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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
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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
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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
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5 Applications of the Integral
5£®1 The Area of a Plane Region
5£®2 Volumes of Solids£ºSlabs£®Disks£¬Wlashers
5£®3 Volumes of Solids of Revolution£ºShells
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
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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
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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
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8 Indeterminate Forms and Improper
Integrals
8£®1 Indeterminate Forms of Type 0/0
8£®2 Other Indeterminate Forms
8£®3 Improper Integrals£º Infinite Limits of Integration
8£®4 Improper Integrals£º Infinite Integrands
8£®5 Chapter Review
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9 Infinite Series
9£®1 Infinite Sequences
9£®2 Infinite Series
9£®3 Positive Series£º The Integral Test
9£®4 Positive Series£º 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
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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
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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
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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
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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
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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

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