Calculus

by Finney, Ross L.; Thomas, George B.

• ISBN13: 9780201549775
• ISBN10: 0201549778
• Edition: 2nd
• Format: Hardcover
• Copyright: 1994-01-01
• Publisher: Pearson College Div

Summary

Written by two of today's most experienced and respected calculus educators, every chapter of this new edition emphasizes the book's realistic approach to calculus. Real applications and exercises, a realistic problem-solving framework, and real-world chapter openers make Calculus, Second Edition the choice for today's students.

Table of Contents

Prerequisites for Calculus
Overview	1	(1)
Coordinates, Increments, and Lines	1	(10)
Functions and Graphs	11	(11)
Trigonometric Functions	22	(8)
Shifts, Circles, and Parabolas	30	(11)
Calculus and Computation	41	(7)
Absolute Values (Magnitudes) and Target Values	48	(15)
For Your Review	58	(1)
Practice Exercises	58	(5)
Limits and Continuity
Overview	63	(1)
Limits of Function Values	63	(13)
Limits Involving Infinity	76	(8)
The Sandwich Theorem and (sinθ)/θ	84	(6)
Continuous Functions	90	(11)
Defining Limits Formally with Epsilons and Deltas	101	(12)
For Your Review	109	(1)
Practice Exercises	109	(4)
Derivatives
Overview	113	(1)
Slopes, Tangent Lines, and Derivatives	113	(13)
Differentiation Rules	126	(12)
Velocity, Speed, and Other Rates of Change	138	(14)
Derivatives of Trigonometric Functions	152	(7)
The Chain Rule	159	(9)
Implicit Differentiation and Fractional Powers	168	(8)
Linearizations and Differentials	176	(11)
Newton's Method	187	(14)
For Your Review	195	(1)
Practice Exercises	195	(6)
Applications of Derivatives
Overview	201	(1)
Related Rates of Change	201	(8)
Extreme Values of Functions	209	(9)
How Y' and Y'' Determine the Shape of a Graph	218	(9)
Graphs of Rational Functions--Asymptotes and Dominant Terms	227	(7)
Optimization	234	(12)
The Mean Value Theorem	246	(7)
Antiderivatives, Differential Equations, and Modeling	253	(18)
For Your Review	265	(1)
Practice Exercises	266	(5)
Integration
Overview	271	(1)
Estimating with Finite Sums	271	(11)
Riemann Sums and Definite Integrals	282	(12)
Basic Properties, Area, and the Mean Value Theorem for Integrals	294	(8)
The Fundamental Theorem of Calculus	302	(11)
Indefinite Integrals	313	(9)
Integration by Substitution--Running the Chain Rule Backward	322	(9)
Numerical Integration	331	(16)
For Your Review	342	(1)
Practice Exercises	342	(5)
Transcendental Functions
Overview	347	(1)
Exponential Functions and the Derivative of ex	347	(8)
Inverse Functions and Their Derivatives	355	(6)
Logarithmic Functions and the Derivative of ln x	361	(12)
Exponential and Logarithmic Integrals; ln	373	(6)
Growth and Decay	379	(9)
L'Hopital's Rule	388	(7)
Relative Rates of Growth	395	(6)
Inverse Trigonometric Functions	401	(8)
Derivatives of Inverse Trigonometric Functions; Integrals	409	(7)
Hyperbolic Functions	416	(8)
First Order Differential Equations	424	(15)
For your Review	434	(1)
Practice Exercises	435	(4)
Applications of Integration
Overview	439	(1)
Areas Between Curves	439	(7)
Volumes of Solids of Revolution --- Disks and Washers	446	(10)
Cylindrical Shells --- An Alternative to Washers	456	(6)
Curve Length and Surface Area	462	(10)
Work	472	(7)
Fluid Pressures and Fluid Forces	479	(7)
Centers of Mass	486	(11)
The Basic Pattern and Other Modeling Applications	497	(14)
For Your Review	507	(1)
Practice Exercises	507	(4)
Techniques of Integration
Overview	511	(1)
Basic Integration Formulas	511	(6)
Integration by Parts	517	(7)
Partial Fractions	524	(5)
