托马斯微积分
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作者WEIR,HASS,GIORDANO,WEIR,HASS,G
出版社高等教育出版社
ISBN9787040452532
出版时间2016-06
版次1
装帧平装
开本16开
纸张胶版纸
页数684页
定价66.2元
上书时间2024-02-05
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基本信息
书名:托马斯微积分
定价：66.20元
作者:WEIR,HASS,GIORDANO,WEIR,HASS,GIORDANO
出版社：高等教育出版社
出版日期：2016-06-01
ISBN：9787040452532
字数：
页码：684
版次：
装帧：平装
开本：16开
商品重量：
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内容提要
韦尔、哈斯、吉尔当诺主的《托马斯微积分(上1版)(英文版)》1951年出版版，是一本深受美国广大教师和学生欢迎的教材，不少学校和教师采用它作为微积分课程的教材，在相当一段时间里，它是麻省理工学院微积分课程所用的教材之一。 本书具有以下几个突出特色：取材于科学和工程领域中的重要应用实例以及配置丰富的习题；对每个重要专题均用语言的、代数的、数值的、图像的方式予以陈述i重视数值计算和程序应用；切实融入数学建模和数学实验的思想和方法；每个新专题都通过清楚的、易于理解的例子启发式地引入，可读性强；配有丰富的教学资源，可用于教师教学和学生学习。
目录
PrefacePretiminaries1.1 Real Numbers and the Real Line1.2 Lines, Circles, and Parabolas1.3 Functions and Their Graphs1.4 Identifying Functions; Mathematical Models1.5 Combining Functions; Shifting and Scaling Graphs1.6 Trigonometric Functions1.7 Graphing with Calculators and ComputersQUESTIONS TO GUIDE YOUR REVIEWPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESLimits and Continuity2.1 Rates of Change and Limits2.2 Calculating Limits Using the Limit Laws2.3 The Precise Definition of a Limit2.4 One-Sided Limits and Limits at Infinity2.5 Infinite Limits and Vertical Asymptotes2.6 Continuity2.7 Tangents and DerivativesQUESTIONS TO GUIDE YOUR REVIEWPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESDifferentiatio3.1 The Derivative as a Functio3.2 Differentiation Rules3.3 The Derivative as a Rate of Change3.4 Derivatives of Trigonometric Functions3.5 The Chain Rule and Parametric Equations3.6 Implicit Differentiatio3.7 Related Rates3.8 Linearization and DifferentialsQUESTIONS TO GUIDE YOUR REVIEWPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESAppticaUons of Derivatives4.1 Extreme Values of Functions4.2 The Mean Value Theorem4.3 Monotonic Functions and the First Derivative Test4.4 Concavity and Curve Sketching4.5 Applied Optimization Problems4.6 Indeterminate Forms and IgH6pital's Rule4.7 Newton's Method4.8 AntiderivativesQUESTIONS TO GUIDE YOUR REVIEWPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESIntegratio5.1 Estimating with Finite Sums5.2 Sigma Notation and Limits of Finite Sums5.3 The Definite Integral5.4 The Fundamental Theorem of Calculus5.5 Indefinite Integrals and the Substitution Rule5.6 Substitution and Area Between CurvesQUESTIONS TO GUIDE YoUR REvIEwPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESApptications of Definite Integrats6.1 Volumes by Slicing and Rotation About an Axis6.2 Volumes by Cylindrical Shells6.3 Lengths of Plane Curves6.4 Moments and Centers of Mass6.5 Areas of Surfaces of Revolution and the Theorems of Pappus6.6 Work6.7 Fluid Pressures and ForcesQUESTIONS TO GUIDE YOUR REVIEWPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESTranscendentat Functions7.1 Inverse Functions and Their Derivatives7.2 Natural Logarithms7.3 The Exponential Functio7.4 ax and logax7.5 Exponential Growth and Decay7.6 Relative Rates of Growth7.7 Inverse Trigonometric Functions7.8 Hyperbolic FunctionsQUESTIONS TO GLADE YOUR REVIEWPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESTechniques of Integration 58.1 Basic Integration Formulas8.2 Integration by Parts8.3 Integration of Rational Functions by Partial Fractions8.4 Trigonometric Integrals8.5 Trigonometric Substitutions8.6 Integral Tables and Comouter Algebra Systems8.7 Numerical Integratio8.8 Improper IntegralsQUESTIONS TO GUIDE YOUR REVIEWPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESFurther Applications of