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內容簡介

　　本書是一本在美國大學中使用麵比較廣泛的微積分教材。有重視應用、便於自學、習題數量與內容比較豐富等特點。而與其他美國教材的差彆在於嚴謹性，本書許多定理都有較嚴謹的證明，這一點與我國許多現行的理工科微積分教材比較類似。在美國也是另一種風格的教材。
　　本書強調應用，習題數量多，類型多，重視不同數學學科之間的交叉，強調其實際背景，反映當代科技發展。每章之後有附加內容，有利用圖形計算器或數學軟件計算的習題或帶研究性的小題目等。

內頁插圖

目錄

齣版說明
序
Preface

0 Preliminaries
0．1 Real Numbers．Estimation，and Logic
0．2 Inequalities and Absolute Values
0．3 The Rectangular Coordinate System
0．4 Graphs of Equations
0．5 Functions and Their Graphs
0．6 Operations on Functions
0．7 Trigonometric Functions
0．8 Chapter Review
Review and Preview Problems

1 Limits
1．1 Introduction to Limits
1．2 Rigorous Study of Limits
1．3 Limit Theorems
1．4 Limits Involving Trigonometric Functions
1．5 Limits at Infinity；Infinite Limits
1．6 Continuity of Functions
1．7 Chapter Review
Review and Preview Problems

2 The Derivative
2．1 Two Problems with One Theme
2．2 The Derivative
2．3 Rules for Finding Derivatives
2．4 Derivatives of Trigonometric Functions
2．5 The Chain Rule
2．6 Higher-Order Derivatives
2．7 Implicit Differentiation
2．8 Related Rates
2．9 Differentials and Approximations
2．10 Chapter Review
Review and Preview Problems

3 Applications of the Derivative
3．1 Maxima and Minima
3．2 Monotonicity and Concavity
3．3 Local Extrema and Extrema on Open Intervals
3．4 Practical Problems
3．5 Graphing Functions Using Calculus
3．6 The Mean Value Theorem for Derivatives
3．7 Solving Equations Numerically
3．8 Antiderivatives
3．9 Introduction to Differential Equations
3．10 Chapter Review
Review and Preview Problems
4 The Deftnite Integral

4．1 Introduction to Area
4．2 The Definite Integral
4．3 The First Fundamental Theorem of Calculus
4．4 The Second Fundamental Theorem of Calculus and the Method of Substitution
4．5 The Mean Value Theorem for Integrals and the Use of Symmetry
4．6 Numerical Integration
4．7 Chapter Review
Review and Preview Problems

5 Applications of the Integral
5．1 The Area of a Plane Region
5．2 Volumes of Solids：Slabs．Disks，Wlashers
5．3 Volumes of Solids of Revolution：Shells
5．4 Length of a Plane Curve
5．5 Work and Fluid Force
5．6 Moments and Center of Mass
5．7 Probability and Random Variabtes
5．8 Chapter Review322
Review and Preview Problems

6 Transcendental Functions
6．1 The Natural Logarithm Function
6．2 Inverse Functions and Their Derivatives
6．3 The Natural Exponential Function
6．4 General Exponential and Logarithmic Functions
6．5 Exponential Growth and Decay
6．6 First．Order Linear Differential Equations
6．7 Approximations for Differential Equations
6．8 The Inverse Trigonometric Functions and Their Derivatives
6．9 The Hyperbolic Functions and Their Inverses
6．10 Chapter Review
Review and Preview Problems

7 Techniques of Integration
7．1 Basic Integration Rules
7．2 Integration by Parts
7．3 Some Trigonometric Integrals
7．4 Rationalizing Substitutions
7．5 Integration of Rational Functions Using Partial Fractions
7．6 Strategies for Integration
7．7 Chapter Review
Review and Preview Problems

8 Indeterminate Forms and Improper
Integrals
8．1 Indeterminate Forms of Type 0/0
8．2 Other Indeterminate Forms
8．3 Improper Integrals： Infinite Limits of Integration
8．4 Improper Integrals： Infinite Integrands
8．5 Chapter Review
Review and Preview Problems

9 Infinite Series
9．1 Infinite Sequences
9．2 Infinite Series
9．3 Positive Series： The Integral Test
9．4 Positive Series： Other Tests
9．5 Alternating Series， Absolute Convergence， and Conditional Convergence
9．6 Power Series
9．7 Operations on Power Series
9．8 Taylor and Maclaurin Series
9．9 The Taylor Approximation to a Function
9．10 Chapter Review
Review and Preview Problems

