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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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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 39 Differentiation of 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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