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Franklin P. — Differential and integral calculus
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Название: Differential and integral calculusАвтор: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1953Количество страниц: 679Добавлена в каталог: 02.05.2013Операции: Положить на полку |
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Increments 30 Increments, law of finite 477 Indefinite integrals 91 Independent variables 4 477 Indeterminate forms 452—457 Induction, mathematical 39 Inequality symbols 2 Infinite series 397 Infinite series, absolutely convergent 417 Infinite series, alternating 415 Infinite series, convergent 401 Infinite series, divergent 401 402 Infinite series, sum of an 401 Infinite series, tests for, comparison 406 409 Infinite series, tests for, integral 405 Infinite series, tests for, ratio 412 Infinitesimals 18 Infinitesimals, theorems on 19 infinity 11 Inflection, point of 55 Integrable combinations 587 Integral curve 579 Integral test for series 405 Integrals 90 see Integrals, double 542 Integrals, improper 318 Integrals, indefinite 91 Integrals, repeated 540 Integrals, table of 627 Integrals, table of, use of 356 Integrals, triple 561 integrand 91 Integrating factors 584 588 Integration 90 Integration between limits 98 Integration by parts 347 Integration by substitution 303 342—347 355 Integration of exponential functions 336 Integration of polynomials 92 Integration of powers 92 322 Integration of rational fractions 351 Integration of trigonometric functions 334 337—342 Integration, constant of 91 580 Integration, element of 84 Integration, fundamental theorem of 291 Integration, leading to, inverse functions 329 Integration, leading to, logarithms 327 Integration, numerical 459 460 463 Integration, using series 226 429 435 438 interval 2 Interval of convergence 421 Inverse functions 70 Inverse hyperbolic functions 473 Inverse trigonometric functions 163—169 Involute 237 Involute of the circle 217 Isothermal expansion 393 Kepler's laws 625 l'Hospital's rule 453 454 456 Leading term, principle of 12 Lemniscate 218 251 Length of arc see "Arc length" Limacon 248 limits of functions 8 10 Limits of integration 98 Limits of variables 7 Limits, calculation of 9 Limits, operations on 8 Limits, theorems on 20 Line, secant 27 524 see "Tangent Linear dependence 604 Linear differential equation 578 583 603 Locus of an equation 5 110 Logarithmic differentiation 196 Logarithmic functions 182 Logarithmic spiral 257 Logarithms, computation of 439 Logarithms, differentiation of 193 195 Logarithms, natural and common 189 Logarithms, natural and common, tables of 630 632 Logarithms, rules for 183 Maclaurin's series 432 Maclaurin's series with the remainder 451 Maclaurin's series, special 434 438 Mathematical induction 39 Maximum and minimum 54 60 74 77 Maximum and minimum of a function of two variables 496 Mean value 366 Mean value by multiple integration 574 Mean value theorem 45 447 Mean Value Theorem, Cauchy's 447 Meridian section 530 Mid-point 113 513 Minimum see "Maximum and minimum" Moment of inertia 380 Moment of inertia about a parallel-axis 387 Moment of inertia of a plane area 382 Moment of inertia of a plane area by double integration 556 Moment of inertia of a solid 386 Moment of inertia of a solid by triple integration 569 573 Moment of inertia polar 384 Moments 369—390 Moments, about straight lines 369 389 Moments, about straight lines, by double integration 554 Moments, bending 619 Moments, with respect to planes 374 Moments, with respect to planes, by triple integration 567 569 573 Motion, harmonic, damped 204 Motion, harmonic, simple 173 Motion, in a plane 622 Motion, on curves 87 Motion, on straight lines 51 613 Natural logarithms 189 Natural logarithms, table of 630 Newton's method of solving equations 57 286 466 Normal length of 140 Normal length of, polar 265 Normal length of, to a plane curve 135 Normal length of, to a surface 528 Notation, for derivatives 33 478 Notation, for sums 290 398 Number scale 1 Number, complex 467 Number, real 1 Numerical integration 459 460 463 Numerical value 20 Octant, first 505 Open interval 2 Order of a differential equation 578 Ordinary differential equation 578 Ordinates 5 Ordinates, composition of 161 Orthogonal trajectories 583 P-series 405 408 Pappus, theorems of 378 parabola 121 Parabola in polar form 253 