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Calculus of a Single Variable

by ; ;
Edition:
6th
ISBN13:

9780395885789

ISBN10:
0395885787
Format:
Paperback
Pub. Date:
11/6/1997
Publisher(s):
Cengage Learning
List Price: $292.66

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Summary

This text combines the theoretical instruction of calculus with current best-practise strategies.

Table of Contents

A Word from the Authors (Preface) ix
Index of Applications xxxi
Preparation for Calculus
1(38)
Graphs and Models
3(8)
Linear Models and Rates of Change
11(9)
Functions and Their Graphs
20(11)
Fitting Models to Data
31(8)
Review Exercises
37(2)
Limits and Their Properties
39(50)
A Preview of Calculus
41(6)
Finding Limits Graphically and Numerically
47(9)
Evaluating Limits Analytically
56(11)
Continuity and One-Sided Limits
67(12)
Infinite Limits
79(10)
Review Exercises
87(2)
Differentiation
89(64)
The Derivative and the Tangent Line Problem
91(11)
Basic Differentiation Rules and Rates of Change
102(12)
The Product and Quotient Rules and Higher-Order Derivatives
114(10)
The Chain Rule
124(10)
Implicit Differentiation
134(7)
Related Rates
141(12)
Review Exercises
150(3)
Applications of Differentiation
153(86)
Extrema on an Interval
155(8)
Rolle's Theorem and the Mean Value Theorem
163(6)
Increasing and Decreasing Functions and the First Derivative Test
169(10)
Concavity and the Second Derivative Test
179(8)
Limits at Infinity
187(9)
A Summary of Curve Sketching
196(9)
Optimization Problems
205(10)
Newton's Method
215(6)
Differentials
221(7)
Business and Economics Applications
228(11)
Review Exercises
235(4)
Integration
239(70)
Antiderivatives and Indefinite Integration
241(11)
Area
252(12)
Riemann Sums and Definite Integrals
264(10)
The Fundamental Theorem of Calculus
274(13)
Integration by Substitution
287(12)
Numerical Integration
299(10)
Review Exercises
306(3)
Logarithmic, Exponential, and Other Transcendental Functions
309(96)
The Natural Logarithmic Function and Differentiation
311(10)
The Natural Logarithmic Function and Integration
321(8)
Inverse Functions
329(9)
Exponential Functions: Differentiation and Integration
338(10)
Bases Other than e and Applications
348(10)
Differential Equations: Growth and Decay
358(8)
Differential Equations: Separation of Variables
366(11)
Inverse Trigonometric Functions and Differentiation
377(8)
Inverse Trigonometric Functions and Integration
385(7)
Hyperbolic Functions
392(13)
Review Exercises
402(3)
Applications of Integration
405(68)
Area of a Region Between Two Curves
407(9)
Volume: The Disc Method
416(11)
Volume: The Shell Method
427(8)
Arc Length and Surfaces of Revolution
435(10)
Work
445(9)
Moments, Centers of Mass, and Centroids
454(11)
Fluid Pressure and Fluid Force
465(8)
Review Exercises
471(2)
Integration Techniques, L'Hopital's Rule, and Improper Integrals
473(72)
Basic Integration Rules
475(6)
Integration by Parts
481(9)
Trigonometric Integrals
490(9)
Trigonometric Substitution
499(9)
Partial Fractions
508(9)
Integration by Tables and Other Integration Techniques
517(6)
Indeterminate Forms and L'Hopital's Rule
523(10)
Improper Integrals
533(12)
Review Exercises
542(3)
Infinite Series
545(90)
Sequences
547(11)
Series and Convergence
558(10)
The Integral Test and P-Series
568(6)
Comparisons of Series
574(7)
Alternating Series
581(7)
The Ratio and Root Tests
588(8)
Taylor Polynomials and Approximations
596(10)
Power Series
606(9)
Representation of Functions by Power Series
615(7)
Taylor and Maclaurin Series
622(13)
Review Exercises
632(3)
Conics, Parametric Equations, and Polar Coordinates
635(2)
Conics and Calculus
637(15)
Plane Curves and Parametric Equations
652(10)
Parametric Equations and Calculus
662(9)
Polar Coordinates and Polar Graphs
671(10)
Area and Arc Length in Polar Coordinates
681(8)
Polar Equations of Conics and Kepler's Laws
689(7)
Review Exercises
696
Appendix A Precalculus Review A1
A.1 Real Numbers and the Real Line
A1
A.2 The Cartesian Plane
A10
A.3 Review of Trigonometric Functions
A17
Appendix B Proofs of Selected Theorems A28
Appendix C Basic Differentiation Rules for Elementary Functions A44
Appendix D Integration Tables A45
Appendix E Rotation and the General Second-Degree Equation A51
Appendix F Complex Numbers A57
Answers to Odd-Numbered Exercises A69
Index A159


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