Calculus : early transcendental functions / created by Ron Larson and Bruce H Edwards

Includes bibliographical references and index

A Word from the Authors x
Textbook Features xiv
Preparation for Calculus
1 (60)
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)
Inverse Functions
37 (12)
Exponential and Logarithmic Functions
49 (12)
Review Exercises
57 (2)
P.S. Problem Solving
59 (2)
Limits and Their Properties
61 (54)
A Preview of Calculus
62 (6)
Finding Limits Graphically and Numerically
68 (11)
Evaluating Limits Analytically
79 (11)
Continuity and One-Sided Limits
90 (13)
Infinite Limits
103 (12)
Graphs and Limits of Trigonometric Functions
110 (1)
Review Exercises
111 (2)
P.S. Problem Solving
113 (2)
Differentiation
115 (88)
The Derivative and the Tangent Line Problem
116 (11)
Basic Differentiation Rules and Rates of Change
127 (13)
Product and Quotient Rules and Higher-Order Derivatives
140 (11)
The Chain Rule
151 (15)
Implicit Differentiation
166 (9)
Optical Illusions
174 (1)
Derivatives of Inverse Functions
175 (7)
Related Rates
182 (9)
Newton's Method
191 (12)
Review Exercises
197 (4)
P.S. Problem Solving
201 (2)
Applications of Differentiation
203 (80)
Extrema on an Interval
204 (8)
Rolle's Theorem and the Mean Value Theorem
212 (7)
Increasing and Decreasing Functions and the First Derivative Test
219 (11)
Rainbows
229 (1)
Concavity and the Second Derivative Test
230 (8)
Limits at Infinity
238 (11)
A Summary of Curve Sketching
249 (10)
Optimization Problems
259 (12)
Connecticut River
270 (1)
Differentials
271 (12)
Review Exercises
278 (3)
P.S. Problem Solving
281 (2)
Integration
283 (104)
Antiderivatives and Indefinite Integration
284 (11)
Area
295 (12)
Riemann Sums and Definite Integrals
307 (11)
The Fundamental Theorem of Calculus
318 (15)
Demonstrating the Fundamental Theorem
332 (1)
Integration by Substitution
333 (14)
Numerical Integration
347 (7)
The Natural Logarithmic Function: Integration
354 (9)
Inverse Trigonometric Functions: Integration
363 (8)
Hyperbolic Functions
371 (16)
St. Louis Arch
381 (1)
Review Exercises
382 (3)
P.S. Problem Solving
385 (2)
Differential Equations
387 (60)
Slope Fields and Euler's Method
388 (9)
Differential Equations: Growth and Decay
397 (8)
Differential Equations: Separation of Variables
405 (14)
The Logistic Equation
419 (7)
First-Order Linear Differential Equations
426 (9)
Weight Loss
434 (1)
Predator-Prey Differential Equations
435 (12)
Review Exercises
442 (3)
P.S. Problem Solving
445 (2)
Applications of Integration
447 (72)
Area of a Region Between Two Curves
448 (10)
Volume: The Disk Method
458 (11)
Volume: The Shell Method
469 (9)
Saturn
477 (1)
Arc Length and Surfaces of Revolution
478 (11)
Work
489 (9)
Tidal Energy
497 (1)
Moments, Centers of Mass, and Centroids
498 (11)
Fluid Pressure and Fluid Force
509 (10)
Review Exercises
515 (2)
P.S. Problem Solving
517 (2)
Integration Techniques, L'Hopital's Rule, and Improper Integrals
519 (76)
Basic Integration Rules
520 (7)
Integration by Parts
527 (9)
Trigonometric Integrals
536 (9)
Power Lines
544 (1)
Trigonometric Substitution
545 (9)
Partial Fractions
554 (9)
Integration by Tables and Other Integration Techniques
563 (6)
Indeterminate Forms and L'Hopital's Rule
569 (11)
Improper Integrals
580 (15)
Review Exercises
591 (2)
P.S. Problem Solving
593 (2)
Infinite Series
595 (100)
Sequences
596 (12)
Series and Convergence
608 (11)
Cantor's Disappearing Table
618 (1)
The Integral Test and p-Series
619 (7)
The Harmonic Series
625 (1)
Comparisons of Series
626 (7)
Solera Method
632 (1)
Alternating Series
633 (8)
The Ratio and Root Tests
641 (9)
Taylor Polynomials and Approximations
650 (11)
Power Series
661 (10)
Representation of Functions by Power Series
671 (7)
Taylor and Maclaurin Series
678 (17)
Review Exercises
690 (3)
P.S. Problem Solving
693 (2)
