← 学习库 OpenStax Calculus Vol 2 目录

Index

Calculus Volume 2Index

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A absolute convergence 5.5 Alternating Series absolute error 3.6 Numerical Integration air resistance 4.5 First-Order Linear Equations Airy’s equation 6.4 Working with Taylor Series algebraic function 3.1 Integration by Parts alternating series 5.5 Alternating Series alternating series test 5.5 Alternating Series angular coordinate 7.3 Polar Coordinates annuities 6.2 Properties of Power Series annuity payments 6 Review Exercises *aphelion* 1.3 The Fundamental Theorem of Calculus arc length 2.4 Arc Length of a Curve and Surface Area Archimedean spiral 7.3 Polar Coordinates Archimedes 1.1 Approximating Areas *area density* 2.5 Physical Applications area under the curve 1.1 Approximating Areas arithmetic sequence 5.1 Sequences asymptotically semi-stable solution 4.2 Direction Fields and Numerical Methods asymptotically stable solution 4.2 Direction Fields and Numerical Methods asymptotically unstable solution 4.2 Direction Fields and Numerical Methods autonomous differential equation 4.3 Separable Equations average value of the function 1.2 The Definite Integral B bald eagle 1.4 Integration Formulas and the Net Change Theorem binomial series 6.4 Working with Taylor Series bounded above 5.1 Sequences bounded below 5.1 Sequences bounded sequence 5.1 Sequences C carbon dating 2.8 Exponential Growth and Decay cardioid 7.3 Polar Coordinates carrying capacity 4.4 The Logistic Equation catenary 2.9 Calculus of the Hyperbolic Functions center of mass 2.6 Moments and Centers of Mass centroid 2.6 Moments and Centers of Mass chambered nautilus Introduction, 7.3 Polar Coordinates change of variables 1.5 Substitution *cissoid of Diocles* 7.4 Area and Arc Length in Polar Coordinates comparison test 5.4 Comparison Tests compound interest 2.8 Exponential Growth and Decay computer algebra systems (CAS) 3.5 Other Strategies for Integration conditional convergence 5.5 Alternating Series conic section 7.5 Conic Sections convergence of a series 5.2 Infinite Series convergent sequence 5.1 Sequences *coupon collector’s problem* 5.3 The Divergence and Integral Tests cross-section 2.2 Determining Volumes by Slicing curtate cycloid 7.1 Parametric Equations cusps 7.1 Parametric Equations cycloid 7.1 Parametric Equations D deceleration 1.4 Integration Formulas and the Net Change Theorem definite integral 1.2 The Definite Integral density function 2.5 Physical Applications differential equation 4.1 Basics of Differential Equations direction field (slope field) 4.2 Direction Fields and Numerical Methods directrix 7.5 Conic Sections discriminant 7.5 Conic Sections disease epidemics 4.2 Direction Fields and Numerical Methods disk method 2.2 Determining Volumes by Slicing displacement 1.2 The Definite Integral, 1.4 Integration Formulas and the Net Change Theorem divergence of a series 5.2 Infinite Series divergence test 5.3 The Divergence and Integral Tests divergent sequence 5.1 Sequences doubling time 2.8 Exponential Growth and Decay drugs in the bloodstream 4.3 Separable Equations *dummy variable* 1.1 Approximating Areas, 1.2 The Definite Integral E Earth’s orbit 7.1 Parametric Equations eccentricity 7.5 Conic Sections elliptic integral 6.4 Working with Taylor Series *epitrochoid* 7.1 Parametric Equations equilibrium solution 4.2 Direction Fields and Numerical Methods *Euler transform* 5.5 Alternating Series Euler’s constant 5.2 Infinite Series Euler’s formula 6 Review Exercises Euler’s Method 4.2 Direction Fields and Numerical Methods evaluation theorem 1.3 The Fundamental Theorem of Calculus even function 1.4 Integration Formulas and the Net Change Theorem explicit formulas 5.1 Sequences exponential decay 2.8 Exponential Growth and Decay exponential growth 2.8 Exponential Growth and Decay F *f*ave 1.2 The Definite Integral federal income tax 1.4 Integration Formulas and the Net Change Theorem Fibonacci numbers 5.1 Sequences focal parameter 7.5 Conic Sections