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Demidovich B. (ed.) — Problems in mathematical analysis
Demidovich B. (ed.) — Problems in mathematical analysis

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Название: Problems in mathematical analysis

Автор: Demidovich B. (ed.)

Аннотация:

This collection of problems and exercises in mathematical anaUysis covers the maximum requirements of general courses inhigher mathematics for higher technical schools. It contains over3,000 problems sequentially arranged in Chapters I to X coveringall branches of higher mathematics (with the exception ofanalytical geometry) given in college courses. Particular attention isgiven to the most important sections of the course that requireestablished skills (the finding of limits, differentiation techniques,the graphing of functions, integration techniques, the applicationsof definite integrals, series, the solution of differential equations)


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-е издание

Год издания: 1970

Количество страниц: 496

Добавлена в каталог: 06.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute error      367
Absolute value of a real number      11
Absolutely convergent series      296 297
Acceleration vector      236
Adams' formula      390
Adams' method      389 390 392
Agnesi, witch of      18 156 480
Algebraic functions      48
Angle between two surfaces      219
Angle of contingence      102 243
Angle of contingence of second kind      243
Antiderivative      140 141
Antiderivative, generalized      143
Approximate numbers      367
Approximate numbers, addition of      368
Approximate numbers, division of      368
Approximate numbers, multiplication of      368
Approximate numbers, powers of      368
Approximate numbers, roots of      368
Approximate numbers, subtraction of      368
Approximation, successive      377 385
Arc length of a curve      158—161
Arc length of a space curve      234
Archimedes, spiral of      20 65 66 105 487
Area in polar coordinates      155 256
Area in rectangular coordinates      153 256
Area of a plane region      256
Area of a surface      166—168 259
Argument      11
Astroid      20 63 105 486
Asymptote      93
Asymptote, left horizontal      94
Asymptote, left inclined      94
Asymptote, right horizontal      93
Asymptote, right inclined      93
Asymptote, vertical      93
Bending point      84
Bernoulli's equation      333
Bernoulli's lemniscate      155 486
Beta-function      146 150
Binormal      238
boundary conditions      363
Branch of a hyperbola      20 480
Broken-line method, Euler's      326
Cardioid      20 105 486
Catenary      104 105 484
Catenoid      168
Cauchy's integral test      295
Cauchy's test      293 295
Cauchy's theorem      75 326
Cavalieri's "lemon"      165
Centre of curvature      103
Change of variable      211—217
Change of variable in a definite integral      146
Change of variable in a double integral      252—254
Change of variable in an indefinite integral      113
Characteristic equation      356
Characteristic points      96
Chebyshev's conditions      127
Chord method      376
circle      20 104
Circle of convergence      306
Circle of curvature      103
Circle, osculating      103
Circulation of a vector      289
Cissoid      232
Cissoid of Diodes      18 485
Clairaut's equation      339
Closed interval      11
Coefficients, Fourier      318 393 394
Comparison Test      143 293 294
Composite function      12 49
Concave down      91
Concave up      91
Concavity, direction of      91
Conchoid      232
Condition, Lipschitz      385
Conditional extremum      223—225
Conditionally (not absolutely) convergent series      296
Conditions, boundary      363
Conditions, Chebyshev's      127
Conditions, Dirichlet      318 319
Conditions, initial      323 363
Contingence, Angle of      102 243
Continuity of functions      36
Continuous function      36
Continuous function, properties of      38
Convergence, circle of      306
Convergence, interval of      305
Convergence, radius of      305
Convergence, region of      304
Convergence, uniform      306
Convergent improper integral      143 270
Convergent Series      293
Coordinates of centre of gravity      170
Coordinates, generalized polar      255
Correct decimal places in a broad sense      367
Correct decimal places in a narrow sense      367
Cosine curve      481
Cotangent curve      481
Coupling equation      223
Critical point of the second kind      92
Critical points      84
Cubic parabola      17 105 234 480
Curl of a vector field      288
Curvature, centre of      103
Curvature, circle of      103
Curvature, of a curve      102 242
Curvature, radius of      102
Curvature, second      243
Curve, cosine      481
Curve, cotangent      481
Curve, discriminant      232 234
Curve, Gaussian      92
Curve, integral      322
Curve, logarithmic      484
Curve, probability      19 484
Curve, sine      481
Curve, tangent      481
Cusp      230
Cycloid      105 106 486
d'Alembert's test      295
Decreasing function      83
Definite integral      138
DEL      288
Dependent variable      11
Derivative      43
Derivative of a function in a given direction      193
Derivative of an implicit function      57
Derivative of an inverse function      57
Derivative of functions, represented parametrically      57
Derivative of the second order      66
Derivative, left-hand      44
Derivative, logarithmic      55
Derivative, nth      67
Derivative, right-hand      44
Derivative, second      66
Derivatives of higher orders      66—69
