Calculus of a Single Variable

by Larson, Ron; Hostetler, Robert P.; Edwards, Bruce H.

• ISBN13: 9780395885789
• ISBN10: 0395885787
• Edition: 6th
• Format: Paperback
• Copyright: 1997-11-06
• Publisher: Brooks Cole

Summary

This text combines the theoretical instruction of calculus with current best-practise strategies.

Table of Contents

A Word from the Authors (Preface)	ix
Index of Applications	xxxi
Preparation for Calculus	1	(38)
Graphs and Models	3	(8)
Linear Models and Rates of Change	11	(9)
Functions and Their Graphs	20	(11)
Fitting Models to Data	31	(8)
Review Exercises	37	(2)
Limits and Their Properties	39	(50)
A Preview of Calculus	41	(6)
Finding Limits Graphically and Numerically	47	(9)
Evaluating Limits Analytically	56	(11)
Continuity and One-Sided Limits	67	(12)
Infinite Limits	79	(10)
Review Exercises	87	(2)
Differentiation	89	(64)
The Derivative and the Tangent Line Problem	91	(11)
Basic Differentiation Rules and Rates of Change	102	(12)
The Product and Quotient Rules and Higher-Order Derivatives	114	(10)
The Chain Rule	124	(10)
Implicit Differentiation	134	(7)
Related Rates	141	(12)
Review Exercises	150	(3)
Applications of Differentiation	153	(86)
Extrema on an Interval	155	(8)
Rolle's Theorem and the Mean Value Theorem	163	(6)
Increasing and Decreasing Functions and the First Derivative Test	169	(10)
Concavity and the Second Derivative Test	179	(8)
Limits at Infinity	187	(9)
A Summary of Curve Sketching	196	(9)
Optimization Problems	205	(10)
Newton's Method	215	(6)
Differentials	221	(7)
Business and Economics Applications	228	(11)
Review Exercises	235	(4)
Integration	239	(70)
Antiderivatives and Indefinite Integration	241	(11)
Area	252	(12)
Riemann Sums and Definite Integrals	264	(10)
The Fundamental Theorem of Calculus	274	(13)
Integration by Substitution	287	(12)
Numerical Integration	299	(10)
Review Exercises	306	(3)
Logarithmic, Exponential, and Other Transcendental Functions	309	(96)
The Natural Logarithmic Function and Differentiation	311	(10)
The Natural Logarithmic Function and Integration	321	(8)
Inverse Functions	329	(9)
Exponential Functions: Differentiation and Integration	338	(10)
Bases Other than e and Applications	348	(10)
Differential Equations: Growth and Decay	358	(8)
Differential Equations: Separation of Variables	366	(11)
Inverse Trigonometric Functions and Differentiation	377	(8)
Inverse Trigonometric Functions and Integration	385	(7)
Hyperbolic Functions	392	(13)
Review Exercises	402	(3)
Applications of Integration	405	(68)
Area of a Region Between Two Curves	407	(9)
Volume: The Disc Method	416	(11)
Volume: The Shell Method	427	(8)
Arc Length and Surfaces of Revolution	435	(10)
Work	445	(9)
Moments, Centers of Mass, and Centroids	454	(11)
Fluid Pressure and Fluid Force	465	(8)
Review Exercises	471	(2)
Integration Techniques, L'Hopital's Rule, and Improper Integrals	473	(72)
Basic Integration Rules	475	(6)
Integration by Parts	481	(9)
Trigonometric Integrals	490	(9)
Trigonometric Substitution	499	(9)
Partial Fractions	508	(9)
Integration by Tables and Other Integration Techniques	517	(6)
Indeterminate Forms and L'Hopital's Rule	523	(10)
Improper Integrals	533	(12)
Review Exercises	542	(3)
Infinite Series	545	(90)
Sequences	547	(11)
Series and Convergence	558	(10)
The Integral Test and P-Series	568	(6)
Comparisons of Series	574	(7)
Alternating Series	581	(7)
The Ratio and Root Tests	588	(8)
Taylor Polynomials and Approximations	596	(10)
Power Series	606	(9)
Representation of Functions by Power Series	615	(7)
Taylor and Maclaurin Series	622	(13)
Review Exercises	632	(3)
Conics, Parametric Equations, and Polar Coordinates	635	(2)
Conics and Calculus	637	(15)
Plane Curves and Parametric Equations	652	(10)
Parametric Equations and Calculus	662	(9)
Polar Coordinates and Polar Graphs	671	(10)
Area and Arc Length in Polar Coordinates	681	(8)
Polar Equations of Conics and Kepler's Laws	689	(7)
Review Exercises	696
Appendix A Precalculus Review	A1
A.1 Real Numbers and the Real Line	A1
A.2 The Cartesian Plane	A10
A.3 Review of Trigonometric Functions	A17
Appendix B Proofs of Selected Theorems	A28
Appendix C Basic Differentiation Rules for Elementary Functions	A44
Appendix D Integration Tables	A45
Appendix E Rotation and the General Second-Degree Equation	A51
Appendix F Complex Numbers	A57
Answers to Odd-Numbered Exercises	A69
Index	A159