Calculus

by Varberg, Dale; Purcell, Edwin, deceased; Rigdon, Steve

• ISBN13: 9780131429246
• ISBN10: 0131429248
• Edition: 9th
• Format: Hardcover
• Copyright: 2006-02-28
• Publisher: Pearson
• More Book Details

Summary

Clear and Concise. Varberg focuses on the most critical concepts. This popular calculus text remains the shortest mainstream calculus book available yet coversallrelevant material needed by, and appropriate to, the study of calculus at this level. It's conciseness and clarity helps you focus on, and understand, critical concepts in calculus without them getting bogged down and lost in excessive and unnecessary detail. It is accurate, without being excessively rigorous, up-to-date without being faddish.

Table of Contents

Preface	ix
Preliminaries	1	(54)
Real Numbers, Estimation, and Logic	1	(7)
Inequalities and Absolute Values	8	(8)
The Rectangular Coordinate System	16	(8)
Graphs of Equations	24	(5)
Functions and Their Graphs	29	(6)
Operations on Functions	35	(6)
Trigonometric Functions	41	(10)
Chapter Review	51	(4)
Review and Preview Problems	54	(1)
Limits	55	(38)
Introduction to Limits	55	(6)
Rigorous Study of Limits	61	(7)
Limit Theorems	68	(5)
Limits Involving Trigonometric Functions	73	(4)
Limits at Infinity; Infinite Limits	77	(5)
Continuity of Functions	82	(8)
Chapter Review	90	(3)
Review and Preview Problems	92	(1)
The Derivative	93	(58)
Two Problems with One Theme	93	(7)
The Derivative	100	(7)
Rules for Finding Derivatives	107	(7)
Derivatives of Trigonometric Functions	114	(4)
The Chain Rule	118	(7)
Higher-Order Derivatives	125	(5)
Implicit Differentiation	130	(5)
Related Rates	135	(7)
Differentials and Approximations	142	(5)
Chapter Review	147	(4)
Review and Preview Problems	150	(1)
Applications of the Derivative	151	(64)
Maxima and Minima	151	(4)
Monotonicity and Concavity	155	(7)
Local Extrema and Extrema on Open Intervals	162	(5)
Practical Problems	167	(11)
Graphing Functions Using Calculus	178	(7)
The Mean Value Theorem for Derivatives	185	(5)
Solving Equations Numerically	190	(7)
Antiderivatives	197	(6)
Introduction to Differential Equations	203	(6)
Chapter Review	209	(6)
Review and Preview Problems	214	(1)
The Definite Integral	215	(60)
Introduction to Area	215	(9)
The Definite Integral	224	(8)
The First Fundamental Theorem of Calculus	232	(11)
The Second Fundamental Theorem of Calculus and the Method of Substitution	243	(10)
The Mean Value Theorem for Integrals and the Use of Symmetry	253	(7)
Numerical Integration	260	(10)
Chapter Review	270	(5)
Review and Preview Problems	274	(1)
Applications of the Integral	275	(50)
The Area of a Plane Region	275	(6)
Volumes of Solids: Slabs, Disks, Washers	281	(7)
Volumes of Solids of Revolution: Shells	288	(6)
Length of a Plane Curve	294	(7)
Work and Fluid Force	301	(7)
Moments and Center of Mass	308	(8)
Probability and Random Variables	316	(6)
Chapter Review	322	(3)
Review and Preview Problems	324	(1)
Transcendental Functions	325	(58)
The Natural Logarithm Function	325	(6)
Inverse Functions and Their Derivatives	331	(6)
The Natural Exponential Function	337	(5)
General Exponential and Logarithmic Functions	342	(5)
Exponential Growth and Decay	347	(8)
First-Order Linear Differential Equations	355	(4)
Approximations for Differential Equations	359	(6)
