Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Shankar R. — Basic Training In Mathematics Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter Название: Basic Training In Mathematics Автор: Shankar R. Аннотация: Based on course material used by the author at Yale University, this practical text addresses the widening gap found between the mathematics required for upper-level courses in the physical sciences and the knowledge of incoming students. This superb book offers students an excellent opportunity to strengthen their mathematical skills by solving various problems in differential calculus. By covering material in its simplest form, students can look forward to a smooth entry into any course in the physical sciences. Язык: Рубрика: Математика/Математическая Физика/Учебники/ Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1995 Количество страниц: 390 Добавлена в каталог: 25.04.2005 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID Предметный указатель operator      284 Absolute convergence      80 118 Absolute value      92 action      309 Active transformation      208 Adjoint matrix      220 Adjoint operation      254 Ampere’s Law      198 Analytic continuation      142 Analytic function      107 109 Analytic function, analytic continuation of      142 Analytic function, branch points of      113 Analytic function, Cauchy — Riemann Equations for (CRE)      1 Analytic function, derivative of      114 Analytic function, diagnostic for      109 Analytic function, domain of analyticity of      110 Analytic function, essential singularities of      113 Analytic function, exp(z)      119 Analytic function, harmonic functions—relation to      114 Analytic function, hyperbolic functions      119 Analytic function, integrals of      128 Analytic function, Laplace’s equation, relation to      115 Analytic function, ln(z)      121 Analytic function, meromorphic functions      113 Analytic function, permanence of functional relations      143 Analytic function, poles of      111 Analytic function, power series definition of      116 Analytic function, removable singularity of      113 Analytic function, residue theorem for      132 134 Analytic function, singularities of      111 Analytic function, Taylor series for      139 Analytic function, trigonometric functions      115 Anti-analytic functions      109 Antiderivative      37 Antihermitian      221 Antilinearity of inner product      240 Antisymmetric tensor      297 Area vector      155 Axioms of vector space      230 Bernoulli’s equation      318 327 Bessel functions      335 Bessel’s equation      327 Binomial theorem      18 Box product      155 (see also “Scalar triple product”) Bra      239 253 Branch point      113 Branch point of ln function      124 Cauchy — Riemann Equations (CRE)      109 Cauchy’s Theorem      132 134 Cayley — Hamilton theorem      263 Chain rule      3 Characteristic polynomial      257 Circulation      172 Cofactor matrix      215 Column vector      206 Commutator      210 Comparison test for series      77 Complementary function      103 313 complex numbers      89 Complex numbers, absolute value of      92 Complex numbers, application to LCR circuit      98 Complex numbers, argument of      96 Complex numbers, cartesian form of      90 Complex numbers, complex conjugate of      91 Complex numbers, Euler’s identity for      95 Complex numbers, imaginary part of      90 Complex numbers, phase of      96 Complex numbers, polar form of      94 Complex numbers, purely imaginary      90 Complex numbers, real part of      90 Complex numbers, unimodular      97 Complex variable      107 (see also “Analytic function”) Complimentary function      313 components of vector      236 Conditional convergence      80 Conservative field      162 Constraints      55 Continuity equation for charge      193 Continuity equation for heat      336 Continuity of function in one variable      1 Continuity of function in two variables      107 Contraction of tensors      296 Contravariant tensor      299 Convergence of series      75 Convergence of series, absolute convergence      80 118 Convergence of series, complex series      116 Convergence of series, conditional convergence      80 Convergence of series, radius of      118 Coupled mass problem      267 Covariant tensor      299 Cross product      153 Cross product, as a determinant      217 Cross product, in terms of components      156 Curl      172 174 177 Curl, as a determinant      217 Curl, in noncartesian coordinates      181 Current density      162 Cylindrical coordinates      66 D operator      187 279 D operator, eigenbasis of -iD      279 D operator, Fourier series      281 Dagger      220 De Moivre’s Theorem      98 Definite integral      34 Definite integral, lower limit of      24 Definite integral, upper limit of      24 Degeneracy      263 Dependent variable      1 Derivative      2 Determinant      212 214 Determinants      214 Determinants and cross product      217 Determinants and curl      217 Differential calculus      1 Differential calculus, chain rule      3 Differential calculus, dependent variable      1 Differential calculus, differentials      29 Differential calculus, exponential and log functions      5 Differential calculus, hyperbolic functions      13 Differential calculus, implicit differentiation      28 Differential calculus, independent variable      1 Differential calculus, inverse hyperbolic functions      18 Differential calculus, inverse trigonometric functions      22 Differential calculus, linearity of derivative      3 Differential calculus, ln(1+y)      15 Differential calculus, L’Hopital’s rule      24 Differential calculus, plotting functions      23 Differential calculus, radian measure      19 Differential calculus, series for hyperbolic functions      19 Differential calculus, Taylor series      8 Differential calculus, trigonometric functions      19 Differential equations      305 Differential equations, for damped oscillator      311 Differential equations, Frobenius method      318 Differential equations, Green’s function method for      344 Differential equations, heat