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Bayin S.S. — Mathematical Methods in Science and Engineering
Bayin S.S. — Mathematical Methods in Science and Engineering

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Название: Mathematical Methods in Science and Engineering

Автор: Bayin S.S.


An innovative treatment of mathematical methods for a multidisciplinary audience

Clearly and elegantly presented, Mathematical Methods in Science and Engineering provides a coherent treatment of mathematical methods, bringing advanced mathematical tools to a multidisciplinary audience. The growing interest in interdisciplinary studies has brought scientists from many disciplines such as physics, mathematics, chemistry, biology, economics, and finance together, which has increased the demand for courses in upper-level mathematical techniques. This book succeeds in not only being tuned in to the existing practical needs of this multidisciplinary audience, but also plays a role in the development of new interdisciplinary science by introducing new techniques to students and researchers.

Mathematical Methods in Science and Engineering's modular structure affords instructors enough flexibility to use this book for several different advanced undergraduate and graduate level courses. Each chapter serves as a review of its subject and can be read independently, thus it also serves as a valuable reference and refresher for scientists and beginning researchers.

There are a growing number of research areas in applied sciences, such as earthquakes, rupture, financial markets, and crashes, that employ the techniques of fractional calculus and path integrals. The book's two unique chapters on these subjects, written in a style that makes these advanced techniques accessible to a multidisciplinary audience, are an indispensable tool for researchers and instructors who want to add something new to their compulsory courses.

Mathematical Methods in Science andEngineering includes:
* Comprehensive chapters on coordinates and tensors and on continuous groups and their representations
* An emphasis on physical motivation and the multidisciplinary nature of the methods discussed
* A coherent treatment of carefully selected topics in a style that makes advanced mathematical tools accessible to a multidisciplinary audience
* Exercises at the end of every chapter and plentiful examples throughout the book

Mathematical Methods in Science and Engineering is not only appropriate as a text for advanced undergraduate and graduate physics programs, but is also appropriate for engineering science and mechanical engineering departments due to its unique chapter coverage and easily accessible style. Readers are expected to be familiar with topics typically covered in the first three years of science and engineering undergraduate programs. Thoroughly class-tested, this book has been used in classes by more than 1,000 students over the past eighteen years. 2

