Calculus of a Single Variable

by Larson, Ron

• ISBN13: 9780618149162
• ISBN10: 0618149163
• Edition: 7th
• Format: Hardcover
• Copyright: 2001-07-13
• Publisher: CENGAGE Learning

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