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Ayres F.J., Mendelson E. — Schaum's Outline of Calculus
Ayres F.J., Mendelson E. — Schaum's Outline of Calculus

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Название: Schaum's Outline of Calculus

Авторы: Ayres F.J., Mendelson E.

Аннотация:

Students can gain a thorough understanding of differential and integral calculus with this powerful study tool. They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide­­—more than 104,000 copies were bought of the prior edition—­­includes problems and examples using graphing calculators.


Язык: en

Рубрика: Математика/Анализ/Учебники по элементарному анализу/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 484

Добавлена в каталог: 06.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$e$      133 268
Abscissa      8
Absolute convergence      345
Absolute maximum and miminum      106
Absolute value      1
Acceleration, angular      112
Acceleration, in curvilinear motion      165
Acceleration, in rectilinear motion      112 247
Acceleration, tangential and normal components of      166
Acceleration, vector      165
Alternating series      345
Analytic proofs of geometric theorems      10
Angle, between two curves      91 173
Angle, of inclination      172
Angular velocity and acceleration      112
Antiderivative      206
Approximate integration      375
Approximations      371
Approximations, by differentials      196
Approximations, by the law of the mean      185
Approximations, of roots      197
Arc length      148 321
Arc length, by integration      305
Arc length, derivative of      148 174
Area, by integration      260
Area, in polar coordinates      316
Area, of a curved surface      451
Area, of a surface of revolution      309
Asymptote      40 201
Average ordinate      267
Average rate of change      73
Axis of rotation      272
Binormal vector      424
Bliss's theorem      252
Center of curvature      149
Centroid, of arcs      213 321
Centroid, of plane area      284 316 442
Centroid, of surface of revolution      321
Centroid, of volume      457
Chain rule      80 386
circle      31
Circle, equation of      31
Circle, of curvature      149
Circle, osculating      149
circular motion      112
Comparison Test      338
Complementary function      476
Completing the square      32
Components, of a vector      156
Components, of acceleration      166
Composite functions      80
Concavity      97 187
Conditional convergence      345
Conic sections      40
Constant of integration      206
Continuity      68 380
Convergence of series      333
Convergence of series, absolute      345
Convergence of series, conditional      345
Coordinate system, cylindrical and spherical      456
Coordinate system, linear      1
Coordinate system, polar      172
Coordinate system, rectangular      8
Cosecant      120
Cosine      120
Cotangent      120
Critical numbers, points, values      96
Cubic curve      42
Curl      427
Curvature      148 174
Curve tracing      201
Curvilinear motion      165 174
Cylindrical coordinates      456
Decay constant      269
Definite integral      251
Delta neighborhood      4
Derivative      73
Derivative, directional      417
Derivative, higher order      81 88
Derivative, of arc length      148 174
Derivative, partial      380
Derivative, second      81
Derivative, total      387
Differentiability      74
Differential      196
Differential equations      470
Differential equations, second-order      476
Differential, approximation by      196
Differential, partial      386
Differential, total      386
Differentiation      79
Differentiation, implicit      88
Differentiation, logarithmic      133
Differentiation, of exponential functions      133 269
Differentiation, of hyperbolic functions      141
Differentiation, of inverse hyperbolic functions      141
Differentiation, of inverse trigonometric functions      129
Differentiation, of logarithmic functions      133 268
Differentiation, of trigonometric functions      122
Differentiation, of vector functions      158
Differentiation, partial      380
Direction cosines      399 402
Direction numbers      402
Directional derivative      417
Directrix of a parabola      43
Disc method      272
Discontinuity      68
Distance formula      10
Divergence of a vector function      427
Domain of a function      52
Double integral      435
Ellipses      39
Ellipses, center, eccentricity, foci, major axis, minor axis of      45
Equations, graphs of      39
Evolute      149
Expansion in power series      360
Exponential functions      133 269
Exponential growth and decay      269
Extended law of the mean      184
Extent of a graph      201
First-derivative test      97
Fluid pressure      297
Foci, of a hyperbola      46
Foci, of an ellipse      45
Focus of a parabola      43
Force, work done by a      301
Functions      52
Functions, composite      80
Functions, continuous      68
Functions, decreasing      96
Functions, domain of      52
Functions, exponential      133 269
Functions, graphs of      53
Functions, homogeneous      393
Functions, hyperbolic      141
Functions, implicit      88 394
Functions, increasing      96
Functions, inverse      79
Functions, inverse trigonometric      129
Functions, logarithmic      133 268