Integratio9.1 Slope Fields and Separable Differential Equations9.2 First-Order Linear Differential Equations9.3 Euler's Method9.4 Graphical Solutions of Autonomous Differential Equations9.5 Applications of First-Order Differential EquationsQUESTIONS TO GUIDE YOUR REVIEWPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESConic Sections and Polar Coordinates10.1 Conic Sections and Quadratic Equations10.2 Classifying Conic Sections by Eccentricity10.3 Quadratic Equations and Rotations10.4 Conics and Parametric Equations; The Cycloid10.5 Polar Coordinates10.6 Graphing in Polar Coordinates10.7 Areas and Lengths in Polar Coordinates10.8 Conic Sections in Polar CoordinatesQUESTIONS TO GUIDE YOUR REVIEWPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESInfinite Sequences and Series11.1 Sequences11.2 Infinite Series11.3 The Integral Test11.4 Comparison Tests11.5 The Ratio and Root Tests _11.6 Alternating Series, Absolute and Conditional Convergence11.7 Power Series11.8 Taylor and Maclaurin Series11.9 Convergence of Taylor Series; Error Estimates11.10 Applications of Power Series11.11 Fourier SeriesQUESTIONS TO GUIDE YOUR REVIEWPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESVectors and the Geometry of Space12.1 Three-Dimensional Coordinate Systems12.2 Vectors12.3 The Dot Product12.4 The Cross Product12.5 Lines and Planes in Space12.6 Cylinders and Quadric SurfacesQUESTIONS TO GUIDE YOUR REVIEWPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESVector-Va[ued Functions and Motion in Space13.1 Vector Functions 90613.2 Modeling Projectile Motion 92013.3 Arc Length and the Unit Tangent Vector T 93113.4 Curvature and the Unit Normal Vector N 93613.5 Torsion and the Unit Binormal Vector B 94313.6 Planetary Motion and Satellites 950QUESTIONS TO GUIDE YOUR REVIEW 959PRACTICE EXERCISES 960ADDITIONAL AND ADVANCED EXERCISES 962Partiat Derivatives14. l Functions of Several Variables14.2 Limits and Continuity in Higher Dimensions14.3 Partial Derivatives14.4 The Chain Rule14.5 Directional Derivatives and Gradient Vectors14.6 Tangent Planes and Differentials14.7 Extreme Values and Saddle Points14.8 Lagrange Multipliers14.9 Partial Derivatives with Constrained Variables14.10 Taylor's Formula for Two VariablesQUESTIONS TO GUIDE YOUR REVIEWPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESMutUpte Integrats15.1 Double Integrals15.2 Areas, Moments, and Centers of Mass15.3 Double Integrals in Polar Form15.4 Triple Integrals in Rectangular Coordinates15.5 Masses and Moments in Three Dimensions15.6 Triple Integrals in Cylindrical and Spherical Coordinates15.7 Substitutions in Multiple IntegralsQUESTIONS TO GUIDE YOUR REVIEWPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESIntegration in Vector Fietds16.1 Line Integrals16.2 Vector Fields, Work, Circulation, and Flux16.3 Path Independence, Potential Functions, and Conservative Fields16.4 Green's Theorem in the Plane16.5 Surface Area and Surface Integrals16.6 Parametrized Surfaces16.7 Stokes' Theorem16.8 The Divergence Theorem and a Unified TheoryQUESTIONS TO GUIDE YOUR RnVIEWPRACTICE EXERCISESADDITIONAL AND ADVANCED EXERCISESAppendicesA.1 Mathematical InductioA.2 Proofs of Limit TheoremsA.3 Commonly Occurring LimitsA.4 Theory of the Real NumbersA.5 Complex NumbersA.6 The Distributive Law for Vector Cross ProductsA.7 The Mixed Derivative Theorem and the Increment TheoremA.8 The Area ofa Parallelogram's Projection on a PlaneA.9 Basic Algebra, Geometry, and Trigonometry FormulasAnswersIndexA Brief TaMe of IntegralsCredits
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