Derivatives, one-sided      43
Derivatives, table of      47
Descartes, folium of      20 21 232 485
Determinant, functional      264
Determining coefficients, first method of      122
Determining coefficients, second method of      122
Diagonal table      389
Dicriminant curve      232 234
Difference of two convergent series      298
Differential equation      322
Differential equation, homogeneous linear      349
Differential equation, inhomogeneous linear      349
Differential equations of higher powers, first-order      337
Differential equations, first-order      324
Differential equations, forming      329
Differential equations, higher-order      345
Differential equations, linear      349 351
Differential of an arc      101 234
Differential, first-order      71
Differential, higher-order      198
Differential, principal properties of      72
Differential, second      198
Differential, second-order      72
Differential, total, integration of      202—204
Differentials of third and higher orders      72
Differentials, method of      343
Differentiating a composite function      47
Differentiation      43
Differentiation of implicit functions      205—208
Differentiation, tabular      46
Diodes, cissoid of      18 485
Direction field      325
Direction of concavity      91
Dirichlet, conditions      318 319
Dirichlet, function      40
Dirichlet, series      295 296
Dirichlet, Theorem      318
Discontinuity      37
Discontinuity of the first kind      37
Discontinuity of the second kind      38
Discontinuity, infinite      38
Discontinuity, removable      37
Discontinuous function      270
Discriminant      222
Divergence of a vector field      288
Divergent improper integral      143 270
Divergent series      293 294
Domain      11
Domain of definition      11
Double integral      246
Double integral in curvilinear coordinates      253
Double integral in polar coordinates      252
Double integral in rectangular coordinates      246
Double point      230
Elimination, method of      359
ellipse      18 20 104 485
Energy, kinetic      174
Envelope of a family of plane curves      232
Envelope, equations of      232
Epicycloid      283
Equal effects, principle of      369
Equation of a normal      60 218
Equation of a tangent      60
Equation of a tangent plane      218
Equation with variables separable      327 328
Equation, Bernoulli's      333
Equation, characteristic      356
Equation, Clairaut's      339
Equation, coupling      223
Equation, differential      322
Equation, Euler's      357
Equation, exact differential      335
Equation, first-order differential      324
Equation, homogeneous      330 351 356
Equation, homogeneous linear differential      332 349
Equation, inhomogeneous      349 351 356
Equation, Lagrange's      339
Equation, Laplace's      289 291
Equation, linear      332
Equivalent functions      33
Error, absolute      367
Error, limiting absolute      367
Error, limiting relative      367
Error, relative      367
Euler integral      146
Euler — Poisson integral      272
Euler's broken-line method      326
Euler's equation      357
Even function      13
Evolute of a curve      103
Evolvent of a circle      486
Evolvent of a curve      104
Exact differential equation      335
Exponential functions      49 55 483
Extremal point      84
Extremum of a function      83 83 222
Extremum, conditional      223—225
Factor, integrating      335
Field theory      288—292
Field, direction field      325
Field, nonstationary scalar or vector      288
Field, potential vector      289
Field, scalar      288
Field, solenoidal vector      289
Field, stationary scalar or vector      288
Field, vector      288
First-order differential      71
First-order differential equations      324
Flow lines      288
Flux of a vector field      288
Folium of Descartes      20 21 232 485
Force lines      288
Form, Lagrange's      311
Formula, Adams'      390
Formula, Green's      276 281 282
Formula, Lagrange's      145
Formula, Lagrange's interpolation      374
Formula, Leibniz      67
Formula, Maclaurin's      77 220
Formula, Newton — Leibniz      140 141 275
Formula, Newton's interpolation      372
Formula, Ostrogradsky — Gauss      286—288
Formula, parabolic      382
Formula, Simpson's      382—384
Formula, Stokes'      285 286 289
Formula, Taylor's      77 220
Formula, trapezoidal      382
Formulas, reduction      130 135
Four-leafed rose      487
Fourier coefficients      318 393 394
Fourier series      318 319
Fraction, proper rational      121
Function      11
Function of a function      12
Function, composite      12 49
Function, continuous      36
Function, continuous, properties of      38
Function, decreasing      83
Function, Dirichlet      40
Function, discontinuous      270
Function, even      13
Function, implicit      12
Function, increasing      83
Function, Lagrange      223 224
Function, multiple-valued      11
Function, periodic      14
Function, single-valued      11
Function, vector      235
Functional determinant      264
Functional series      304
Functions, algebraic      48
Functions, equivalent      33
Functions, exponential      49 55 483
Functions, hyperbolic      49 484
Functions, hyperbolic, integration of      133
Functions, inverse      12
Functions, inverse circular      48
Functions, inverse hyperbolic      49
Functions, inverse trigonometric      482 483
Functions, linearly dependent      349
Functions, linearly independent      349
Functions, logarithmic      49
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