← 学习库 OpenStax Calculus Vol 1 目录

Index

Calculus Volume 1Index

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A absolute extremum 4.3 Maxima and Minima absolute maximum 4.3 Maxima and Minima absolute minimum 4.3 Maxima and Minima absolute value function 1.1 Review of Functions acceleration 3.1 Defining the Derivative, 3.4 Derivatives as Rates of Change algebraic function 1.2 Basic Classes of Functions amount of change 3.4 Derivatives as Rates of Change antiderivative 4.10 Antiderivatives *aphelion* 5.3 The Fundamental Theorem of Calculus arc length 6.4 Arc Length of a Curve and Surface Area Archimedes 2.3 The Limit Laws, 5.1 Approximating Areas *area density* 6.5 Physical Applications Area Problem 2.1 A Preview of Calculus area under the curve 5.1 Approximating Areas average rate of change 3.4 Derivatives as Rates of Change average value of the function 5.2 The Definite Integral average velocity 2.1 A Preview of Calculus, 3.1 Defining the Derivative B bald eagle 5.4 Integration Formulas and the Net Change Theorem base 1.5 Exponential and Logarithmic Functions C carbon dating 6.8 Exponential Growth and Decay catenary 6.9 Calculus of the Hyperbolic Functions center of mass 6.6 Moments and Centers of Mass centroid 6.6 Moments and Centers of Mass chain rule 3.6 The Chain Rule change of variables 5.5 Substitution chaos 4.9 Newton’s Method *common logarithm* 1.5 Exponential and Logarithmic Functions composite function 1.1 Review of Functions compound interest 6.8 Exponential Growth and Decay compounding interest 1.5 Exponential and Logarithmic Functions concave down 4.5 Derivatives and the Shape of a Graph concave up 4.5 Derivatives and the Shape of a Graph concavity 4.5 Derivatives and the Shape of a Graph concavity test 4.5 Derivatives and the Shape of a Graph *conditional statement* 2.5 The Precise Definition of a Limit *constant function* 1.2 Basic Classes of Functions Constant multiple law for limits 2.3 The Limit Laws Constant Multiple Rule 3.3 Differentiation Rules constant rule 3.3 Differentiation Rules continuity over an interval 2.4 Continuity continuous at a point 2.4 Continuity continuous from the left 2.4 Continuity continuous from the right 2.4 Continuity critical number 4.3 Maxima and Minima cross-section 6.2 Determining Volumes by Slicing cubic function 1.2 Basic Classes of Functions D deceleration 5.4 Integration Formulas and the Net Change Theorem decreasing on the interval $I$ 1.1 Review of Functions definite integral 5.2 The Definite Integral degree 1.2 Basic Classes of Functions density function 6.5 Physical Applications dependent variable 1.1 Review of Functions derivative 3.1 Defining the Derivative derivative function 3.2 The Derivative as a Function Difference law for limits 2.3 The Limit Laws difference quotient 3.1 Defining the Derivative Difference Rule 3.3 Differentiation Rules differentiable at $a$ 3.2 The Derivative as a Function differentiable function 3.2 The Derivative as a Function differentiable on $S$ 3.2 The Derivative as a Function Differential calculus 2.1 A Preview of Calculus differential form 4.2 Linear Approximations and Differentials differentials 4.2 Linear Approximations and Differentials differentiation 3.1 Defining the Derivative discontinuous at a point 2.4 Continuity disk method 6.2 Determining Volumes by Slicing displacement 5.2 The Definite Integral, 5.4 Integration Formulas and the Net Change Theorem domain 1.1 Review of Functions doubling time 6.8 Exponential Growth and Decay *dummy variable* 5.1 Approximating Areas, 5.2 The Definite Integral E earthquake 1.5 Exponential and Logarithmic Functions *end behavior* 1.2 Basic Classes of Functions, 4.6 Limits at Infinity and Asymptotes *endpoints* 1.1 Review of Functions epsilon-delta definition of the limit 2.5 The Precise Definition of a Limit evaluation theorem 5.3 The Fundamental Theorem of Calculus even function 1.1 Review of Functions, 5.4 Integration Formulas and the Net Change Theorem *existential quantifier* 2.5 The Precise Definition of a Limit exponent 1.5 Exponential and Logarithmic Functions exponential decay 6.8 Exponential Growth and Decay exponential growth 6.8 Exponential Growth and Decay Extreme Value Theorem 4.3 Maxima and Minima F *f*ave 5.2 The Definite Integral federal income tax 5.4 Integration Formulas and the Net Change Theorem Fermat’s theorem 4.3 Maxima and Minima first derivative test 4.5 Derivatives and the Shape of a Graph folium of Descartes 3.8 Implicit Differentiation fruit flies 5.6 Integrals