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 679

Добавлена в каталог: 05.12.2009

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Предметный указатель
Abel test      444
Abel’s formula      569
Absolute convergence      432
Active and passive views      174
Addition of velocities      201
Addition theorem, sspherical harmonics      264
Advanced Green’s functions      624
Algebra of vectors      164
Alternating series, Leibniz rule      439
Analytic continuation      350
Analytic functions, Cauchy — Riemann conditions      297
Angular momentum operators, eigenvalue equations quantum mechanics      255
Angular momentum operators, matrix elements quantum mechanics      257
Angular momentum, factorization method      143
Angular momentum, quantum mechanics      249
Argument      294
Associated Laguerre polynomials      45 51
Associated Laguerre polynomials, generating function      52
Associated Laguerre polynomials, orthogonality and completeness      53
Associated Laguerre polynomials, recursion relations      53
Associated Laguerre polynomials, Rodriguez formula      53
Associated Legendre equation      13 28
Associated Legendre equation, factorization method      137
Associated Legendre polynomials      30
Associated Legendre polynomials, orthogonality and completeness      31
Asymptotic series      462
Bernoulli numbers      453
Bernoulli periodic function      454
Bernoulli polynomials, generating function      453
Bessel functions, boundary conditions      91
Bessel functions, channel waves tsunamis      93
Bessel functions, factorization method      155
Bessel functions, first kind      86
Bessel functions, flexible chain problem      92
Bessel functions, generating functions      89
Bessel functions, integral definitions      90
Bessel functions, modified Bessel functions      88
Bessel functions, orthogonality and completeness      90
Bessel functions, recursion relations      90
Bessel functions, second kind      87
Bessel functions, spherical      88
Bessel functions, third kind      87
Bessel functions, Wronskians      95
Bessel’s equation      86
Bessel’s equation, Laplace transforms      507
beta function      362
Binomial coefficient      447
Binomial formula, relativistic energy      447
Binomial theorem      447
Bloch equation      640
Bohr energy levels      45
Boosts, Lorentz transformation      244
Boundary conditions, Dirichlet      109
Boundary conditions, Green’s functions      572 594
Boundary conditions, Hermitian operators      110
Boundary conditions, inhomogeneous Green’s functions      575
Boundary conditions, Neumann      109
Boundary conditions, single point Green’s functions      572
Boundary conditions, Sturm — Liouville system      108
Boundary conditions, unmixed mixed      109
Branch cut, Riemann sheet      306
Branch line      306
Branch point      306
Bromwich integral, inverse Laplace transform Laplace transform      492
Caputo derivative      429
Cartesian coordinates      163
Cartesian tensors      178
Cartesian tensors, contraction      179
Cartesian tensors, pseudotensor tensor density      180
Cartesian tensors, rank      178
Cartesian tensors, trace      179
Casimir effect      466
Casimir effect, MEMS      468
Cauchy formula      388
Cauchy integral formula, fractional derivative      390
Cauchy integral theorem      336
Cauchy principal value      365
Cauchy theorem      339
Cauchy theorem, convergence tests      435
Cauchy — Goursat theorem      335
Cauchy — Riemann conditions      297
Chebyshev equation      75
Chebyshev equation, second kind      76
Chebyshev polynomials, another definition      78
Chebyshev polynomials, first kind      75 76
Chebyshev polynomials, Gegenbauer polynomials      76
Chebyshev polynomials, generating function      78
Chebyshev polynomials, orthogonality and completeness      78
Chebyshev polynomials, second kind      76
Chebyshev series, Raabe test      437
Christoffel symbols, first kind      192
Christoffel symbols, second kind      192
Commutation relations, angular momentum      249
Completeness of eigenfunctions      276
Complex algebra      293
Complex conjugate      295
complex derivative      296
Complex functions      295
Complex numbers, argument      294
Complex numbers, conjugate      295
Complex numbers, modulus      294
Complex plane      294
Complex techniques, definite integrals      352
Conditional convergence      432
Conditional convergence, Abel test      444
Condon — Shortley phase      140
Condon — Shortley phase, spherical harmonics      34
Confluent Gauss equation      104
Conformal mappings      313
Conformal mappings, electrostatics      314
Conformal mappings, fluid mechanics      318
Conjugate harmonic functions      299
Continuous groups, generators      278
Continuous groups, Lie groups      224 278
Continuous random walk, fractional derivatives      424
Contour integral techniques      352
Contour integral, complex      335
Contour integrals, special functions      369
Contraction of indices      188
Contravariant/covariant components      186
Convergence tests, Cauchy root test      433
Convergence tests, comparison      433
Convergence tests, Gauss test      436
Convergence tests, integral test      434
Convergence tests, Raabe test      435
Convergence tests, ratio test      433
Convergence, absolute conditional      432
Convolution theorem, Fourier transforms      485
Convolution theorem, Laplace transforms      498
Covariance      197
Covariant divergence      194
Covariant/contra variant components      182
Curl      193
Cut line      306
De Moivre’s Formula      295
Derivative and integral, unification for integer orders      385
Derivative, n-fold      382
Differential equations, conversion to integral equations      550
Differentiation of vectors      166
Differintegrals, composition      400
Differintegrals, CTRW Brownian motion      424
Differintegrals, dependence on the lower limit      408
Differintegrals, evaluation of definite integrals      421
Differintegrals, extraordinary differential equations      417
Differintegrals, Fokker — Planck equation      427
Differintegrals, heat transfer equation      415
Differintegrals, homogeneity      399
Differintegrals, Leibniz rule      407
Differintegrals, linearity      399
Differintegrals, properties      399
Differintegrals, right and left handed      407
