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Shankar R. — Basic Training In Mathematics
Shankar R. — Basic Training In Mathematics

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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: en

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
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Предметный указатель
$D^2$ 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 $D^2$ 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 $D^2$      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
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