Calculus of a Single Variable

by Larson, Ron

• ISBN13: 9780618503049
• ISBN10: 0618503048
• Edition: 8th
• Format: Hardcover
• Copyright: 2005-01-19
• Publisher: ITP DELMAR

Table of Contents

A Word from the Authors	x
Integrated Learning System for Calculus	xii
Features	xviii
Preparation for Calculus	1	(40)
Graphs and Models	2	(8)
Linear Models and Rates of Change	10	(9)
Functions and Their Graphs	19	(12)
Fitting Models to Data	31	(6)
Review Exercises	37	(2)
P.S. Problem Solving	39	(2)
Limits and Their Properties	41	(54)
A Preview of Calculus	42	(6)
Finding Limits Graphically and Numerically	48	(11)
Evaluating Limits Analytically	59	(11)
Continuity and One-Sided Limits	70	(13)
Infinite Limits	83	(7)
Section Project: Graphs and Limits of Trigonometric Functions	90	(5)
Review Exercises	91	(2)
P.S. Problem Solving	93	(2)
Differentiation	95	(68)
The Derivative and the Tangent Line Problem	96	(11)
Basic Differentiation Rules and Rates of Change	107	(12)
Product and Quotient Rules and Higher-Order Derivatives	119	(11)
The Chain Rule	130	(11)
Implicit Differentiation	141	(7)
Section Project: Optical Illusions	148	(15)
Related Rates	149	(9)
Review Exercises	158	(3)
P.S. Problem Solving	161	(2)
Applications of Differentiation	163	(84)
Extrema on an Interval	164	(8)
Rolle's Theorem and the Mean Value Theorem	172	(7)
Increasing and Decreasing Functions and the First Derivative Test	179	(10)
Section Project: Rainbows	189	(39)
Concavity and the Second Derivative Test	190	(8)
Limits at Infinity	198	(11)
A Summary of Curve Sketching	209	(9)
Optimization Problems	218	(10)
Section Project: Connecticut River	228	(19)
Newton's Method	229	(6)
Differentials	235	(7)
Review Exercises	242	(3)
P.S. Problem Solving	245	(2)
Integration	247	(74)
Antiderivatives and Indefinite Integration	248	(11)
Area	259	(12)
Riemann Sums and Definite Integrals	271	(11)
The Fundamental Theorem of Calculus	282	(12)
Section Project: Demonstrating the Fundamental Theorem	294	(27)
Integration by Substitution	295	(14)
Numerical Integration	309	(7)
Review Exercises	316	(3)
P.S. Problem Solving	319	(2)
Logarithmic, Exponential, and Other Transcendental Functions	321	(82)
The Natural Logarithmic Function: Differentiation	322	(10)
The Natural Logarithmic Function: Integration	332	(9)
Inverse Functions	341	(9)
Exponential Functions: Differentiation and Integration	350	(10)
Bases Other Than e and Applications	360	(10)
Section Project: Using Graphing Utilities to Estimate Slope	370	(28)
Inverse Trigonometric Functions: Differentiation	371	(9)
Inverse Trigonometric Functions: Integration	380	(8)
Hyperbolic Functions	388	(10)
Section Project: St. Louis Arch	398	(5)
Review Exercises	399	(2)
P.S. Problem Solving	401	(2)
Differential Equations	403	(42)
Slope Fields and Euler's Method	404	(9)
Differential Equations: Growth and Decay	413	(8)
Separation of Variables and the Logistic Equation	421	(11)
First-Order Linear Differential Equations	432	(8)
Section Project: Weight Loss	440	(5)
Review Exercises	441	(2)
P.S. Problem Solving	443	(2)
Applications of Integration	445	(72)
Area of a Region Between Two Curves	446	(10)
Volume: The Disk Method	456	(11)
Volume: The Shell Method	467	(8)
Section Project: Saturn	475	(20)
Arc Length and Surfaces of Revolution	476	(11)
Work	487	(8)
Section Project: Tidal Energy	495	(22)
Moments, Centers of Mass, and Centroids	496	(11)
Fluid Pressure and Fluid Force	507	(6)
Review Exercises	513	(2)
P.S. Problem Solving	515	(2)
Integration Techniques, L'Hopital's Rule, and Improper Integrals	517	(76)
Basic Integration Rules	518	(7)
Integration by Parts	525	(9)
Trigonometric Integrals	534	(8)
Section Project: Power Lines	542	(51)
Trigonometric Substitution	543	(9)
Partial Fractions	552	(9)
Integration by Tables and Other Integration Techniques	561	(6)
Indeterminate Forms and L'Hospital's Rule	567	(11)
Improper Integrals	578	(11)
Review Exercises	589	(2)
P.S. Problem Solving	591	(2)
Infinite Series	593	(100)
Sequences	594	(12)
Series and Convergence	606	(10)
Section Project: Cantor's Disappearing Table	616	(7)
The Integral Test and p-Series	617	(6)
Section Project: The Harmonic Series	623	(7)
Comparisons of Series	624	(6)
Section Project: Solera Method	630	(63)
Alternating Series	631	(8)
The Ratio and Root Tests	639	(9)
Taylor Polynomials and Approximations	648	(11)
Power Series	659	(10)
Representation of Functions by Power Series	669	(7)
Taylor and Maclaurin Series	676	(12)
Review Exercises	688	(3)
P.S. Problem Solving	691	(2)
Conies, Parametric Equations, and Polar Coordinates	693
Conies and Calculus	694	(15)
Plane Curves and Parametric Equations	709	(9)
Section Project: Cycloids	718	(20)
Parametric Equations and Calculus	719	(10)
Polar Coordinates and Polar Graphs	729	(9)
Section Project: Anamorphic Art	738
Area and Arc Length in Polar Coordinates	739	(9)
Polar Equations of Conies and Kepler's Laws	748	(8)
Review Exercises	756	(3)
P.S. Problem Solving	759
Appendix A Proofs of Selected Theorems	1	(19)
Appendix B Integration Tables	20	(7)
Additional Appendices
Appendix C Additional Topics in Differential Equations
Exact First-Order Equations
Second-Order Homogeneous Linear Equations
Second-Order Nonhomogeneous Linear Equations
Series Solutions of Differential Equations
Appendix D Precalculus Review
Real Numbers and the Real Number Line
The Cartesian Plane
Review of Trigonometric Functions
Appendix E Rotation and General Second-Degree Equation
Appendix F Complex Numbers
Appendix G Business and Economic Applications
Answers to Odd-Numbered Exercises	27	(82)
Index of Applications	109	(4)
Index	113