Conics, Parametric Equations, and Polar Coordinates
695 (68)
Conics and Calculus
696 (15)
Plane Curves and Parametric Equations
711 (10)
Cycloids
720 (1)
Parametric Equations and Calculus
721 (10)
Polar Coordinates and Polar Graphs
731 (10)
Anamorphic Art
740 (1)
Area and Arc Length in Polar Coordinates
741 (9)
Polar Equations of Conics and Kepler's Laws
750 (13)
Review Exercises
758 (3)
P.S. Problem Solving
761 (2)
Vectors and the Geometry of Space
763 (70)
Vectors in the Plane
764 (11)
Space Coordinates and Vectors in Space
775 (8)
The Dot Product of Two Vectors
783 (9)
The Cross Product of Two Vectors in Space
792 (8)
Lines and Planes in Space
800 (12)
Distances in Space
811 (1)
Surfaces in Space
812 (10)
Cylindrical and Spherical Coordinates
822 (11)
Review Exercises
829 (2)
P.S. Problem Solving
831 (2)
Vector-Valued Functions
833 (52)
Vector-Valued Functions
834 (8)
Witch of Agnesi
841 (1)
Differentiation and Integration of Vector-Valued Functions
842 (8)
Velocity and Acceleration
850 (9)
Tangent Vectors and Normal Vectors
859 (10)
Arc Length and Curvature
869 (16)
Review Exercises
881 (2)
P.S. Problem Solving
883 (2)
Functions of Several Variables
885 (98)
Introduction to Functions of Several Variables
886 (12)
Limits and Continuity
898 (10)
Partial Derivatives
908 (10)
Moire Fringes
917 (1)
Differentials
918 (7)
Chain Rules for Functions of Several Variables
925 (8)
Directional Derivatives and Gradients
933 (12)
Tangent Planes and Normal Lines
945 (9)
Wildflowers
953 (1)
Extrema of Functions of Two Variables
954 (8)
Applications of Extrema of Functions of Two Variables
962 (8)
Building a Pipeline
969 (1)
Lagrange Multipliers
970 (13)
Review Exercises
978 (3)
P.S. Problem Solving
981 (2)
Multiple Integration
983 (74)
Iterated Integrals and Area in the Plane
984 (8)
Double Integrals and Volume
992 (12)
Change of Variables: Polar Coordinates
1004 (8)
Center of Mass and Moments of Inertia
1012 (8)
Center of Pressure on a Sail
1019 (1)
Surface Area
1020 (7)
Capillary Action
1026 (1)
Triple Integrals and Applications
1027 (11)
Triple Integrals in Cylindrical and Spherical Coordinates
1038 (7)
Wrinkled and Bumpy Spheres
1044 (1)
Change of Variables: Jacobians
1045 (12)
Review Exercises
1052 (3)
P.S. Problem Solving
1055 (2)
Vector Analysis
1057
Vector Fields
1058 (11)
Line Integrals
1069 (14)
Conservative Vector Fields and Independence of Path
1083 (10)
Green's Theorem
1093 (9)
Hyperbolic and Trigonometric Functions
1101 (1)
Parametric Surfaces
1102 (10)
Surface Integrals
1112 (12)
Hyperboloid of One Sheet
1123 (1)
Divergence Theorem
1124 (8)
Stokes's Theorem
1132
Review Exercises
1138 (2)
The Planimeter
1140 (1)
P.S. Problem Solving
1141
Appendices
Appendix A Proofs of Selected Theorems
2 (17)
Appendix B Integration Tables
19 (5)
Appendix C Precalculus Review
24 (27)
C.1 Real Numbers and the Real Number Line
24 (9)
C.2 The Cartesian Plane
33 (7)
C.3 Review of Trigonometric Functions
40 (11)
Answers to Odd-Numbered Exercises 51 (128)
Index 179

This three-semester calculus textbook presents the principles and applications of calculus. Topics include: continuity and limits, differentiation and integration of algebraic and trigonometric functions, fundamental theorem of the calculus, applications of the derivative to curve sketching, rectilinear motion, maximum/minimum problems, and related rates, applications to the integral to problems of area, volume, arc length, and work. In addition to the beginning concepts of calculus this text also provides instruction in the differentiation and integration of transcendental functions, standard techniques of integration, curves in polar coordinates, and sequences and series, multivariable calculus, partial differentiation, two- and three dimensional vectors, Stokes and divergence theorems, and differential equations