Trigonometric Substitutions	529	(5)
Integral Tables	534	(8)
Improper Integrals	542	(15)
For Your Review	552	(1)
Practice Exercises	552	(5)
Infinite Series
Overview	557	(1)
Sequences	557	(10)
Infinite Series	567	(9)
Series with Nonnegative Terms---Comparison and Integral Tests	576	(9)
Series with Nonnegative Terms---Ratio and Root Tests	585	(6)
Alternating Series and Absolute Convergence	591	(6)
Power Series	597	(8)
Taylor and Maclaurin Series	605	(14)
Calculations with Taylor Series	619	(10)
For Your Review	626	(1)
Practice Exercises	626	(3)
Conic Sections, Parametrized Curves, and Polar Coordinates
Overview	629	(1)
Conic Sections and Quadratic Equations	629	(16)
The Graphs of Quadratic Equations in x and y; Rotations About the Origin	645	(5)
Parametrizations of Curves	650	(6)
Calculus with Parametrized Curves	656	(6)
Polar Coordinates	662	(5)
Polar Graphs	667	(7)
Polar Equations for Conic Sections	674	(6)
Integration in Polar Coordinates	680	(11)
For Your Review	686	(1)
Practice Exercises	687	(4)
Vectors and Analytic Geometry in Space
Overview	691	(1)
Vectors in the Plane	691	(9)
Cartesian (Rectangular) Coordinates and Vectors in Space	700	(10)
Dot Products	710	(8)
Cross Products	718	(6)
Lines and Planes in Space	724	(7)
Surfaces in Space	731	(10)
Cylindrical and Spherical Coordinates	741	(10)
For Your Review	746	(1)
Practice Exercises	747	(4)
Vector-Valued Functions
Overview	751	(1)
Vector-Valued Functions and Space Curves	751	(11)
Modeling Projectile Motion	762	(9)
Arc Length and the Unit Tangent Vector T	771	(5)
Curvature, Torsion, and the TNB Frame	776	(12)
Planetary Motion and Satellites	788	(11)
For Your Review	795	(1)
Practice Exercises	795	(4)
Partial Derivatives
Overview	799	(1)
Functions of Several Independent Variables	799	(9)
Limits and Continuity	808	(6)
Partial Derivatives	814	(9)
Differentiability, Linearization, and Differentials	823	(10)
The Chain Rule	833	(8)
Directional Derivatives, Gradient Vectors, and Tangent Planes	841	(12)
Maxima, Minima, and Saddle Points	853	(11)
Lagrange Multipliers	864	(13)
For Your Review	873	(1)
Practice Exercises	873	(4)
Multiple Integrals
Overview	877	(1)
Double Integrals	877	(10)
Areas, Moments, and Centers of Mass	887	(6)
Double Integrals in Polar Form	893	(6)
Triple Integrals in Rectangular Coordinates	899	(7)
Masses and Moments in Three Dimensions	906	(4)
Triple Integrals in Cylindrical and Spherical Coordinates	910	(9)
Substitutions in Multiple Integrals	919	(12)
For Your Review	927	(1)
Practice Exercises	927	(4)
Integration in Vector Fields
Overview	931	(1)
Line Integrals	931	(6)
Vector Fields, Work, Circulation, and Flux	937	(9)
Path Independence, Potential Functions, and Conservative Fields	946	(8)
Green's Theorem in the Plane	954	(11)
Surface Area and Surface Integrals	965	(10)
Parametrized Surfaces	975	(8)
Stokes's Theorem	983	(10)
The Divergence Theorem	993
For Your Review	1001	(1)
Practice Exercises	1001
Appendices
A.1 Formulas from Precalculus Mathematics	A-1	(1)
A.2 Proofs of the Limit Theorems in Chapter 2	A-6	(1)
A.3 A Proof of the Chain Rule for Functions of a Single Variable	A-9	(1)
A.4 Mathematical Induction	A-10	(1)
A.5 Simpson's One-Third Rule	A-13	(1)
A.6 Limits That Arise Frequently	A-14	(1)
A.7 Determinants and Cramer's Rule	A-16	(1)
A.8 Path Independence of ∫ F. dr Implies F = ∇f	A-24	(1)
A.9 Complex Numbers	A-25	(1)
A.10 Tables for sin x, cos x, tan x, ex, e--x, and ln x	A-26	(1)
Answers	A-29	(1)
Index	I-1	(1)
A Brief Table of Integrals	T-1