Involving Exponential and Logarithmic Functions frustum 6.4 Arc Length of a Curve and Surface Area function 1.1 Review of Functions Fundamental Theorem of Calculus 5.3 The Fundamental Theorem of Calculus Fundamental Theorem of Calculus, Part 1 5.3 The Fundamental Theorem of Calculus Fundamental Theorem of Calculus, Part 2 5.3 The Fundamental Theorem of Calculus G graph of a function 1.1 Review of Functions growth of bacteria 5.6 Integrals Involving Exponential and Logarithmic Functions H half-life 6.8 Exponential Growth and Decay hanging cables 6.9 Calculus of the Hyperbolic Functions higher-order derivatives 3.2 The Derivative as a Function Holling type I equation 3.4 Derivatives as Rates of Change Hooke’s law 6.5 Physical Applications Hoover Dam 6.5 Physical Applications horizontal asymptote 4.6 Limits at Infinity and Asymptotes horizontal line test 1.4 Inverse Functions hydrostatic pressure 6.5 Physical Applications hyperbolic functions 1.5 Exponential and Logarithmic Functions I iceboat 5.4 Integration Formulas and the Net Change Theorem implicit differentiation 3.8 Implicit Differentiation increasing on the interval $I$ 1.1 Review of Functions indefinite integral 4.10 Antiderivatives independent variable 1.1 Review of Functions indeterminate forms 4.8 L’Hôpital’s Rule *index* 5.1 Approximating Areas infinite discontinuity 2.4 Continuity infinite limit at infinity 4.6 Limits at Infinity and Asymptotes infinite limits 2.2 The Limit of a Function inflection point 4.5 Derivatives and the Shape of a Graph initial-value problem 4.10 Antiderivatives *input* 1.1 Review of Functions instantaneous rate of change 3.1 Defining the Derivative instantaneous velocity 2.1 A Preview of Calculus, 3.1 Defining the Derivative integrable function 5.2 The Definite Integral Integral calculus 2.1 A Preview of Calculus integrand 5.2 The Definite Integral integration by substitution 5.5 Substitution interior points 3.2 The Derivative as a Function Intermediate Value Theorem 2.4 Continuity interval notation 1.1 Review of Functions intuitive definition of the limit 2.2 The Limit of a Function inverse function 1.4 Inverse Functions inverse hyperbolic functions 1.5 Exponential and Logarithmic Functions inverse trigonometric functions 1.4 Inverse Functions iterative process 4.9 Newton’s Method J *joule* 6.5 Physical Applications jump discontinuity 2.4 Continuity L L’Hôpital’s rule 4.8 L’Hôpital’s Rule lamina 6.6 Moments and Centers of Mass *leading coefficient* 1.2 Basic Classes of Functions left-endpoint approximation 5.1 Approximating Areas Leibniz 3.1 Defining the Derivative, 5.2 The Definite Integral limit 2.1 A Preview of Calculus limit at infinity 4.6 Limits at Infinity and Asymptotes, 4.6 Limits at Infinity and Asymptotes limit laws 2.3 The Limit Laws limits of integration 5.2 The Definite Integral linear approximation 4.2 Linear Approximations and Differentials linear function 1.2 Basic Classes of Functions linearization 4.2 Linear Approximations and Differentials local extremum 4.3 Maxima and Minima local maximum 4.3 Maxima and Minima local minimum 4.3 Maxima and Minima logarithmic differentiation 3.9 Derivatives of Exponential and Logarithmic Functions logarithmic function 1.2 Basic Classes of Functions lower sum 5.1 Approximating Areas M Mandelbrot set 4.9 Newton’s Method marginal cost 3.4 Derivatives as Rates of Change marginal profit 3.4 Derivatives as Rates of Change mathematical models 1.2 Basic Classes of Functions maximizing revenue 4.7 Applied Optimization Problems Mean Value Theorem 4.4 The Mean Value Theorem Mean Value Theorem for Integrals 5.3 The Fundamental Theorem of Calculus method of cylindrical shells. 6.3 Volumes of Revolution: Cylindrical Shells *method of exhaustion* 5.1 Approximating Areas moment 6.6 Moments and Centers of Mass multivariable calculus 2.1 A Preview of Calculus N natural exponential function 1.5 Exponential and Logarithmic Functions, 3.9 Derivatives of Exponential and Logarithmic Functions natural logarithm 1.5 Exponential and Logarithmic Functions natural logarithmic function 3.9 Derivatives of Exponential and Logarithmic Functions net change theorem 5.4 Integration Formulas and the Net Change Theorem net signed area 5.2 The Definite Integral Newton 3.1 Defining the Derivative, 5.3 The Fundamental Theorem of Calculus Newton’s law of cooling 6.8 Exponential Growth and Decay Newton’s method 4.9 Newton’s Method number $e$ 1.5 Exponential and Logarithmic Functions O oblique asymptote 4.6 Limits at Infinity and Asymptotes odd function 1.1 Review of Functions, 5.4 Integration Formulas and the Net Change Theorem one-sided limit 2.2 The Limit of a Function one-to-one function 1.4 Inverse Functions optimization problems 4.7 Applied Optimization Problems *output* 1.1 Review of Functions P partition 5.1 Approximating Areas Pascal’s principle 6.5 Physical Applications *pascals* 6.5 Physical Applications percentage error 4.2 Linear Approximations and Differentials *perihelion* 5.3 The Fundamental Theorem of Calculus periodic functions. 