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Franklin P. — Differential and integral calculus
Franklin P. — Differential and integral calculus

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Название: Differential and integral calculus

Автор: Franklin P.

Аннотация:

This book is designed to serve as a basic but full introduction to the field of differential and integral calculus. It is a fine textbook for a two or three-semester course, especially as it contains review material on trigonometric, exponential and logarithmic fUnctions and highlights of plane and solid analytic geometry-prerequisites which may not have been previously covered by the student. It is equally valuable as supplementary reading for classwork or as a self-instruction text. After establishing the basis for differential calculus in the first chapter, the author moves quickly to the discussion of integration of pOwer functions, leaving the more complex study of the definite integral regarded as the limit of a summation until later in the book. Among Other topics covered are parametric funCtions, force components in polar coordinates, Duhamel's theorem, extrema of functions of two or more variables, methods and applicalions of integration, infinite series, Taylor'S series, and multiple integrals. A chapter on vectors and surfaces in space is in line with the most modern approach to undergraduate teaching.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1953

Количество страниц: 679

Добавлена в каталог: 02.05.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abscissa      5
Absolute convergence      417
Absolute value      2 436
Acceleration      24 51
Acceleration vector      230 526
Acceleration vector, components of      239 260
Acceleration vector, components of, in three dimensions      526
Acceleration vector, components of, radial and transverse      271
Acceleration vector, components of, tangential and normal      240
Acceleration, angular      170
Acceleration, positive and negative      52
Adiabatic expansion      303
Alternating series      415
Amplitude      173
Anchor ring      360
angle      144
Angle between two curves      139
Angle between two curves, from polar form      260
Angle between two planes      510
Angle between two straight lines      113
Angle between two straight lines, in space      515
Angle from radius vector to tangent      254
Angular acceleration      170
Angular velocity      170
Approximations, by differentials      282 489
Approximations, by series      440
Arc length      86 305 362
Arc length from parametric form      310 313
Arc length from polar form      309
Arc length of a space curve      525
Arc length, differential of      87 223 308
Arc length, differential of, in polar form      264 309
Arcs, concave, upward and downward      54
Area      96 101 294 357
Area as a limit      288
Area by double integration      544
Area by double integration in polar coordinates      549
Area from parametric form      303
Area from polar form      297 358
Area of a curved surface      559
Area of a surface of revolution      313 363
Argument      4
Arithmetic progression      292 399
Astroid      358
Astroid, evolute of the ellipse      234 502
Asymptotes      15
Asymptotes from polar form      265
Asymptotes of a hyperbola      130
Attraction, gravitational      393
Average value      366
Average value by multiple integration      574
Average, weighted      367
Axis of a hyperbola      129
Axis of a parabola      122
Axis of a quadric surface      532
Axis of an ellipse      126
Axis of revolution      530
Axis of symmetry      142
Axis, coordinate      5 504
Beams, deflection of      619
Bending moment      619
Bernoulli's differential equation      584
Binomial series      426
Cables, equilibrium of      618
Cardioid      361 365
Cartesian coordinates      5
Catenary      476 621
Cauchy's mean value theorem      447
Center, of gravity      369
Center, of gravity, of a solid      375
Center, of gravity, of a solid, by triple integration      567 573
Center, of pressure      390
Centroid, of a plane arc      373
Centroid, of a plane area      370
Centroid, of a plane area, by double integration      554
Centroid, of a solid of revolution      375
Centroid, of a surface of revolution      376
circle      120 211
Circle as special ellipse      120
Circle in polar form      252
Circle, sector of      145 298
Circuits, electrical and mechanical      617
Circular measure      144
Clairaut's differential equation      560
Closed interval      2
Comparison tests for series      406
Comparison tests for series, using limits      409
Complex number      467
Components of vectors      512
Composition of ordinates      161
Compound interest law      198
Computation from series      416 428 439
Concave arcs, upward or downward      54
Cone, elliptic      534
Cone, of revolution      530
Constant      4
Constant function      8
Constant, arbitrary      91
Constant, of integration      91 580
Continuous function      13
Continuous function of two variables      477
Convergence, absolute      417
Convergence, interval of      421
Convergent improper integrals      318
Convergent infinite series      401
Coordinate axes      5 504
Coordinates in space      504
Coordinates in space, cylindrical      551
Coordinates in space, spherical      572
Coordinates, Cartesian      5
Coordinates, polar      245
Coordinates, rectangular      5
Cosecants      149
Cosecants, differentiation of      160
cosines      145
Cosines, differentiation of      157
Cosines, Law of      151
Cotangents      148
Cotangents, differentiation of      159
Cubical parabola      226
Curvature      223 227
Curvature in polar form      267
Curvature, center of      230
Curvature, circle of      230
Curvature, radius of      229
Curve tracing      142
Curves, in polar form      246
Curves, rose-leaf      248 256
Curves, slopes of      see "Slopes"
Curves, smooth      28 305
Curves, space      524
Curves, transition      225
Cycloid      212
Cycloid, evolute of      235
Cylindrical coordinates      551
Cylindrical surfaces      529
