9780618149162

Calculus of a Single Variable

by
  • ISBN13:

    9780618149162

  • ISBN10:

    0618149163

  • Edition: 7th
  • Format: Hardcover
  • Copyright: 7/13/2001
  • Publisher: CENGAGE Learning
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Summary

Ideal for the single-variable, one-, or two-semester calculus course, "Calculus of a Single Variable, 7/e, contains the first 9 chapers of "Calculus with Analytic Geometry, 7/e. For a description, see Larson et al., "Calculus with Analytic Geometry, 7/e.

Table of Contents

A Word from the Authors (Preface) ix
Features xi
Preparation for Calculus
1(39)
Eruptions of Old Faithful
1(1)
Graphs and Models
2(8)
Linear Models and Rates of Change
10(9)
Functions and Their Graphs
19(11)
Fitting Models to Data
30(10)
Review Exercises
36(2)
Problem Solving
38(2)
Limits and Their Properties
40(52)
Swimming Speed: Taking It to the Limit
40(2)
A Preview of Calculus
42(6)
Finding Limits Graphically and Numerically
48(9)
Evaluating Limits Analytically
57(11)
Continuity and One-Sided Limits
68(12)
Infinite Limits
80(12)
Section Project: Graphs and Limits of Trigonometric Functions
87(1)
Review Exercises
88(2)
Problem Solving
90(2)
Differentiation
92(66)
Gravity: Finding It Experimentally
92(2)
The Derivative and the Tangent Line Problem
94(11)
Basic Differentiation Rules and Rates of Change
105(12)
The Product and Quotient Rules and Higher-Order Derivatives
117(10)
The Chain Rule
127(10)
Implicit Differentiation
137(7)
Section Project: Optical Illusions
143(1)
Related Rates
144(14)
Review Exercises
153(3)
Problem Solving
156(2)
Applications of Differentiation
158(82)
Packaging: The Optimal Form
158(2)
Extrema on an Interval
160(8)
Rolle's Theorem and the Mean Value Theorem
168(6)
Increasing and Decreasing Functions and the First Derivative Test
174(10)
Section Project: Rainbows
183(1)
Concavity and the Second Derivative Test
184(8)
Limits at Infinity
192(10)
A Summary of Curve Sketching
202(9)
Optimization Problems
211(11)
Section Project: Connecticut River
211(11)
Newton's Method
222(6)
Differentials
228(12)
Review Exercises
235(3)
Problem Solving
238(2)
Integration
240(72)
The Wankel Rotary Engine and Area
240(2)
Antiderivatives and Indefinite Integration
242(11)
Area
253(12)
Reimann Sums and Definite Integrals
265(10)
The Fundamental Theorem of Calculus
275(13)
Section Project: Demonstrating the Fundamental Theorem
287(1)
Integration by Substitution
288(12)
Numerical Integration
300(12)
Review Exercises
307(3)
Problem Solving
310(2)
Logarithmic, Exponential, and Other Transcendental Functions
312(98)
Plastics and Cooling
312(2)
The Natural Logarithmic Function: Differentiation
314(10)
The Natural Logarithmic Function: Integration
324(8)
Inverse Functions
332(9)
Exponential Functions: Differentiation and Integration
341(10)
Bases Other Than e and Applications
351(10)
Section Project: Using Graphing Utilities to Estimate Slope
360(1)
Differential Equations: Growth and Decay
361(8)
Differential Equations: Separation of Variables
369(11)
Inverse Trigonometric Functions: Differentiation
380(8)
Inverse Trigonometric Functions: Integration
388(7)
Hyperbolic Functions
395(15)
Section Project: St. Louis Arch
405(1)
Review Exercises
405(3)
Problem Solving
408(2)
Applications of Integration
410(70)
Constructing an Arch Dam
410(2)
Area of a Region Between Two Curves
412(9)
Volume: The Disk Method
421(11)
Volume: The Shell Method
432(8)
Section Project: Saturn
439(1)
Arc Length and Surfaces of Revolution
440(10)
Work
450(9)
Section Project: Tidal Energy
458(1)
Moments, Centers of Mass, and Centroids
459(11)
Fluid Pressure and Fluid Force
470(10)
Review Exercises
476(2)
Problem Solving
478(2)
Integration Techniques, L'Hopital's Rule, and Improper Integrals
480(74)
Making a Mercator Map
480(2)
Basic Integration Rules
482(6)
Integration by Parts
488(9)
Trigonometric Integrals
497(9)
Section Project: Power Lines
505(1)
Trigonometric Substitution
506(9)
Partial Fractions
515(9)
Integration by Tables and Other Integration Techniques
524(6)
Indeterminate Forms and L'Hopital's Rule
530(10)
Improper Integrals
540(14)
Review Exercises
550(2)
Problem Solving
552(2)
Infinite Series
554(94)
The Koch Snowflake: Infinite Perimeter?
554(2)
Sequences
556(11)
Series and Convergence
567(10)
Section Project: Cantor's Disappearing Table
576(1)
The Integral Test and p-Series
577(6)
Section Project: The Harmonic Series
582(1)
Comparisons of Series
583(7)
Section Project: Solera Method
589(1)
Alternating Series
590(7)
The Ratio and Root Tests
597(8)
Taylor Polynomials and Approximations
605(11)
Power Series
616(9)
Representation of Functions by Power Series
625(7)
Taylor and Maclaurin Series
632(16)
Review Exercises
643(3)
Problem Solving
646(2)
Conics, Parametric Equations, and Polar Coordinates
648(1)
Exploring New Planets
648(2)
Conics and Calculus
650(15)
Plane Curves and Parametric Equations
665(9)
Section Project: Cycloids
674(1)
Parametric Equations and Calculus
675(9)
Polar Coordinates and Polar Graphs
684(9)
Section Project: Anamorphic Art
693(1)
Area and Arc Length in Polar Coordinates
694(8)
Polar Equations of Conics and Kepler's Laws
702(7)
Review Exercises
709(3)
Problem Solving
712
Appendices 1(1)
Appendix A Additional Topics in Differential Equations
2(7)
Appendix B Proofs of Selected Theorems
9(18)
Appendix C Integration Tables
27(6)
Appendix D Precalculus Review
Appendix E Rotation and the General Second-Degree Equation
Appendix F Complex Numbers
Appendix G Business and Economic Applications
Answers to Odd-Numbered Exercises 33(96)
Index of Applications 129(4)
Index 133

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