1.3 Trigonometric Functions piecewise-defined function 1.2 Basic Classes of Functions *piecewise-defined functions* 1.1 Review of Functions point-slope equation 1.2 Basic Classes of Functions polynomial function 1.2 Basic Classes of Functions population growth 1.5 Exponential and Logarithmic Functions, 6.8 Exponential Growth and Decay population growth rates 3.4 Derivatives as Rates of Change power function 1.2 Basic Classes of Functions Power law for limits 2.3 The Limit Laws power rule 3.3 Differentiation Rules price–demand function 5.6 Integrals Involving Exponential and Logarithmic Functions Product law for limits 2.3 The Limit Laws product rule 3.3 Differentiation Rules propagated error 4.2 Linear Approximations and Differentials Pythagorean theorem 4.1 Related Rates Q quadratic function 1.2 Basic Classes of Functions Quotient law for limits 2.3 The Limit Laws quotient rule 3.3 Differentiation Rules R *radial density* 6.5 Physical Applications radians 1.3 Trigonometric Functions range 1.1 Review of Functions rate of change 2.1 A Preview of Calculus, 5.4 Integration Formulas and the Net Change Theorem rational function 1.2 Basic Classes of Functions Regiomontanus’ problem 4 Review Exercises regular partition 5.1 Approximating Areas related rates 4.1 Related Rates relative error 4.2 Linear Approximations and Differentials removable discontinuity 2.4 Continuity restricted domain 1.4 Inverse Functions *Richter scale* 1.5 Exponential and Logarithmic Functions Riemann sum 5.1 Approximating Areas right-endpoint approximation 5.1 Approximating Areas Rolle’s theorem 4.4 The Mean Value Theorem root function 1.2 Basic Classes of Functions Root law for limits 2.3 The Limit Laws S secant 2.1 A Preview of Calculus secant method 4.9 Newton’s Method second derivative test 4.5 Derivatives and the Shape of a Graph sigma notation 5.1 Approximating Areas *simple interest* 6.8 Exponential Growth and Decay skydiver 5.3 The Fundamental Theorem of Calculus slicing method 6.2 Determining Volumes by Slicing slope 1.2 Basic Classes of Functions slope-intercept form 1.2 Basic Classes of Functions *smooth* 6.4 Arc Length of a Curve and Surface Area solid of revolution 6.2 Determining Volumes by Slicing speed 3.4 Derivatives as Rates of Change *spring constant* 6.5 Physical Applications squeeze theorem 2.3 The Limit Laws standard form of a line 1.2 Basic Classes of Functions Sum law for limits 2.3 The Limit Laws Sum Rule 3.3 Differentiation Rules summation notation 5.1 Approximating Areas sums and powers of integers 5.1 Approximating Areas Surface area 6.4 Arc Length of a Curve and Surface Area symmetry about the origin 1.1 Review of Functions symmetry about the *y*-axis 1.1 Review of Functions symmetry principle 6.6 Moments and Centers of Mass T table of values 1.1 Review of Functions tangent 2.1 A Preview of Calculus tangent line approximation 4.2 Linear Approximations and Differentials Tangent Problem 2.1 A Preview of Calculus theorem of Pappus for volume 6.6 Moments and Centers of Mass total area 5.2 The Definite Integral Tour de France 5.4 Integration Formulas and the Net Change Theorem transcendental functions 1.2 Basic Classes of Functions transformation of a function 1.2 Basic Classes of Functions triangle inequality 2.5 The Precise Definition of a Limit trigonometric functions 1.3 Trigonometric Functions trigonometric identity 1.3 Trigonometric Functions U *universal quantifier* 2.5 The Precise Definition of a Limit upper sum 5.1 Approximating Areas V variable of integration 5.2 The Definite Integral velocity 5.4 Integration Formulas and the Net Change Theorem vertical asymptote 2.2 The Limit of a Function vertical line test 1.1 Review of Functions W washer method 6.2 Determining Volumes by Slicing wingsuits 5.3 The Fundamental Theorem of Calculus work 6.5 Physical Applications Z zeroes of functions 4.9 Newton’s Method zeros of a function 1.1 Review of Functions

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