托馬斯微積分（上冊(cè)）

前言

在我國(guó)已經(jīng)加入WTO、經(jīng)濟(jì)全球化的今天，為適應(yīng)當(dāng)前我國(guó)高校各類創(chuàng)新人才培養(yǎng)的需要，大力推進(jìn)教育部倡導(dǎo)的雙語(yǔ)教學(xué)，配合教育部實(shí)施的“高等學(xué)校教學(xué)質(zhì)量與教學(xué)改革工程”和“精品課程”建設(shè)的需要，高等教育出版社有計(jì)劃、大規(guī)模地開(kāi)展了海外優(yōu)秀數(shù)學(xué)類系列教材的引進(jìn)工作。 高等教育出版社和Pearson Education，John Wiley & Sons，McGraw-Hill，Thomson Learning等國(guó)外出版公司進(jìn)行了廣泛接觸，經(jīng)國(guó)外出版公司的推薦并在國(guó)內(nèi)專家的協(xié)助下，提交引進(jìn)版權(quán)總數(shù)100余種。收到樣書后，我們聘請(qǐng)了國(guó)內(nèi)高校一線教師、專家、學(xué)者參與這些原版教材的評(píng)介工作，并參考國(guó)內(nèi)相關(guān)專業(yè)的課程設(shè)置和教學(xué)實(shí)際情況。

內(nèi)容概要

托馬斯微積分（英文版），ISBN：9787040144246，作者：（ ）Ross L.Finney等著

作者簡(jiǎn)介

作者：（美國(guó)）吉爾當(dāng)諾 編者：（美國(guó)）芬尼

書籍目錄

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．a(chǎn)nd 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．a(chǎn)nd 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．a(chǎn)nd 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．a(chǎn)nd    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．a(chǎn)nd 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．a(chǎn)nd 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

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《托馬斯微積分》(上)(第10版影印版)與我國(guó)現(xiàn)行通用高等數(shù)學(xué)教材相比，其基本內(nèi)容和結(jié)構(gòu)框架有著許多近似之處，但在題材選取和處理上又有更多不同特色，尤其是，突出應(yīng)用和數(shù)學(xué)建模，重視數(shù)值計(jì)算和程序應(yīng)用。在適時(shí)引進(jìn)現(xiàn)代數(shù)學(xué)和新學(xué)科知識(shí)等方面，更有不少精彩之處。

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