Parabola, cubical 226 Parabola, semicubical 138 234 502 Paraboloid 533 Parallel-axis theorem 387 PARAMETER 87 210 Parametric equations 210 Partial derivative 478 Partial differential equation 479 493 578 Partial fractions 351 Partial sum of a series 399 Percentage error 284 401 Perihelion 623 Period 173 Plane, equation of 510 517 Plane, tangent 528 Planet, orbit of 623 625 Point of inflection 55 Polar coordinates 245 Polar moment of inertia 384 Pole 244 Power series 420 424 Power series, operations on 427 435 Pressure, liquid 106 312 390 Pressure, liquid, center of 390 Projections 506 Psi 393 Quadrants 5 145 Quadratic expressions 332 Quadratic formula 49 Quadric surfaces 531 Radian measure 144 Radius vector 245 Radius, of curvature 229 Radius, of curvature, in polar form 267 Radius, of gyration 381 Range of a variable 4 Rates, of change 23 24 31 Rates, related 79 Ratio test for series 412 Ratio test for series, refined 413 Rational functions 14 17 Real number 1 Rectangular coordinates 5 Relative error 284 491 Remainder in Taylor's series 450 Repeated integrals 540 Revolution, axis of 530 Rolle's theorem 447 Roots of equations 57 286 466 Rose-leaf curves 248 256 scalar 511 Scalar product 514 Scale, number 1 Secant line 27 524 Secants, differentiation of 159 Secants, trigonometric 149 Second derivatives 50 Second derivatives from parametric form 220 280 Second derivatives, partial 492 Second derivatives, positive and negative 55 Second-degree equations 120—132 133—134 Second-degree equations of surfaces 531 Sector of a circle 145 298 Semicubical parabola 138 234 502 SEQUENCE 397 Series 398 see "Maclaurin's "Power "Taylor's Series, alternating 415 Series, binomial 426 Series, comparison tests for 406 409 Series, geometric 401 402 Series, partial sum of 399 Series, ratio test for 412 413 simple harmonic motion 173 Simpson's rule 463 SINEs 145 Sines, differentiation of 156 Sines, law of 150 Singular solutions 590 Slopes 26 28 Slopes of curves 28 Slopes of curves, from parametric form 217 279 Slopes of curves, from polar form 258 Slopes of straight lines 26 Smooth curve 28 305 Solutions of differential equations 579 Solutions of differential equations, general 580 Solutions of differential equations, particular 580 596 605 Solutions of differential equations, singular 590 Speed 52 87 526 Speed, increasing or decreasing 52 Sphere 528 532 Spherical coordinates 572 Spheroid 532 Spiral, logarithmic or equiangular 257 Spiral, of Archimedes 248 Spiral, transition 226 straight lines 26 110 Straight lines in space 508 Straight lines, angle between 113 Straight lines, equations of 26 110 210 Straight lines, equations of, in polar form 251 Straight lines, motion on 51 613 Straight lines, slopes of 26 Subnormal 140 Subnormal, polar 265 Subtangent 140 Subtangent, polar 265 Sums, notation for 290 398 Surfaces 527 Surfaces of revolution 530 Surfaces of revolution, area of 313 363 Surfaces, area of curved 559 Surfaces, cylindrical 529 Surfaces, quadric 534 Symmetry, axis of 142 Tables, common logarithm 632 Tables, exponential and hyperbolic function 631 Tables, integral 627 Tables, natural logarithm 630 Tables, trigonometric function 634 Tangent line 28 135 Tangent line to a space curve 525 Tangent line, horizontal or vertical 136 217 Tangent plane 528 Tangent, length of 140 Tangent, polar 264 Tangents, differentiation of 158 Tangents, trigonometric 148 Taylor's series 443 Taylor's series for two variables 495 Taylor's series with the remainder 450 Taylor's series, incremental form of 444 Taylor's series, special 446 Torus 360 Total differential 480 485 Transition curves 225 Transition spiral 226 Trapezoidal rule 460 Trigonometric functions 144 Trigonometric functions of complex values 467 470 Trigonometric functions, differentiation of 155—160 Trigonometric functions, graphs of 161 Trigonometric functions, inverse 163—169 Trigonometric functions, table of 634 Trigonometric identities 147—150 Triple integrals 561 Trochoid 213 Undetermined coefficients 609 Unit vectors 240 269 512 Value, absolute 2 436 Value, numerical 2 Variables 4 Variables, limits of 7 Vector product 520 Vectors in space 510 Vectors in space, components of 512 Vectors, differentiation of 526 Vectors, radius 245 Vectors, unit 240 269 512 Velocity 23 51 Velocity in space 526 Velocity vector 238 526 Velocity vector, components of 238 240 269 526
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