The Inverse Trigonometric Functions and Their Derivatives	365	(9)
The Hyperbolic Functions and Their Inverses	374	(6)
Chapter Review	380	(3)
Review and Preview Problems	382	(1)
Techniques of Integration	383	(40)
Basic Integration Rules	383	(4)
Integration by Parts	387	(6)
Some Trigonometric Integrals	393	(6)
Rationalizing Substitutions	399	(5)
Integration of Rational Functions Using Partial Fractions	404	(7)
Strategies for Integration	411	(8)
Chapter Review	419	(4)
Review and Preview Problems	422	(1)
Indeterminate Forms and Improper Integrals	423	(26)
Indeterminate Forms of Type 0/0	423	(5)
Other Indeterminate Forms	428	(5)
Improper Integrals: Infinite Limits of Integration	433	(9)
Improper Integrals: Infinite Integrands	442	(4)
Chapter Review	446	(3)
Review and Preview Problems	448	(1)
Infinite Series	449	(60)
Infinite Sequences	449	(6)
Infinite Series	455	(8)
Positive Series: The Integral Test	463	(5)
Positive Series: Other Tests	468	(6)
Alternating Series, Absolute Convergence, and Conditional Convergence	474	(5)
Power Series	479	(5)
Operations on Power Series	484	(5)
Taylor and Maclaurin Series	489	(8)
The Taylor Approximation to a Function	497	(7)
Chapter Review	504	(5)
Review and Preview Problems	508	(1)
Conics and Polar Coordinates	509	(46)
The Parabola	509	(4)
Ellipses and Hyperbolas	513	(10)
Translation and Rotation of Axes	523	(7)
Parametric Representation of Curves in the Plane	530	(7)
The Polar Coordinate System	537	(5)
Graphs of Polar Equations	542	(5)
Calculus in Polar Coordinates	547	(5)
Chapter Review	552	(3)
Review and Preview Problems	554	(1)
Geometry in Space and Vectors	555	(62)
Cartesian Coordinates in Three-Space	555	(5)
Vectors	560	(6)
The Dot Product	566	(8)
The Cross Product	574	(5)
Vector-Valued Functions and Curvilinear Motion	579	(10)
Lines and Tangent Lines in Three-Space	589	(4)
Curvature and Components of Acceleration	593	(10)
Surfaces in Three-Space	603	(6)
Cylindrical and Spherical Coordinates	609	(4)
Chapter Review	613	(4)
Review and Preview Problems	616	(1)
Derivatives for Functions of Two or More Variables	617	(58)
Functions of Two or More Variables	617	(7)
Partial Derivatives	624	(5)
Limits and Continuity	629	(6)
Differentiability	635	(6)
Directional Derivatives and Gradients	641	(6)
The Chain Rule	647	(5)
Tangent Planes and Approximations	652	(5)
Maxima and Minima	657	(9)
The Method of Lagrange Multipliers	666	(6)
Chapter Review	672	(3)
Review and Preview Problems	674	(1)
Multiple Integrals	675	(56)
Double Integrals over Rectangles	675	(5)
Iterated Integrals	680	(4)
Double Integrals over Nonrectangular Regions	684	(7)
Double Integrals in Polar Coordinates	691	(5)
Applications of Double Integrals	696	(4)
Surface Area	700	(6)
Triple Integrals in Cartesian Coordinates	706	(7)
Triple Integrals in Cylindrical and Spherical Coordinates	713	(5)
Change of Variables in Multiple Integrals	718	(10)
Chapter Review	728	(3)
Review and Preview Problems	730	(1)
Vector Calculus	731
Vector Fields	731	(4)
Line Integrals	735	(7)
Independence of Path	742	(7)
Green's Theorem in the Plane	749	(6)
Surface Integrals	755	(9)
Gauss's Divergence Theorem	764	(6)
Stokes's Theorem	770	(3)
Chapter Review	773
Appendix	1	(6)
A.1 Mathematical Induction	1	(2)
A.2 Proofs of Several Theorems	3	(4)
Answers to Odd-Numbered Problems	7
Index	1	(1)
Photo Credits	1