equations      336 Differential equations, linear      306 Differential equations, nonlinear      306 Differential equations, order of      306 Differential equations, ordinary      305 (see also “Ordinary differential equations”) Differential equations, partial      305 (see also “Partial differential equations”) Differential equations, superposition principle for      306 Differential equations, wave equations      329 Differential operators      187 Differentials      29 Dimensionality      235 246 Dirac delta function      197 288 Dirac matrices      227 Displacement current      199 Divergence      182 Divergence, in other coordinates      186 Domain of analyticity      110 Domain of integration      61 Domain, simply connected      129 Dot product      151 Dot product, and inner product      237 Dot product, in terms of components      151 Drum, circular      332 Drum, square      330 Dual spaces      253 Dummy variable      43 e - the base of natural logs, power series definition      7 e - the base of natural logs, second definition      12 Eigenfunction      280 Eigenvalue problem      255 Eigenvalue problem, characteristic polynomial      257 Eigenvalue problem, degenerate case      263 Eigenvalue problem, of operator      284 Eigenvalue problem, of -iD operator      279 Eigenvalue problem, of coupled masses      263 Eigenvalue problem, of D operator      310 Eigenvalue problem, of quadratic forms      274 Eigenvalues      255 Eigenvectors      255 Einstein convention      296 Electrodynamics      193 Electrodynamics, Ampere’s law      198 Electrodynamics, continuity equation      193 Electrodynamics, displacement current      199 Electrodynamics, Lorentz force law      194 Electrodynamics, Maxwell’s equations      200 Electrodynamics, scalar potential      201 Electrodynamics, vector potential      201 Electrodynamics, wave equation      200 202 Epsilon neighborhood      110 Essential singularity      113 Essential singularity, relation to Taylor series      142 Euler’s identity      94 Exponential function, exp(elephant)      94 Exponential function, exp(x)      5 12 Exponential function, exp(z)      119 Field of vector space      231 Field, scalar and vector      158 Field, vector space      231 First order ordinary differential equation      315 Flux      163 Fourier integrals      287 Fourier series      281 Fourier series, coefficients of      281 Fourier series, completeness of      292 Fourier series, convergence of      286 Fourier series, exponential form      281 Fourier series, trigonometric      285 Fourier series, uniform convergence of      286 Fourier transform      287 Frobenius method      318 Frobenius method, indicial equation      325 Frobenius method, recursion relation in      318 Frobenius method, with singular coefficients      324 Function spaces      277 Function spaces, eigenvalue problem of 284 Function spaces, eigenvalue problem of -iD      279 Function spaces, inner product in      278 Function spaces, orthonormal basis for      279 Gamma function      43 Gauge transformation      202 Gaussian integral      71 Gauss’s theorem      184 Gibbs’ oscillation      338 Gradient      167 Gradient, and Lagrange multipliers      170 Gradient, in noncartesian coordinates      177 Gram — Schmidt Theorem      240 244 Gram — Schmidt Theorem, applied to Legendre polynomials      324 Green’s function method      344 Green’s Theorem      174 Hamiltonian      273 Harmonic function      115 Heat equation      336 Heat equation, derivation of      337 Heat equation, in d = 2      340 Heat equation, in d= 1      337 Heat equation, in polar coordinates      343 Hermite polynomials      323 Hermitian      221 Hermitian operators, and coupled masses      267 Hermitian operators, and orthogonal functions      279 Hermitian operators, and quadratic forms      274 Hermitian operators, diagonalization of      294 Hermitian operators, orthogonality of eigenvectors      260 Hermitian operators, reality of eigenvalues      260 Higher derivative vector operators      189 Hilbert space      278 Homology      191 Hyper complex numbers      125 Hyperbolic functions      13 Hyperbolic functions, in complex plane      119 Hyperbolic functions, Power series for      19 Hyperbolic functions, relation to trigonometric functions      121 Imaginary part      90 Impedance      101 Implicit differentiation      28 Indefinite integral      39 Independent variable      1 Indicial equation      325 Inner product spaces      237 239 Inner product spaces, postulates of      239 Integral calculus      28 Integral calculus, in many variables      61 Integral test for series      78 Integrals, analytical way      36 Integrals, and evaluation of areas      37 40 Integrals, antiderivative      37 Integrals, basics      33 Integrals, change of variables in      44 Integrals, composition law for      41 Integrals, definite      34 Integrals, dummy variables in      43 Integrals, in cylindrical coordinates      66 Integrals, in polar coordinates      64 Integrals, in spherical coordinates      66 Integrals, integrand      34 Integrals, integration by parts      42 Integrals, Jacobian      45 Integrals, linearity of      41 Integrals, lower limit of      32 Integrals, multiple      61 Integrals, numerical way      36 Integrals, of gaussian function      71 Integrals, of solid angle      70 Integrals, parametric differentiation      46 Integrals, primitive      37 Integrals, scale factor      65 Integrals, tricks of the trade      44 Integrals, upper limit of      34 Integrals, variable of      34 integrand      34 Integration by parts      42 Integration variable      34 Interval of convergence      10 81 Inverse hyperbolic functions      18 Inverse hyperbolic functions, miscellaneous problems in      25 Inverse matrix      211 212 216 Inverse trigonometric functions      22 Jacobian      45 65 Jacobian as a determinant      71 218 Lagrange multipliers      55 Lagrange multipliers and gradients      170 Laguerre’s equation      328 Laplace’s equation      115 340 344
1 2 Реклама     © Электронная библиотека попечительского совета мехмата МГУ, 2004-2021 | | О проекте