Differintegrals, scale transformation      400
Differintegrals, semidifferential equations      419
Differintegrals, series      400
Differintegrals, some examples      409
Differintegrals, special functions      424
Differintegrals, techniques      413
Diffusion equation      379
Diffusion equation, Brownian motion path integrals      633
Diffusion equation, Feynman — Kac formula      639
Diffusion equation, Fourier transforms      488
Diffusion equation, propagator      610
Dipoles      23
Dirac — Delta function      481
Direction cosines      167
Divergence      194
Divergent series      465
Divergent series, Casimir effect      466
Divergent series, quantum vacuum energyy      467
Doppler shift      208
Dot product      165
Double factorial      377
Dual field strength tensor      212
d’Alembert operator      72 209 215 473 619
Eigenvalue problems Green’s functions      579
Einstein summation convention      188
Elastic beam, deformation      527
Electrostatics, Green’s functions      604
Entire function      297 347
Equivalent representations      246
ESKC relation      635
Essential singular point      347
Euler angles      172
Euler equation      518
Euler equation, another form      520
Euler — Maclaurin sum formula      454
Euler — Masheroni constant      471
Euler’s theorem      228
Expansion theorem      113
Expansion theorem, eigenfunctions      276
Extension, prolongation generators      282
Extraordinary differential equations      417
Factorization method, associated Legendre equation      137
Factorization method, Bessel functions      155
Factorization method, Gegenbauer polynomials      153
Factorization method, harmonic oscillator      156
Factorization method, single electron atom      151
Factorization method, solutions      130
Factorization method, spherical harmonics      141
Factorization method, Sturm — Liouville equation      123
Factorization method, symmetric top problem      154
Factorization method, technique and categories      132
Factorization method, theory      124
Feynman path integral, momentum space      659
Feynman path integral, quadratic momentum dependence      661
Feynman path integral, Schroedinger equation      655
Feynman — Kac formula      639
Feynman — Kac formula, derivation      641
Fick’s equation      380
Field strength tensor      212
First canonical form, self-adjoint differential operator Sturm — Liouville operator      108
Flexible chain, Bessel’s equation      84
Flow around an obstacle, conformal mappings      319
Fokker-Planck equation, fractional derivatives      427
Four-momentum, conservation      205
Four-scalars      204
Four-tensors      202
Four-vector space      274
Four-vectors      204
Four-velocity      204
Fourier integral      479
Fourier transforms      481
Fourier transforms in three dimensions      486
Fourier transforms, convolution theorem      485
Fourier transforms, cosine sine      482
Fourier transforms, diffusion equation      488
Fourier transforms, existence      486
Fourier transforms, Parceval theorems      487
Fourier transforms, partial differential equations      484
Fourier transforms, transform of a derivative      484
Fractional derivatives, Caputo definition      429
Fractional derivatives, Cauchy integral formula      390
Fractional derivatives, Gruenwald definition differintegrals      385
Fractional derivatives, Laplace transforms      396
Fractional derivatives, notation      381
Fractional derivatives, Riemann formula      395
Fractional derivatives, Riemann — Liouville definition      387
Fredholm equation      548
Frobenius method      13 16
Function spaces, Hilbert space      274
Fundamental tensor      184
Galilean transformation      215
Gamma function      360 462
Gamma function, infinite product      471
Gauss equation, special functions      104
Gegenbauer equation      75
Gegenbauer equation, factorization method      153
Gegenbauer polynomials      75
Gegenbauer polynomials, Bessel functions      89
Gegenbauer polynomials, Chebyshev polynomials      78
Gegenbauer polynomials, commutation relations      227
Gegenbauer polynomials, cosmology      72
Gegenbauer polynomials, differential      228
Gegenbauer polynomials, extension prolongation      282
Gegenbauer polynomials, generating function      75
Gegenbauer polynomials, Hermite polynomials      60
Gegenbauer polynomials, Laguerre polynomials      46
Gegenbauer polynomials, Legendre polynomials      19
Gegenbauer polynomials, normal form      280
Gegenbauer polynomials, orthogonality and completeness      75
Gegenbauer polynomials, R(3)      227
Gegenbauer polynomials, transformations      279
Generalized Fourier series      114
Generating function, associated Laguerre polynomials      52
Generators, continuous groups Lie groups      278
Geodesics      197
Gradient      193
Green’s functions      10
Green’s functions, advanced and retarded      621
Green’s functions, all space      584
Green’s functions, boundary conditions      568
Green’s functions, compounding propagators      609
Green’s functions, construction      569
Green’s functions, defining equation      572
Green’s functions, differential equations      572
Green’s functions, Dirac-delta function      583
Green’s functions, eigenfunction expansions      579
Green’s functions, first-order time dependence      606
Green’s functions, general boundary conditions      604
Green’s functions, harmonic oscillator      591
Green’s functions, Helmholtz equation      582
Green’s functions, inhomogeneous boundary conditions      575
Green’s functions, integral equations      568
Green’s functions, Laplace operator      597
Green’s functions, Lippmann-Schwinger equation      603
Green’s functions, one-dimensional      567
Green’s functions, point source      609
Green’s functions, Poisson equation      597
Green’s functions, propagators      609
Green’s functions, Schroedinger’s equation      597
Green’s functions, second-order time dependence      616
Green’s functions, three-dimensional      593
Green’s functions, three-dimensional continuum limit      594
Green’s functions, wave equation      618
Griinwald      385
Group invariants      231
Group representations      246
Group representations, R(3)      248
Group representations, SU(2)      269
Group spaces      272
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