Cylindrical surfaces, quadric      534
Damped harmonic motion      204
Decreasing functions      46
Definite integrals      99 288
Definite integrals, change of variable in      303
Definite integrals, differentiation of      302
Definite integrals, properties of      300
Definite integrals, Wallis'      351 629
Deflection of beams      619
Degree, angular unit      144
Degree, of a differential equation      578
Dependent variable      4 477
derivatives      32 see
Derivatives, directional      536
Derivatives, notation for      33 478
Derivatives, partial      478
Derivatives, positive and negative      47
Derivatives, second-order      see "Second derivatives"
Determinant      521n
Differentiable function      32
Differential      83 274
Differential equations      578
Differential equations, applications of      592—600 613—626
Differential equations, applications of, geometric      592
Differential equations, applications of, involving rates      596
Differential equations, applications of, physical      596—600 613—626
Differential equations, applications of, to motion      613 622
Differential equations, Bernoulli      584
Differential equations, Clairaut      590
Differential equations, degree of      578
Differential equations, Euler — Caucliy      613
Differential equations, exact      587
Differential equations, first-order, first-degree      582
Differential equations, first-order, higher-degree      589
Differential equations, homogeneous      586 604n
Differential equations, linear      578 583 603
Differential equations, linear, reducible to      584
Differential equations, linear, with constant coefficients      605 608
Differential equations, order of      578
Differential equations, ordinary      578
Differential equations, partial      479 493 578
Differential equations, second-order      601
Differential equations, separable      582
Differential, formulas for      276
Differential, found from the derivative      276
Differential, total      480 485
Differentiating operators      33 404 606
Differentiation      34
Differentiation of $u^{n}$      39
Differentiation of $u^{v}$      197
Differentiation of a constant      37
Differentiation of composite functions      68
Differentiation of composite functions, partial      483 485
Differentiation of cu      40
Differentiation of exponential functions      194 195
Differentiation of fractions      64
Differentiation of inverse functions      70
Differentiation of inverse trigonometric functions      165—169
Differentiation of logarithms      193 195
Differentiation of polynomials      43
Differentiation of powers      65
Differentiation of products      38
Differentiation of sums      42
Differentiation of trigonometric functions      155—160
Differentiation of vectors      526
Differentiation of x      38
Differentiation, geometric      82
Differentiation, implicit      72 279 487
Differentiation, linearity of      42
Differentiation, logarithmic      196
Differentiation, partial      478
Direction angles      505
Direction cosines      505
Direction ratios      505
Directional derivative      536
Directrix      252
Directrix of a parabola      121
Discontinuous function      13 17
Distance between two points      119
Distance between two points in space      507
Distance, from line to point      117
Distance, from plane to point      518
Divergent improper integrals      318
Divergent infinite series      401
Divergent infinite series, test for      402
Double integrals      512
Duhamel's theorems      311 543 562
e      184
Eccentricity      126 130 253
Electrical and mechanical circuits      017
Element of integration      84
ellipse      124
Ellipse in parametric form      211
Ellipse in polar form      253
Ellipsoid      531
Elliptic cone      534
Envelopes      500
Envelopes, evolutes as      502
Epicycloid      214
Equilibrium of cables      618
Errors, percentage      284 491
Errors, small      283 489
Euler — Cauchy differential equation      613
Euler's expressions      468
Evolutes      233
Evolutes as envelopes      502
Evolutes, properties of      236
Expansion, adiabatic      393
Exponential functions      182
Exponential functions of complex values      467 470
Exponential functions, differentiation of      194 195
Exponential functions, integration of      336
Exponential functions, table of      631
Exponents, laws of      182
Factor Theorem      48n
Factorial number      398
First octant      505
First-degree equations      27 110
First-degree equations of planes      510 517
Focus, of a hyperbola      128 253
Focus, of a parabola      121 253
Focus, Of an ellipse      124 253
frequency      173
Functions      4
Functions of complex values      467
Functions of two variables      477
Functions, composite      68
Functions, constant      8
Functions, continuous      13 477
Functions, decreasing      46
Functions, differentiable      32
Functions, discontinuous      13 17
Functions, graphs of      5 55
Functions, implicit      72
Functions, increasing      45
Functions, inverse      70
Functions, limits of      8 10
Functions, logarithmic      182
Functions, rational      14 17
Fundamental system of solutions      604
Fundamental theorem of the integral calculus      291
Fundamental theorem of the integral calculus for double integrals      543
Fundamental theorem of the integral calculus for triple integrals      562
Fundamental theorem of the integral calculus, Duhamel modifications of      311 543 562
Geometric progression      399
Gradient      536
Graphs of functions      5 55
Gravitational attraction      393
Gravity, center of      see "Centroid"
Gyration, radius of      381
Hospital      see "L'Hospital's rule"
Hyperbola      128
Hyperbola in polar form      253
Hyperbolic functions      470
Hyperbolic functions, inverse      473
Hyperbolic functions, table of      631
Hyperboloid      532 533
Hypocycloid      215
i      467
Imaginary unit      467
Implicit differentiation      72 279 487
Implicit functions      72
Improper integrals      318
Increasing functions      45
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