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.

Full Product Details

Author:   Brian E. Blank ,  Steven G. Krantz
Publisher:   John Wiley and Sons Ltd
Imprint:   Wiley-Blackwell
Dimensions:   Width: 21.50cm , Height: 3.60cm , Length: 25.50cm
Weight:   1.554kg
ISBN:  

9780470413197

ISBN 10:   0470413190
Pages:   772
Publication Date:   01 June 2008
Audience:   College/higher education ,  Tertiary & Higher Education
Format:   Mixed media product
Publisher's Status:   Out of Stock Indefinitely
Availability:   Out of stock  

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'H opital'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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