Functions, one-to-one      79
Functions, range of      52
Functions, trigonometric      120
Fundamental theorem of integral calculus      252
Generalized law of the mean      184
Gradient      417 426
Graphs of equations      39
Graphs of functions      53
Growth constant      269
Halflife      269
Homogeneous bodies      284
Homogeneous, equation      470
Homogeneous, function      393 470
Hyperbolas      40
Hyperbolas, asymptotes of      40
Hyperbolas, center, conjugate axes, eccentricity, foci, transverse axes, vertices of      46
Hyperbolas, equilateral      49
Hyperbolic functions      141
Hyperbolic functions, differentiation      141
Hyperbolic functions, integration of      244
Hyperbolic functions, inverse      141
Implicit differentiation      88
Implicit functions      88 394
Improper integrals      326
Increment      73
Indefinite integral      206
Indeterminate forms      190
Inequalities      2
Infinite sequences      58 322
Infinite sequences, general term of      58
Infinite sequences, limit of      58
Infinite series      333
infinity      60
Inflection point      97
Instantaneous rate of change      73
Integral, definite      251
Integral, double      435
Integral, improper      326
Integral, indefinite      206
Integral, iterated      436
Integral, line      427
Integral, test for convergence      338
Integral, triple      456
integrand      206 251
Integrating factor      470
Integration, approximate      375
Integration, by partial fractions      234
Integration, by parts      219
Integration, by substitution      207 239
Integration, by trigonometric substitutions      230
Integration, of exponential functions      269
Integration, of hyperbolic functions      244
Integration, of trigonometric functions      225
Integration, standard formulas of      206
Intercepts      201
Interval of convergence      354
Intervals      2
Inverse function      79
Inverse trigonometric functions      129
Inverse-hyperbolic functions      141
Irreducible polynomial      234
Iterated integral      436
Latus rectum of a parabola      43
Law of the mean      183
Length of arc      305 321
Limit, of a function      58 380
Limit, of a sequence      58
Limit, right and left      59
Line      17 402
Line integral      427
Line, equations of      19 402
Line, slope of      17
Linear differential equation of the first order      470
Logarithmic differentiation      133
Logarithmic functions      133 268
L’Hospital's rule      190
Maclaurin's formula      367
Maclaurin's series      360
Mass      284 466
Maximum and minimum, applications      106
Maximum and minimum, of functions of a single variable      96
Maximum and minimum, of functions of several variables      418
Mean, law of the      183
Midpoint formulas      10
Moments of inertia, of arcs      213
Moments of inertia, of plane area      292 442
Moments of inertia, of surface of revolution      213
Moments of inertia, of volume      292 458
Moments of plane areas and solids      284
Motion, circular      112
Motion, curvilinear      165
Motion, rectilinear      112
Natural logarithm      268
Normal line to a plane curve      91
Normal line to a plane curve, equation of      91
Normal line to a surface      411
Normal plane to a space curve      411 424
Octants      398
One-to-one function      79
Operations on series      349
Ordinate      8
Osculating circle      149
Osculating plane      424
Pappus, theorems of      285 213
Parabolas      39
Parabolas, focus, directrix, latus rectum, vertex of      43
Parallel-axis theorem      292
Parametric equations      145 424
Partial derivatives      380
Partial differential      386
Partial fraction      234
Particular solution      476
Plane      402
Point of inflection      97
Point-slope equation of a line      20
Polar coordinates      172
Pole      172
Polynomial test for convergence      343
Position vector      398
Power series      354
Power series, approximations using      372 376
Power series, differentiation of      355
Power series, integration of      355
Power series, interval of convergence of      354
Power series, uniform convergence of      355
Principal normal      424
Prismoidal formula      376
Quadrants      9
Radian measure      120
Radius, of curvature      148
Radius, of gyration      292
Range of a function      52
Rate of change      73
Ratio Test      338 345
Real numbers      1
Rectangular coordinate system      8
Rectifying plane      424
Rectilinear motion      112
Reduction formulas      219
Related rates      116
Relative maximum and minimum      96 418
Remainder after n terms of a series      350 367
Right-handed system      398
Rolle's theorem      183
Root test for convergence      344
Scalars      155
Secant function      120
Second-derivative test      97
Sequences      58 332
Sequences, bounded      332
Sequences, convergent and divergent      332
Sequences, limit of      332
Sequences, nondecreasing and nonincreasing      332
Series, infinite      333
Series, infinite, alternating      345
Series, infinite, computations with      371
Series, infinite, convergent      333
Series, infinite, divergent      333
Series, infinite, geometric      335
Series, infinite, harmonic      335
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