focus 7.5 Conic Sections Fresnel integrals 6.4 Working with Taylor Series fruit flies 1.6 Integrals Involving Exponential and Logarithmic Functions frustum 2.4 Arc Length of a Curve and Surface Area Fundamental Theorem of Calculus 1.3 The Fundamental Theorem of Calculus Fundamental Theorem of Calculus, Part 1 1.3 The Fundamental Theorem of Calculus Fundamental Theorem of Calculus, Part 2 1.3 The Fundamental Theorem of Calculus G *Gabriel’s Horn* 3.7 Improper Integrals general form 7.5 Conic Sections general solution 4.1 Basics of Differential Equations geometric sequence 5.1 Sequences geometric series 5.2 Infinite Series golden ratio 5.1 Sequences Gompertz equation 4.4 The Logistic Equation growth of bacteria 1.6 Integrals Involving Exponential and Logarithmic Functions growth rate 4.4 The Logistic Equation H half-life 2.8 Exponential Growth and Decay hanging cables 2.9 Calculus of the Hyperbolic Functions harmonic series 5.2 Infinite Series Hooke’s law 2.5 Physical Applications Hoover Dam 2.5 Physical Applications hydrostatic pressure 2.5 Physical Applications hypocycloid 7.1 Parametric Equations I iceboat 1.4 Integration Formulas and the Net Change Theorem improper integral 3.7 Improper Integrals indefinite integrals 3.1 Integration by Parts *index* 1.1 Approximating Areas index variable 5.1 Sequences infinite sequence 5.1 Sequences infinite series 5.2 Infinite Series initial population 4.4 The Logistic Equation initial value 4.1 Basics of Differential Equations initial velocity 4.1 Basics of Differential Equations initial-value problem 4.1 Basics of Differential Equations integrable function 1.2 The Definite Integral integral test 5.3 The Divergence and Integral Tests integrand 1.2 The Definite Integral integrating factor 4.5 First-Order Linear Equations integration by parts 3.1 Integration by Parts integration by substitution 1.5 Substitution integration tables 3.5 Other Strategies for Integration interval of convergence 6.1 Power Series and Functions J *joule* 2.5 Physical Applications K Koch’s snowflake 5.2 Infinite Series L lamina 2.6 Moments and Centers of Mass Laplace transform 3.7 Improper Integrals, 3.7 Improper Integrals left-endpoint approximation 1.1 Approximating Areas Leibniz 1.2 The Definite Integral limaçon 7.3 Polar Coordinates limit comparison test 5.4 Comparison Tests limit of the sequence 5.1 Sequences limits of integration 1.2 The Definite Integral linear 4.5 First-Order Linear Equations logarithmic function 3.1 Integration by Parts logistic differential equation 4.4 The Logistic Equation lower sum 1.1 Approximating Areas M Maclaurin polynomials 6.3 Taylor and Maclaurin Series Maclaurin series 6.3 Taylor and Maclaurin Series major axis 7.5 Conic Sections Mean Value Theorem for Integrals 1.3 The Fundamental Theorem of Calculus method of cylindrical shells. 2.3 Volumes of Revolution: Cylindrical Shells *method of equating coefficients* 3.4 Partial Fractions *method of exhaustion* 1.1 Approximating Areas *method of strategic substitution* 3.4 Partial Fractions midpoint rule 3.6 Numerical Integration minor axis 7.5 Conic Sections moment 2.6 Moments and Centers of Mass monotone sequence 5.1 Sequences N nappes 7.5 Conic Sections net change theorem 1.4 Integration Formulas and the Net Change Theorem net signed area 1.2 The Definite Integral Newton 1.3 The Fundamental Theorem of Calculus Newton’s law of cooling 2.8 Exponential Growth and Decay, 4.3 Separable Equations Newton’s second law of motion 4.1 Basics of Differential Equations nonelementary integral 6.4 Working with Taylor Series numerical integration 3.6 Numerical Integration O odd function 1.4 Integration Formulas and the Net Change Theorem order of a differential equation 4.1 Basics of Differential Equations orientation 7.1 Parametric Equations P *p*-series 5.3 The Divergence and Integral Tests parameter 7.1 Parametric Equations parameterization of a curve 7.1 Parametric Equations parametric curve 7.1 Parametric Equations parametric equations 7.1 Parametric Equations