9780131429246

Calculus

by ; ;
  • ISBN13:

    9780131429246

  • ISBN10:

    0131429248

  • Edition: 9th
  • Format: Hardcover
  • Copyright: 2/28/2006
  • Publisher: Pearson

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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

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