- 微积分(第1卷第2版)
- - 作者：James Stewart
  - 出版社：世界图书出版公司
  - ISBN：7506266253
  - 出版日期：2011/10/01
  - 页数：645
- 售价：31.2

内容大纲
The first edition was intended to be a synthesis of reform and traditional approaches to calculus instruction.In this second edition I continue to follow that path by empha-sizing conceptual understanding through visual,numerical,and algebraic approaches.The principal way in which this book differs from my more traditional calculus textbooks is that it is more streamlined. For instance,there is no complete chapter on techniques of integration;I don't prove as many theorems;and the material on transcendental functions and on parametric equations is interwoven throughout the book instead of being treated in separate chapters.Instruc-tors who prefer fuller coverage of traditional calculus topics should look at my books Calculus,Fourth Edition and Calculus: Early Transcendentals,Fourth Edition.
作者介绍
目录
A Preview of Calculus
1  Functions and Models
　1.1 Four Ways to Represent a Function
　1.2 Mathematical Models
　1.3 New Functions from Old Functions
　1.4 Graphing Calculators and Computers
　1.5 Exponential Functions
　1.6 Inverse Functions and Logarithms
　1.7 Parametric Curves
　  Laboratory Project Running Circles around Circles
　Review
　Principles of Problem Solving
2  Limits and Derivatives
　2.1 The Tangent and Velocity Problems
　2.2 The Limit of a Function
　2.3 Calculating Limits Using the Limit Laws
　2.4 Continuity
　2.5 Limits Involving Infinity
　2.6 Tangents, Velocities, and Other Rates of Change
　2.7 Derivatives
　  Writing Project: Early Methods for Finding Tangents
　2.8 The Derivative as a Function
　2.9 Linear Approximations
　2.10 What Does f' Say about f?
　Review
　Focus on Problem Solving
3  Differentiation Rules
  3.1  Derivatives of Polynomials and Exponential Functions
    Applied Project Building a Better Roller Coaster
  3.2  The Product and Quotient Rules
  3.3  Rates of Change in the Natural and Social Sciences
  3.4  Derivatives of Trigonometric Functions
  3.5  The Chain Rule
    Laboratory Project Bezier Curves
    Applied Project Where Should a Pilot Start Descent
  3.6  Implicit Differentiation
  3.7  Derivatives of Logarithmic Functions
    Discovery Project Q Hyperbolic Functions
  3.8  Linear Approximations and Differentials
    Laboratory Project ~ Taylor Polynomials
  Review
  Focus on Problem Solving
4  Applications of Differentiation
  4.1  Related Rates
  4.2  Maximum and Minimum Values
    Applied Project The Calculus of Rainbows
  4.3  Derivatives and the Shapes of Curves
  4.4  Graphing with Calculus and Calculators
  4.5  Indeterminate Forms and l'Hospital's Rule
    Writing Project The Origins of l'Hospital's Rule

  4.6  Optimization Problems
    Applied Project The Shape of a Can
  4.7  Applications to Economics
  4.8  Newton's Method
  4.9  Antiderivatives
  Review
  Focus on Problem Solving
5  Integrals
  5.1  Areas and Distances
  5.2  The Definite Integral
  5.3  Evaluating Definite Integrals
    Discovery Project Area Functions
  5.4  The Fundamental Theorem of Calculus
    Writing Project Newton, Leibniz, and the Invention of Calculus
  5.5  The Substitution Rule
  5.6  Integration by Parts
  5.7  Additional Techniques of Integration
  5.8  Integration Using Tables and Computer Algebra Systems
    Discovery Project ~ Patterns in Integrals
  5.9  Approximate Integration
  5.10  Improper Integrals
  Review
  Focus on Problem Solving
6  Applications of Integration
  6.1  More about Areas
  6.2  Volumes
    Discovery Project o Rotating on a Slant
  6.3  Arc Length
    Discovery Project Arc Lengh Contest
  6.4  Average Value of a Function
    Applied Project Where to Sit at the Movies
  6.5  Applications to Physics and Engineering
  6.6  Applications to Economics and Biology
  6.7  Probability
  Review
  Focus on Problem Solving
7  Differential Equations
  7.1  Modeling with Differential Equations
  7.2  Direction Fields and Euler's Method
  7.3  Separable Equations
    Applied Project o Which Is Faster, Going Up or Coming Down
  7.4  Exponential Growth and Decay
    Applied Project o Calculus and Baseball
  7.5  The Logistic Equation
  7.6  Predator-Prey Systems
  Review
  Focus on Problem Solving
8  Infinite Sequences and Series
  8.1  Sequences
    Laboratory Project Logistic Sequences

