Calculus Single Variable / Edition 1

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Overview

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. 
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Product Details

  • ISBN-13: 9780470413197
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 6/16/2008
  • Edition description: Student
  • Edition number: 1
  • Pages: 772
  • Product dimensions: 8.40 (w) x 9.90 (h) x 1.50 (d)

Table of Contents

Preface ix
Features xi
Supplements xv
Acknowledgments xvii
About the Authors xix
1 Basics 1
Preview 1
1.1 Number Systems 2
1.2 Planar Coordinates and Graphing in the Plane 11
1.3 Lines and Their Slopes 21
1.4 Functions and Their Graphs 33
1.5 Combining Functions 45
1.6 Trigonometry 58
Summary of Key Topics 68
Genesis & Development 71
2 Limits 75
Preview 75
2.1 The Concept of Limit 77
2.2 Limit Theorems 87
2.3 Continuity 98
2.4 Infinite Limits and Asymptotes 112
2.5 Limits of Sequences 121
2.6 Exponential Functions 131
Summary of Key Topics 144
Genesis & Development 147
3 The Derivative 151
Preview 151
3.1 Rates of Change and Tangent Lines 152
3.2 The Definition of the Derivative 165
3.3 Rules for Differentiation 175
3.4 Differentiation of Some Basic Functions 185
3.5 The Chain Rule 193
3.6 Inverse Functions and the Natural Logarithm 201
3.7 Higher Derivatives 215
3.8 Implicit Differentiation and Related Rates 222
3.9 Differentials and Approximation of Functions 233
Summary of Key Topics 241
Genesis & Development 245
4 Applications of the Derivative 249
Preview 249
4.1 The Derivative and Graphing 250
4.2 Maxima and Minima of Functions 258
4.3 Applied Maximum-Minimum Problems 265
4.4 Concavity 277
4.5 Graphing Functions 286
4.6 L’Hˆopital’s Rule 298
4.7 The Newton-Raphson Method 305
4.8 Antidifferentiation and Applications 315
4.9 Enrichment: Applications to Economics 326
Summary of Key Topics 338
Genesis & Development 342
5 The Integral 347
Preview 347
5.1 Introduction to Integration—The Area Problem 348
5.2 The Riemann Integral 357
5.3 Rules for Integration 369
5.4 The Fundamental Theorem of Calculus 377
5.5 Integration by Substitution 386
5.6 More on the Calculation of Area 393
5.7 Numerical Techniques of Integration 399
Summary of Key Topics 411
Genesis & Development 414
6 Differential Equations and
Transcendental Functions 419
Preview 419
6.1 First Order Differential Equations 420
6.2 A Calculus Approach to the Logarithm 430
6.3 The Exponential Function 442
6.4 Logarithms and Powers with Arbitrary Bases 450
6.5 Applications of the Exponential Function 463
6.6 Inverse Trigonometric Functions 477
6.7 Enrichment: The Hyperbolic Functions 488
Summary of Key Topics 501
Genesis & Development 505
7 Techniques of Integration 509
Preview 509
7.1 Integration by Parts 510
7.2 Partial Fractions—Linear Factors 517
7.3 Powers and Products of Trigonometric Functions 529
7.4 Integrals Involving Quadratic Expressions 537
7.5 Partial Fractions—Irreducible Quadratic Factors 546
Summary of Key Topics 554
Genesis & Development 557
8 Applications of the Integral 561
Preview 561
8.1 Volumes 562
8.2 Arc Length and Surface Area 575
8.3 The Average Value of a Function 583
8.4 Center of Mass 590
8.5 Work 596
8.6 Improper Integrals—Unbounded Integrands 603
8.7 Improper Integrals—Unbounded Intervals 609
Summary of Key Topics 616
Genesis & Development 619
9 Infinite Series 621
Preview 621
9.1 Series 622
9.2 Determining Convergence 630
9.3 Series with Nonnegative Terms—The Integral Test 634
9.4 Series with Nonnegative Terms—The Comparison Test 642
9.5 Alternating Series 647
9.6 The Ratio and Root Tests 653
Summary of Key Topics 658
Genesis & Development 660
10 Taylor Series 663
Preview 663
10.1 Introduction to Power Series 664
10.2 Operations on Power Series 672
10.3 Taylor Polynomials 684
10.4 Estimating the Error Term—The Rate of Convergence of
Taylor’s Expansion 693
10.5 Taylor Series 697
Summary of Key Topics 705
Genesis & Development 707
Appendix Answers to Selected Exercises 711
Index 759
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