应用微积分

前言

　　本书叙述了一元函数微积分、二元函数微分学和二重积分，简单介绍了常微分方程和级数，还讲述了概率的基本知识。　　作者在修订本版时有两个目的：其一是给学生写一本易读好用的教材，其二是给教师提供一个非常有用的教学工具。所以，作者在本版中采纳了前4版读者的意见，同时有选择地、尽可能完整地加入了最新方法、最新实例。其内容符合我国经济管理专业的要求，对文科各专业也基本适用。　　书中的数学概念、方法、理论都是通过具体直观的过程引入的，没有较严密的推理过程，所以这是一本“直观微积分”的书，这种方式的讲述对文科各专业学生是十分适宜的，可能会使他们获益更多，对管理类专业也基本适合。　　书中采用对函数类分层叙述的方法，先对有理函数介绍微分学，后对指数、对数函数叙述，最后介绍对三角函数的微积分，这种方式特别适用于文科学生。　　本书例题、习题十分丰富，包括了从经济、贸易、社会行为学、生命科学、物理学和其他科学领域中提炼出的最新的、有趣的应用。而且本书插图精美，可帮助学生理解相应内容。　　总之，本书适宜作为文科各专业和某些经济管理专业的本科“微积分”教材。

书籍目录

出版说明序Chapter 1 PRELIMINARIES 1.1 Precalculua Review I 1.2 Precalculus Review II 1.3 The Cartesian Coordinate System 1.4 Straight Lines Chapter I Summary of Principal Formulas and Terms Chapter 1 Review Exercises Chapter 2 FUNCTIONS， LIMITS， AND THE DERIVATIVE 2.1 Functions and Their Graphs Using Technology： Graphing a Function 2.2 The Algebra of Functions PORTFOLIO： Michael Marchlik 2.3 Functions and Mathematical Models Using Technology： Finding the Points of Intersection of Two Graphs and Modeling 2.4 Limits Using Technology： Finding the Limit of a Function 2.5 One.Sided Limits and Continuity Using Technology： Finding the Points of Discontinuity ofa Function 2.6 TheDerivetive Using Technology： Graphing a Function and Its Tangent Lines Chapter 2 Summary of Principal Formulas and Terms Chapter 2 Review Exercises Chapter 3 DIFFERENTIATION 3.1 Basic Rules of Differentiation Using Technology： Finding the Rate of Change of a Function 3.2 The Product and Quotient Rules Using Technology： The Product and Quotient Rules 3.3 The Chain Rule Using Technology： Finding the Derivative of aComposite Function 3.4 Marginal Functions in Economics 3.5 Higher-Order Derivatives Using Technology： Finding the Second Derivative of a Function at aGiven Point 3.6 Implicit Differentiation and Related Rates 3.7 Differentials PORTFOLIO： John Decker Using Technology： Finding the Differential of a Function Chapter 3 Summary of.Principal Formulas and Tems Chapter 3 Review Exercises Chapter 4 APPLICATIONS OF THE DERIVATIVE 4，1 Applications of the First Derivative Using Technology： Using the First Derivative to Analyzea Function 4.2 Applications of the Second Derivative Using Technology： Finding the Inflection Points of a Function 4.3 Curve Sketching Using Technology： Analyzing the Properties of a Function 4，4 Optimization Ⅰ Using Technology： Finding the Absolute Extrema of a Function 4.5 Optimization Ⅱ Chapter 4 Summary of Principal Terms Chapter 4 Review Exercises Chapter 5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 8.1 Exponential Functions Using Technology 5.2 Logarithmic Functions 5.3 Compound Interest PORTFOLIO： Misato Nakazaki 5.4 Differentiation of Exponential Functions Using Technology 5.5 Differentiation ef Logarithmic Functions 5.6 Exponential Functions as Mathematical Models Chapter 5 Summary of Principal Formulas and Terms Chapter 5 Revue Exercises Chapter 6 INTEGRATION 6.1 Antiderlvatlues and the Rules of Integration 6.2 Integration by Substitution 6.3 Area and the Definite Integral 6.4 The Fundamental Theorem of Calculus Using Technology： Evaluating Definite Integrals 6.5 Evaluating Definite Integrals Using Technology： Evaluating Definite Integrals forPiecewise-Defined Functions 6.6 Area Between Two Curves Using Technology： Finding the Area Between Two Curves 6.7 Applications of the Definite Integral to Business and Economics Using Technology： Consumers Surplus and Producers Surplus 6.8 Volumes of Solids of Revolution Chapter 6 Summary of Principal Formulas and Terms Chapter 6 Review Exercises Chapter 7 ADDITIONAL TOPICS IN INTEGRATION 7.1 Integration by Parts 7.2 Integration Using Tables of Integrals 7.3 Numerical Integration PORTFOLIO： James H. Chesebro， M.D. 7，4 Improper Integrals Chapter 7 Summary of Principal Formulas and Terms Chapter 7 Review Exercises Chapter 8 CALCULUS OF SEVERAL VARIABLES 8.1 Functions of Several Variables 8.2 Partial Derlvativas Using Technology： Finding Partial Derivatives at a Given Point 8，3 Maxima and Minima of Functions of Several Variables 8.4 The Method of Least Squares Using Technology： Finding an Equation of a Least-Squares Line 8.5 Constrained Maxima and Minima and the Method ofLagrange Multipliers 8.8 Total Differentials 8.7 Double Integrals 8.8 Applications of Double Integrals Chapter 8 Summary of Principal Terms Chapter 8 Review Exercises Chapter 9 DIFFERENTIAL EQUATIONS 9.1 Differential Equations 9.2 Separation of Variables 9.3 Applications of Separable Differential Equations 9.4 Approximate Solutions of Differential Equations Chapter 9 Summary of Principal Terms Chapter 9 Review Exercises Chapter 10 PROBABILITY AND CALCULUS 10.1 Probability Distributions of Random Variables Using Technology： Graphing a Histogram 10，2 Expected Value and Standard Deviation Using Technology： Finding the Mean and Standard Deviation 10.3 Normal Distributions Chapter IO Summary of Principal Formulas and Terms Chapter I0 Review Exercises Chapter 11 TAYLOR POLYNOMIALS AND INFINITE SERIES 11.1 Taylor Polynomials 11.2 Infinite Sequences 11，3 Infinite Series 11.4 Series with Positive Terms 11.5 Power Series and Taylor Series 11.6 More on Taylor Series 11.7 The Newton-Raphson Method Chapter 11 Summary of Principal Formulas and Terms Chapter 11 Review Exercises Chapter 12 TRIGONOMETRIC FUNCTIONS 12.1 Measurement of Angles 12.2 The Trigonometric Functions 12.3 Differentiation of Trigonometric Functions Using Technology： Analyzing Trigonometric Functions 12.4 Integration of Trigonometric Functions Using Technology： Evaluating Integrals of Trigonometric Functions Chapter 12 Summary of Principal Formulas and Terms Chapter 12 Review Exercises TABLE The Standard Normal Distribution ANSWERS TO ODD-NUMBERED EXERCISES INDEX 教辅材料申请表

作者简介

《应用微积分:管理、生命科学及社会科学专业适用(英文版)(原书第5版)》内容简介：对数学概念、方法、理论都通过直观过程引入。包含了许多从经济、贸易、社会行为学、生命科学、物理学和其他科学领域提炼出的最新的、有趣的应用。适宜作为经济管理及文科的微积分教材。

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