Calculus e4

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Opis: Calculus e4 - James Stewart

The new edition calculus textbook has been thoroughly revised. It continues to embrace the best aspects of reform by combining the traditional theoretical aspects of calculus with creative teaching and learning techniques. This is accomplished by a focus on conceptual understanding, the use of real-world data and real-life applications, projects, and the use of technology (where appropriate). It is widely acknowledged that the main goal of calculus instruction is for the student to understand the basic ideas. This text aims to support such a goal while motivating students through the use of real-world applications, building the essential mathematical reasoning skills, and helping them develop an appreciation and enthusiasm for calculus.Part 1 Functions and models: four ways to represent a function; mathematical models; new functions from old functions; graphing calculators and computers; review; principles of problem solving. Part 2 Limits and rates of change: the tangent and velocity problems; the limit of a function; calculating limits using the limit laws; the precise definition of a limit; continuity; tangents, velocities, and other rates of change; review; problems plus. Part 3 Derivatives: derivatives; the derivative as a function; differentiation formulas; rates of change in the natural and social sciences; derivatives of trigonometric functions; the chain rule; implicit differentiation; higher derivatives; related rates; linear approximations and differentials; review; problems plus. Part 4 Applications of differentiation: maximum and minimum values; the mean value theorem; how derivatives affect the shape of a graph; limits at infinity - horizontal asymptotes; summary of curve sketching; graphing with calculus and calculators; optimization problems; applications to economics; Newton's method; antiderivatives; review; problems plus. Part 5 Integrals: areas and distances; the definite integral; the fundamental theorem of calculus; indefinite integrals and the total change theorem; the substitution rule; review; problems plus. Part 6. Applications of integration: areas between curves; volume; volumes by cylindrical shells; work; average value of a function; review; problems plus. Part 7 Inverse functions: inverse functions; exponential functions and their derivatives; logarithmic functions; derivatives of logarithmic functions; the natural logarithmic function; the natural exponential function; general logarithmic and exponential functions; inverse trigonometric functions; hyperbolic functions; indeterminate forms and l'hospital's rule; review; problems plus. Part 8 Techniques of integration: integration by parts; trigonometric integrals; trigonometric substitution; integration of rational functions by partial fractions; strategy for integration; integration using tables and computer algebra systems; approximate integration; improper integrals; review; problems plus. Part 9 Further applications of integration: arc length; area of a surface of revolution; applications to physics and engineering; applications to economics and biology; probability; review; problems plus. Part 10 Differential equations: modelling with differential equations; direction fields and Euler's method; le equations; exponential growth and decay; the logistic equation; linear equations; predator-prey systems; review; problems plus. Part 11 Parametic equations anb polar co-ordinates: curves defined by parametric equations; tangents and areas; arc length and surface area; polar co-ordinates; areas and lengths in polar co-ordinates; conic sections; conic sections in polar co-ordinates; review; problems plus. Part 12 Infinite sequences and series. (Part contents).


Szczegóły: Calculus e4 - James Stewart

Tytuł: Calculus e4
Autor: James Stewart
Producent: Thomson Learning
ISBN: 9780534359492
Rok produkcji: 1999
Ilość stron: 1127
Oprawa: Twarda
Waga: 2.72 kg


Recenzje: Calculus e4 - James Stewart

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Calculus e4

The new edition calculus textbook has been thoroughly revised. It continues to embrace the best aspects of reform by combining the traditional theoretical aspects of calculus with creative teaching and learning techniques. This is accomplished by a focus on conceptual understanding, the use of real-world data and real-life applications, projects, and the use of technology (where appropriate). It is widely acknowledged that the main goal of calculus instruction is for the student to understand the basic ideas. This text aims to support such a goal while motivating students through the use of real-world applications, building the essential mathematical reasoning skills, and helping them develop an appreciation and enthusiasm for calculus.Part 1 Functions and models: four ways to represent a function; mathematical models; new functions from old functions; graphing calculators and computers; review; principles of problem solving. Part 2 Limits and rates of change: the tangent and velocity problems; the limit of a function; calculating limits using the limit laws; the precise definition of a limit; continuity; tangents, velocities, and other rates of change; review; problems plus. Part 3 Derivatives: derivatives; the derivative as a function; differentiation formulas; rates of change in the natural and social sciences; derivatives of trigonometric functions; the chain rule; implicit differentiation; higher derivatives; related rates; linear approximations and differentials; review; problems plus. Part 4 Applications of differentiation: maximum and minimum values; the mean value theorem; how derivatives affect the shape of a graph; limits at infinity - horizontal asymptotes; summary of curve sketching; graphing with calculus and calculators; optimization problems; applications to economics; Newton's method; antiderivatives; review; problems plus. Part 5 Integrals: areas and distances; the definite integral; the fundamental theorem of calculus; indefinite integrals and the total change theorem; the substitution rule; review; problems plus. Part 6. Applications of integration: areas between curves; volume; volumes by cylindrical shells; work; average value of a function; review; problems plus. Part 7 Inverse functions: inverse functions; exponential functions and their derivatives; logarithmic functions; derivatives of logarithmic functions; the natural logarithmic function; the natural exponential function; general logarithmic and exponential functions; inverse trigonometric functions; hyperbolic functions; indeterminate forms and l'hospital's rule; review; problems plus. Part 8 Techniques of integration: integration by parts; trigonometric integrals; trigonometric substitution; integration of rational functions by partial fractions; strategy for integration; integration using tables and computer algebra systems; approximate integration; improper integrals; review; problems plus. Part 9 Further applications of integration: arc length; area of a surface of revolution; applications to physics and engineering; applications to economics and biology; probability; review; problems plus. Part 10 Differential equations: modelling with differential equations; direction fields and Euler's method; le equations; exponential growth and decay; the logistic equation; linear equations; predator-prey systems; review; problems plus. Part 11 Parametic equations anb polar co-ordinates: curves defined by parametric equations; tangents and areas; arc length and surface area; polar co-ordinates; areas and lengths in polar co-ordinates; conic sections; conic sections in polar co-ordinates; review; problems plus. Part 12 Infinite sequences and series. (Part contents).

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