  8.2  Series
  8.3  The Integral and Comparison Tests; Estimating Sums
  8.4  Other Convergence Tests
  8.5  Power Series
  8.6  Representations of Functions as Power Series
  8.7  Taylor and Maclaurin Series
  8.8  The Binomial Series
    Writing Project How Newton Discovered the Binomial Series
  8.9  Applications of Taylor Polynomials
    Applied Projeet Radiation from the Stars
  8.10  Using Series to Solve Differential Equations
  Review
  Focus on Problem Solving
9  Vectors and the Geometry of Space
  9.1  Three-Dimensional Coordinate Systems
  9.2  Vectors
  9.3  The Dot Product
  9.4  The Cross Product
    Discovery Projeet The Geometry of a Tetrahedron
  9.5  Equations of Lines and Planes
  9.6  Functions and Surfaces
  9.7  Cylindrical and Spherical Coordinates
    Laboratory Project Families of Surfaces
  Review
  Focus oil Problem Solving
10  Vector Functions
  10.1  Vector Functions and Space Curves
  10.2  Derivatives and Integrals of Vector Functions
  10.3  Arc Length and Curvature
  10.4  Motion in Space
    Applied Project Kepler's Laws
  10.5  Parametric Surfaces
  Review
  Focus on Problem Solving
11  Partial Derivatives
  11.1  Functions of Several Variables
  11.2  Limits and Continuity
  11.3  Partial Derivatives
  11.4   Tangent Planes and Linear Approximations
  11.5  The Chain Rule
  11.6  Directional Derivatives and the Gradient Vector
  11.7  Maximum and Minimum Values
    Applied Project Designing a Dumpster
    Discovery Project Quadratic Approximations and Critical Points
  11.8  Lagrange Multipliers
    Applied Project Rocket Science
    Apldied Project Hydro-Turbine Optimization
  Review
  Focus on Problem Solving
12  Multiple Integrals

  12.1  Double Integrals over Rectangles
  12.2  Iterated Integrals
  12.3  Double Integrals over General Regions
  12.4  Double Integrals in Polar Coordinates
  12.5  Applications of Double Integrals
  12.6  Surface Area
  12.7   Triple Integrals
    Discovery Project Volumes of Hyperspheres
  12.8  Triple Integrals in Cylindrical and Spherical Coordinates
    Apldied Project Roller Derby
    Discovery Project The Intersection of Three Cylinders
  12.9  Change of Variables in Multiple Integrals
  Review
  Focus on Problem Solving
13 Vector Calculus
  13.1  Vector Fields
  13.2  Line Integrals
  13.3  The Fundamental Theorem for Line Integrals
  13.4  Green's Theorem
  13.5  Curl and Divergence
  13.6  Surface Integrals
  13.7  Stokes' Theorem
    Writing Project o Three Men and Two Theorems
  13.8  The Divergence Theorem
  13.9  Summary
  Review
  Foeus on Problem Solving
Appendixes
  A  Intervals, Inequalities, and Absolute Values
  B  Coordinate Geometry
  C  Trigonometry
  D  Precise Definitions of Limits
  E  A Few Proofs
  F  Sigma Notation
  G  Integration of Rational Functions by Partial Fractions
  H  Polar Coordinates
  I  Complex Numbers
  J  Answers to Odd-Numbered Exercises
Index

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作者介绍

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