partial fraction decomposition 3.4 Partial Fractions partial sum 5.2 Infinite Series particular solution 4.1 Basics of Differential Equations partition 1.1 Approximating Areas Pascal’s principle 2.5 Physical Applications *pascals* 2.5 Physical Applications *perihelion* 1.3 The Fundamental Theorem of Calculus phase line 4.4 The Logistic Equation polar axis 7.3 Polar Coordinates polar coordinate system 7.3 Polar Coordinates polar equations 7.3 Polar Coordinates pole 7.3 Polar Coordinates Population growth 2.8 Exponential Growth and Decay power reduction formulas 3.2 Trigonometric Integrals power series 6.1 Power Series and Functions *power-reducing identities* 3.2 Trigonometric Integrals present value 6.2 Properties of Power Series price–demand function 1.6 Integrals Involving Exponential and Logarithmic Functions probability density function 3.7 Improper Integrals prolate cycloid 7.1 Parametric Equations R radial coordinate 7.3 Polar Coordinates *radial density* 2.5 Physical Applications radius of convergence 6.1 Power Series and Functions Ramanujan 5.6 Ratio and Root Tests *rate of change* 1.4 Integration Formulas and the Net Change Theorem ratio test 5.6 Ratio and Root Tests rational functions 3.4 Partial Fractions *RC* circuit 4.5 First-Order Linear Equations recurrence relation 5.1 Sequences, 5.1 Sequences regular partition 1.1 Approximating Areas relative error 3.6 Numerical Integration remainder estimate 5.3 The Divergence and Integral Tests Riemann sum 1.1 Approximating Areas Riemann sums 3.6 Numerical Integration right-endpoint approximation 1.1 Approximating Areas root test 5.6 Ratio and Root Tests rose 7.3 Polar Coordinates S separable differential equation 4.3 Separable Equations separation of variables 4.3 Separable Equations Sierpinski triangle 5.2 Infinite Series sigma notation 1.1 Approximating Areas *simple interest* 2.8 Exponential Growth and Decay Simpson’s rule 3.6 Numerical Integration skydiver 1.3 The Fundamental Theorem of Calculus slicing method 2.2 Determining Volumes by Slicing *smooth* 2.4 Arc Length of a Curve and Surface Area solid of revolution 2.2 Determining Volumes by Slicing solution concentrations 4.3 Separable Equations solution curve 4.2 Direction Fields and Numerical Methods solution to a differential equation 4.1 Basics of Differential Equations space-filling curves 7.1 Parametric Equations *spring constant* 2.5 Physical Applications standard form 4.5 First-Order Linear Equations, 7.5 Conic Sections step size 4.2 Direction Fields and Numerical Methods summation notation 1.1 Approximating Areas sums and powers of integers 1.1 Approximating Areas Surface area 2.4 Arc Length of a Curve and Surface Area symmetry 7.3 Polar Coordinates symmetry principle 2.6 Moments and Centers of Mass T Taylor polynomials 6.3 Taylor and Maclaurin Series Taylor series 6.3 Taylor and Maclaurin Series Taylor’s theorem with remainder 6.3 Taylor and Maclaurin Series telescoping series 5.2 Infinite Series term 5.1 Sequences term-by-term differentiation of a power series 6.2 Properties of Power Series term-by-term integration of a power series 6.2 Properties of Power Series theorem of Pappus for volume 2.6 Moments and Centers of Mass threshold population 4.4 The Logistic Equation total area 1.2 The Definite Integral Tour de France 1.4 Integration Formulas and the Net Change Theorem traffic accidents 3.7 Improper Integrals trapezoidal rule 3.6 Numerical Integration trigonometric integrals 3.2 Trigonometric Integrals trigonometric substitution 3.3 Trigonometric Substitution U unbounded sequence 5.1 Sequences upper sum 1.1 Approximating Areas V variable of integration 1.2 The Definite Integral velocity 1.4 Integration Formulas and the Net Change Theorem vertex 7.5 Conic Sections von Bertalanffy growth 5.2 Infinite Series W washer method 2.2 Determining Volumes by Slicing wingsuits 1.3 The Fundamental Theorem of Calculus witch of Agnesi 7.1 Parametric Equations work 2.5 Physical Applications

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