Calculus Single Variable, with Access Code Student Package, Debut Edition

by Brian E. Blank (Washington University in St. Louis); Steven G. Krantz (Washington University in St. Louis)

• ISBN13: 9780470413197
• ISBN10: 0470413190
• Format: Paperback
• Copyright: 2008-06-01
• Publisher: WILEY

Summary

Blank and Krantz's Calculus brings together time-tested methods and innovative thinking to address the needs of today's readers, who come from a wide range of backgrounds and look ahead to a variety of futures. Some study the subject because it is required, others because it will widen their career options. Mathematics majors go into law, medicine, genome research, the technology sector, and many other professions. Blank and Krantz's Calculus strives to empower these readers, enhance their critical thinking skills, and equip them with the knowledge and skills to succeed in the career path they ultimately choose to follow.

Table of Contents

Preface	p. ix
Features	p. xi
Supplements	p. xv
Acknowledgments	p. xvii
About the Authors	p. xix
Basics	p. 1
Preview	p. 1
Number Systems	p. 2
Planar Coordinates and Graphing in the Plane	p. 11
Lines and Their Slopes	p. 21
Functions and Their Graphs	p. 33
Combining Functions	p. 45
Trigonometry	p. 58
Summary of Key Topics	p. 68
Genesis & Development	p. 71
Limits	p. 75
Preview	p. 75
The Concept of Limit	p. 77
Limit Theorems	p. 87
Continuity	p. 98
Infinite Limits and Asymptotes	p. 112
Limits of Sequences	p. 121
Exponential Functions	p. 131
Summary of Key Topics	p. 144
Genesis & Development	p. 147
The Derivative	p. 151
Preview	p. 151
Rates of Change and Tangent Lines	p. 152
The Definition of the Derivative	p. 165
Rules for Differentiation	p. 175
Differentiation of Some Basic Functions	p. 185
The Chain Rule	p. 193
Inverse Functions and the Natural Logarithm	p. 201
Higher Derivatives	p. 215
Implicit Differentiation and Related Rates	p. 222
Differentials and Approximation of Functions	p. 233
Summary of Key Topics	p. 241
Genesis & Development	p. 245
Applications of the Derivative	p. 249
Preview	p. 249
The Derivative and Graphing	p. 250
Maxima and Minima of Functions	p. 258
Applied Maximum-Minimum Problems	p. 265
Concavity	p. 277
Graphing Functions	p. 286
L'H-+opital's Rule	p. 298
The Newton-Raphson Method	p. 305
Antidifferentiation and Applications	p. 315
Enrichment: Applications to Economics	p. 326
Summary of Key Topics	p. 338
Genesis & Development	p. 342
The Integral	p. 347
Preview	p. 347
Introduction to Integration-The Area Problem	p. 348
The Riemann Integral	p. 357
Rules for Integration	p. 369
The Fundamental Theorem of Calculus	p. 377
Integration by Substitution	p. 386
More on the Calculation of Area	p. 393
Numerical Techniques of Integration	p. 399
Summary of Key Topics	p. 411
Genesis & Development	p. 414
Differential Equations and Transcendental Functions	p. 419
Preview	p. 419
First Order Differential Equations	p. 420
A Calculus Approach to the Logarithm	p. 430
The Exponential Function	p. 442
Logarithms and Powers with Arbitrary Bases	p. 450
Applications of the Exponential Function	p. 463
Inverse Trigonometric Functions	p. 477
Enrichment: The Hyperbolic Functions	p. 488
Summary of Key Topics	p. 501
Genesis & Development	p. 505
Techniques of Integration	p. 509
Preview	p. 509
Integration by Parts	p. 510
Partial Fractions-Linear Factors	p. 517
Powers and Products of Trigonometric Functions	p. 529
Integrals Involving Quadratic Expressions	p. 537
Partial Fractions-Irreducible Quadratic Factors	p. 546
Summary of Key Topics	p. 554
Genesis & Development	p. 557
Applications of the Integral	p. 561
Preview	p. 561
Volumes	p. 562
Arc Length and Surface Area	p. 575
The Average Value of a Function	p. 583
Center of Mass	p. 590
Work	p. 596
Improper Integrals-Unbounded Integrands	p. 603
Improper Integrals-Unbounded Intervals	p. 609
Summary of Key Topics	p. 616
Genesis & Development	p. 619
Infinite Series	p. 621
Preview	p. 621
Series	p. 622
Determining Convergence	p. 630
Series with Nonnegative Terms-The Integral Test	p. 634
Series with Nonnegative Terms-The Comparison Test	p. 642
Alternating Series	p. 647
The Ratio and Root Tests	p. 653
Summary of Key Topics	p. 658
Genesis & Development	p. 660
Taylor Series	p. 663
Preview	p. 663
Introduction to Power Series	p. 664
Operations on Power Series	p. 672
Taylor Polynomials	p. 684
Estimating the Error Term-
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