托马斯微积分（上册）

作者简介

托马斯微积分（英文版），ISBN：9787040144246，作者：（ ）Ross L.Finney等著

书籍目录

Preliminaries    1 Lines  1    2 Functions and Graphs  1 0    3 Exponential Functions  24    4 Inverse Functions and Logarithms  3 1    5 Trigonometric Functions and Their lnverses 44    6 Parametric Equations  60    7  Modeling Change  67    QUESTIONS TO GUIDE YOUR REVIEW  76    PRACTICE EXERCISES  77    ADDITIONAL EXERCISES：THEORY．EXAMPS．APPUCATIONS 801  Limits and Continuity    1．1 Rates of Change and Limi85    1．2 Finding Limiand One-Sided Limits  99    1．3 LimiInvolving Infinity  11 2    1．4 Continuity  123    1．5 Tangent Lines  134    QUESTIONS TO GUIDE YOUR REVIEW  1 41    PRACTICE EXERCISES  1 42    ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS  1 432 DeriVatives    2．1 The Derivative as a Function  147    2．2 The Derivative as a Rate of Change  1 60    2．3 Derivatives of Products．Quotients．and Negative Powers  173    2．4 Derivatives of Trigonometric Functions  1 79    2．5 The Chain Rule and Parametric Equations  1 87    2．6 Implicit Difierentiation  1 98    2．7 Related Rates  207    QUESTIONS TO GUIDE YOUR REVIEW  21 6    PRACTICE EXERCISES  21 7    ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPUCATIONS  2213 Applications of Derivatives    3．1 Extreme Values of Functions    225    3．2 The Mcan Value Theorem and Difierential Equations  237    3．3 The Shape of a Graph  245    3．4 Graphical Solutions of Autonomous Differential Equations  257    3．5 Modeling and Optimization  266    3．6 Linearization and Differentials  283    3．7 Newton’S Method  297    QUESTIONS TO GUIDE YOUR REVIEW  305    PRACTICE EXERCISES  305    ADDITIONAL EXERCISES：THEORY,EXAMPLES．APPLICATIONS  3094 Integration    4．1 Indefinite Integrals,Differential Equations．and Modeling  3 1 3    4．2 Integral Rules；Integration by Substitution  322    4．3 Estimating with Finite Sums  329    4．4 Ricmann Sums and Definite Integrals  340    4．5 The Mcan Value and FundamentaI Theorems  351    4．6 SubStitution in Definite Integrals  364    4．7 NumericalIntegration  373    QUESTIONS TO GUIDE YOUR REVIEW  384    PRACTICE EXERCISES  385    ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS  3895 Applications of Integrals    5．1 Volumes by Slicing and Rotation About an Axis  393    5．2 Modeling Volume Using Cylindrical Shells 406    5．3 Lengths of Plane Curves 41 3    5．4 Springs．Pumping．and Lifting 421    5．5 Fluid Forces 432    5．6 Moments and Centers of Mass 439    QUESTIONS TO GUIDE YOUR REVIEW 451    PRACTICE EXERCISES 45 1    ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 4546 Transcendental Functions and Differential Equations    6．1 Logarithms 457    6．2 Exponential Functions 466    6．3 D——e|rivatives of Inverse Trigonometric Functions；Integrals 477    6．4 First．Order Separable Differential Equations 485    6．5 Linear FirSt．Order Differential Equations 499    6．6 Euler‘S Method；Poplulation Models  507    6．7 Hyperbolic Functions  520    QUESTIONS TO GUIDE YOUR REVIEW  530    PRACTICE EXERCISES  531    ADDmONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS  5357 Integration Techniques，L'H6pital’s Rule,and Improper Integrals    7．1 Basic Integration Formulas  539    7．2 Integration by Parts  546    7．3 Partial Fractions  555    7,4 Trigonometric Substitutions  565    7．5 Integral Tables．Computer Algebra Systems．and    Monte Cario Integration  570    7．6 L'HSpitarS Rule  578    7．7 Improper Integrals  586    QUESTIONS TO GUIDE YOUR REVIEW  600    PRACTICE EXERCISES  601    ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS  6038 Infinite Series    8．1 Limis of Sequences of Numbers  608    8．2 Subsequences．Bounded Sequences．and Picard'S Method  61 9    8．3 Infinite Series  627    8．4 Series of Nonnegative Terms  1639    8．5 Alternating Series。Absolute and Conditional Convergence  651    8．6 Power Series  660        8．7 Taylor and Maclaurin Series  669    8．8 Applications of Power Series  683    8．9  Fourier Series 691    8．10 Fourier Cosine and Sine Series  698    QUESTIONS TO GUIDE YOUR REVIEW  707    PRACTICE EXERCISES  708    ADDITIONAL EXERCISES：THEORY,EXAMPS．APPLICATIONS  7 119 Vectors in the Plane and Polar Functions    9．1 Vectors in the Plane  71 7    9．2 Dot Products  728    9．3 Vector-Valued Functions  738    9．4 Modeling Projectile Motion  749    9．5 Polar Coordinates and Graphs  761    9．6 Calculus of Polar Curyes  770    QUESTIONS TO GUIDE YOUR REVIEW    780    PRACTICE EXERCISES  780    ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPUCATIONS  78410 Vectors and M0tion in Space    1O．1 Cartesian(Rectangular)Coordinates and Vectors in Space  787    10．2 Dot and Cross Products  796    10．3 Lines and Planes in Space 807    10．4 cylinders and Ouadric SurfaCes 816    10．5 Vector-Valued Functions and Space Curves 825    10．6 Arc Length and the Unit Tangent Vector T 838    10．7 The TNB Frame；Tangential and Normal Components of Acceleration    10．8 Planetary Motion and Satellites 857    QUESTIONS TO GUIDE YOUR REVIEW 866    PRACTICE EXERCISES 867    ADDITIONAL EXERCISES：THEORY．EXAMPLES．APPLICATIONS 87011 Multivariable Functions and 111eir Derivatives    1 1．1 Functions of SeveraI Variables 873    11．2 Limits and Continuity in Higher Dimensions 882    11．3 PartiaI Derivatives 890    11．4 The Chain Rule  902    11．5 DirectionaI Derivatives．Gradient Vectors．and Tangent Planes  91 1    11．6 Linearization and Difierentials  925    11．7 Extreme Values and Saddle Points  936……12 Multiple Integrals13 Integration in Vector FieldsAppendices

编辑推荐

《托马斯微积分》(上)(第10版影印版)与我国现行通用高等数学教材相比，其基本内容和结构框架有着许多近似之处，但在题材选取和处理上又有更多不同特色，尤其是，突出应用和数学建模，重视数值计算和程序应用。在适时引进现代数学和新学科知识等方面，更有不少精彩之处。

前言

在我国已经加入WTO、经济全球化的今天，为适应当前我国高校各类创新人才培养的需要，大力推进教育部倡导的双语教学，配合教育部实施的“高等学校教学质量与教学改革工程”和“精品课程”建设的需要，高等教育出版社有计划、大规模地开展了海外优秀数学类系列教材的引进工作。 高等教育出版社和Pearson Education，John Wiley & Sons，McGraw-Hill，Thomson Learning等国外出版公司进行了广泛接触，经国外出版公司的推荐并在国内专家的协助下，提交引进版权总数100余种。收到样书后，我们聘请了国内高校一线教师、专家、学者参与这些原版教材的评介工作，并参考国内相关专业的课程设置和教学实际情况。

内容概要

作者：（美国）吉尔当诺 编者：（美国）芬尼

章节摘录

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