 Second order linear differential equation with constant coefficients
226(2)
4 Second order linear differential equation with variable coefficients
228(1)
5 Series solutions - Frobenius Method
229(1)
6 Fuchs theorem
230(1)
7 Problems and questions
231(1)
VIII Bessel Function 232(19)
1 Bessel differential equation
232(5)
2 Generating function for Jn(x)
237(1)
3 Recurrence relations for Jn(x)
238(2)
4 Orthogonality of Jn(x)
240(3)
5 Bessel function of second type
243(1)
6 Trigonometric expansion involving Bessel functions
244(1)
7 Integral form of Bessel functions
245(2)
8 Spherical Bessel functions
247(2)
9 Problems and questions
249(2)
IX Legendre Function 251(17)
1 Legendre differential equation
251(6)
2 Generating function for Pn(x)
257(1)
3 Recurrence relations for Pn(x)
258(2)
4 Orthogonality of Pn(x)
260(1)
5 Rodrigue formula for Pn(x)
261(2)
6 Associated Legendre polynomials
263(3)
7 Problems and questions
266(2)
X Laguerre Function 268(11)
1 Laguerre differential equation
268(2)
2 Generating function for Ln(x)
270(1)
3 Recurrence relations for Ln(x)
271(2)
4 Orthogonality of Ln(x)
273(2)
5 Rodrigue formula for Ln(x)
275(1)
6 Associated Laguerre polynomials
275(2)
7 Problems and questions
277(2)
XI Hermite Function 279(9)
1 Hermite differential equation
279(3)
2 Generating function for Hn(x)
282(1)
3 Recurrence relations for Hn(x)
283(1)
4 Orthogonality of Hn(x)
284(2)
5 Rodrigue formula for Hn(x)
286(1)
6 Problems and questions
286(2)
XII Fourier Series 288(42)
1 Fourier series
289(16)
2 Evaluation of some integrals
305(2)
3 Fourier cosine series and Fourier sine series
307(1)
4 Exponential (complex) form of Fourier series
308(1)
5 Change of interval of Fourier series
309(5)
6 Applications of Fourier series
314(8)
7 Advantages of Fourier series representation
322(1)
8 Fourier integrals
322(4)
9 Problems and questions
326(4)
XIII Fourier Transform 330(28)
1 Fourier transform
331(6)
2 Convolution
337(2)
3 Fourier cosine transform
339(4)
4 Fourier sine transform
343(6)
5 Fourier transform of derivatives
349(1)
6 Fourier cosine transform of derivatives
350(1)
7 Fourier sine transform of derivatives
351(1)
8 Application of Fourier transform
352(1)
9 Dirac delta function
353(1)
10 Problems and questions
354(4)
XIV Laplace Transform 358(24)
1 Introduction
358(2)
2 Properties of Laplace transform
360(4)
3 Laplace transform of derivatives
364(2)
4 Inverse Laplace transform
366(7)
5 Applications of Laplace transform
373(5)
6 Problems and questions
378(4)
XV Group Theory 382(36)
1 Concept of group
382(4)
2 Special unitary group
386(3)
3 Special orthogonal group
389(6)
4 Group multiplication table
395(3)
5 Group symmetry of equilateral triangle
398(2)
6 Group symmetry of a square
400(3)
7 Permutation group
403(2)
8 Conjugate elements
405(5)
9 Isomorphism and homomorphism
410(1)
10 Representation of a group
410(5)
11 Problems and questions
415(3)
XVI Error Analysis 418(16)
1 Random and systematic errors
418(1)
2 Significant figures
419(1)
3 Approximate numbers
420(1)
4 Rounding off numbers
420(3)
5 Presentation of errors
423(2)
6 Index of accuracy
425(1)
7 Error formula
426(7)
8 Problems and questions
433(1)
Appendices 434(6)
Bibliography 440(1)
Index 441