10 Conics and Polar Coordinates
10．1 The Parabola
10．2 Ellipses and Hyperbolas
10．3 Translation and Rotation of Axes
10．4 Parametric Representation of Curves in the Plane
10．5 The Polar Coordinate System
10．6 Graphs of Polar Equations
10．7 Calculus in Polar Coordinates
10．8 Chapter Review
Review and Preview Problems

11 Geometry in Space and Vectors
11．1 Cartesian Coordinates in Three-Space
11．2 Vectors
11．3 The Dot Product
11．4 The Cross Product
11．5 Vector-Valued Functions and Curvilinear Motion
11．6 Lines and Tangent Lines in Three-Space
11．7 Curvature and Components of Acceleration
11．8 Surfaces in Three-Space
11．9 Cylindrical and Spherical Coordinates
11．10 Chapter Review
Review and Preview Problems

12 Derivatives for Functions of Two or More Variables
12．1 Functions of Two or More Variables
12．2 Partial Derivatives
12．3 Limits and Continuity
12．4 Differentiability
12．5 Directional Derivatives and Gradients
12．6 The Chain Rule
12．7 Tangent Planes and Approximations
12．8 Maxima and Minima
12．9 The Method of Lagrange Multipliers
12．10 Chapter Review
Review and Preview Problems

13 Multiple Integrals
13．1 Double Integrals over Rectangles
13．2 Iterated Integrals
13．3 Double Integrals over Nonrectangular Regions
13．4 Double Integrals in Polar Coordinates
13．5 Applications of Double Integrals
13．6 Surface Area
13．7 Triple Integrals in Cartesian Coordinates
13．8 Triple Integrals in Cylindrical and Spherical Coordinates
13．9 Change of Variables in Multiple Integrals
13．10 Chapter Review
Review and Preview Problems

14 Vector Calculus
14．1 Vector Fields
14．2 Line Integrals
14．3 Independence of Path
14．4 Green's Theorem in the Plane
14．5 Surface Integrals
14．6 Gauss's Divergence Theorem
14．7 Stokes's Theorem
14．8 Chapter Review

Appendix
A．1 Mathematical Induction
A．2 Proofs of Several Theorems

教輔材料說明
教輔材料申請錶

前言/序言

　　國內齣版的理工類非數學專業的微積分教材很多，其中不少是有一定特色的。特彆是近幾年來隨著大學數學教學改革的不斷深入，反映在教材建設上，其成果還是比較突齣的。但從我在教學和教改研究中所讀到的教材看，還存在著一些值得討論的問題。
　　第一是教材雖多，但在總的體係結構上大體雷同，受原蘇聯教材的影響還較重。當然，這並不是說這種體係不好，而是太多差異不大的教材，不利於比較和促進教材的建設工作。
　　第二是教材的文風都比較正統，語言不太生動，有種使讀者，特彆是數學基礎差一點的讀者望而生畏之感，也就是教材的可讀性方麵值得改進。
　　第三是習題不夠豐富，題型的變化較少，應用問題，特彆是有真實數據的、符閤我國實際的應用問題很少。
　　由DaleVarberg等編寫的《Calculus》第9版是一本在美國大學中使用麵比較廣泛的微積分教材。該書與在美國采用更廣泛的微積分教材《Thomas Calculus》比較，有不少共同之處，如重視應用、便於自學、習題數量與內容比較豐富等。而較大的差彆是該教材比較強調數學的嚴謹性，例如在極限處理上，雖然也是主要講函數極限，但書中不但有嚴格的δ-8定義，而且用較大的篇幅用其證明一些極限；許多定理都有較嚴謹的證明。這一點與我國許多現行的理工科微積分教材比較類似，在美國也是另一種風格的教材。本書強調應用，習題數量多，類型多，重視不同數學學科之間的交叉，強調其實際背景，反映當代科技發展。每章之後有附加內容，包含利用圖形計算器或數學軟件計算的習題或帶研究性的小題目等。
　　本教材的內容有：一元微積分，包括函數、極限，函數連續性，倒數及其應用，積分及其應用，不定型的極限及廣義積分，級數、數值方法及逼近；多元微積分，包括空間解析幾何，嚮量，多元函數的導數與二重、三重積分，以及嚮量場的微積分；最後是微分方程。
　　總之，這種基礎數學教材的影印齣版，對於我們藉鑒國外好的教學經驗，推動我國的數學教學改革，特彆是對當前提倡的“雙語教學”工作，一定會起到很好的作用，收到良好的效果。
時代教育·國外高校優秀教材精選：微積分（英文版·原書第9版） 下載 mobi epub pdf txt 電子書

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