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Calculus: Single Variable, 2nd Edition

Calculus: Single Variable, 2nd Edition

Brian E. Blank, Steven G. Krantz

ISBN: 978-0-470-91186-0

Apr 2011

832 pages



Blank and Krantz’s Calculus 2e brings together time-tested methods and innovative thinking to address the needs of today’s students, who come from a wide range of backgrounds and look ahead to a variety of futures. Using meaningful examples, credible applications, and incisive technology, Blank and Krantz’s Calculus 2e strives to empower students, enhance their critical thinking skills, and equip them with the knowledge and skills to succeed in the major or discipline they ultimately choose to study. Blank and Krantz’s engaging style and clear writing make the language of mathematics accessible, understandable and enjoyable, while maintaining high standards for mathematical rigor.

Blank and Krantz’s Calculus 2e is available with WileyPLUS, an online teaching and learning environment initially developed for Calculus and Differential Equations courses. WileyPLUS integrates the complete digital textbook with powerful student and instructor resources as well as online auto-graded homework.

Related Resources


Supplementary Resources.


About the Authors.

C H A P T E R 1 Basics.


1 Number Systems.

2 Planar Coordinates and Graphing in the Plane.

3 Lines and Their Slopes.

4 Functions and Their Graphs.

5 Combining Functions.

6 Trigonometry.

Summary of Key Topics.

Review Exercises.

Genesis & Development 1.

C H A P T E R 2 Limits.


1 The Concept of Limit.

2 Limit Theorems.

3 Continuity.

4 Infinite Limits and Asymptotes.

5 Limits of Sequences.

6 Exponential Functions and Logarithms.

Summary of Key Topics.

Review Exercises.

Genesis & Development 2.

C H A P T E R 3 The Derivative.


1 Rates of Change and Tangent Lines.

2 The Derivative.

3 Rules for Differentiation.

4 Differentiation of Some Basic Functions.

5 The Chain Rule.

6 Derivatives of Inverse Functions.

7 Higher Derivatives.

8 Implicit Differentiation.

9 Differentials and Approximation of Functions.

10 Other Transcendental Functions.

Summary of Key Topics.

Review Exercises.

Genesis & Development 3.

C H A P T E R 4 Applications of the Derivative.


1 Related Rates.

2 The Mean Value Theorem.

3 Maxima and Minima of Functions.

4 Applied Maximum-Minimum Problems.

5 Concavity.

6 Graphing Functions.

7 l’Hoˆ pital’s Rule.

8 The Newton-Raphson Method.

9 Antidifferentiation and Applications.

Summary of Key Topics.

Review Exercises.

Genesis & Development 4.

C H A P T E R 5 The Integral.


1 Introduction to Integration—The Area Problem.

2 The Riemann Integral.

3 Rules for Integration.

4 The Fundamental Theorem of Calculus.

5 A Calculus Approach to the Logarithm and Exponential Functions.

6 Integration by Substitution.

7 More on the Calculation of Area.

8 Numerical Techniques of Integration.

Summary of Key Topics.

Review Exercises.

Genesis & Development 5.

C H A P T E R 6 Techniques of Integration.


1 Integration by Parts.

2 Powers and Products of Trigonometric Functions.

3 Trigonometric Substitution.

4 Partial Fractions—Linear Factors.

5 Partial Fractions—Irreducible Quadratic Factors.

6 Improper Integrals—Unbounded Integrands.

7 Improper Integrals—Unbounded Intervals.

Summary of Key Topics.

Review Exercises.

Genesis & Development 6.

C H A P T E R 7 Applications of the Integral.


1 Volumes.

2 Arc Length and Surface Area.

3 The Average Value of a Function.

4 Center of Mass.

5 Work.

6 First Order Differential Equations—Separable Equations.

7 First Order Differential Equations—Linear Equations.

Summary of Key Topics.

Review Exercises.

Genesis & Development 7.

C H A P T E R 8 Infinite Series.


1 Series.

2 The Divergence Test and the Integral Test.

3 The Comparison Tests.

4 Alternating Series.

5 The Ratio and Root Tests.

6 Introduction to Power Series.

7 Representing Functions by Power Series.

8 Taylor Series.

Summary of Key Topics.

Review Exercises.

Genesis & Development 8.

Table of Integrals.

Answers to Selected Exercises.


  • Major reorganization of topics: Table of contents has been reorganized to be more in line with standard syllabi
  • Chapter Review Exercises: This edition now includes chapter review exercises
  • Exercises: More exercises added throughout, especially drill and medium-level exercises
  • Readable rigor: The writing of this text is cogent, clear, and compelling; while carefully maintaining mathematical precision.
  • Depth of Exercises: Exercise sets have real depth and are organized into three parts; skills exercises (Problems for Practice), more challenging and thought-provoking exercises (Further Theory and Practice), and technology exercises (Calculator/Computer Sciences)
  • Pedagogical Features: These include: Insight, A Look Back, A Look Forward, Quick Quiz, Preview, Key/Basic Steps, Summary of Key Topics, Genesis and Development
  • Advanced Students Are Engaged Early: Students who were exposed to calculus in high school are challenged and engaged early; for instance, by early exposure to sequences (in Chapter 2, “Limits”)
  • Technology: Technology is an essential part of modern life. It is used throughout the book in a natural and comfortable manner. Students see how scientists and engineers think about mathematical questions.
  • Real World Applications: Applications are not “made up” or artificial. They are shown as an essential part of the way we think about Mathematics and the world around us.
  • Sequences: These are introduced early and used throughout to motivate key ideas like limits, exponentials and series.