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Calculus Multivariable, 2nd Edition

Brian E. Blank, Steven G. Krantz

ISBN: ES8-0-470-45359-9


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.

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Supplementary Resources.


About the Authors.

C H A P T E R 9 Vectors.


1 Vectors in the Plane.

2 Vectors in Three-Dimensional Space.

3 The Dot Product and Applications.

4 The Cross Product and Triple Product.

5 Lines and Planes in Space.

Summary of Key Topics.

Review Exercises.

Genesis & Development 9.

C H A P T E R 1 0 Vector-Valued Functions.


1 Vector-Valued Functions—Limits, Derivatives, and Continuity.

2 Velocity and Acceleration.

3 Tangent Vectors and Arc Length.

4 Curvature.

5 Applications of Vector-Valued Functions to Motion.

Summary of Key Topics.

Review Exercises.

Genesis & Development 10.

C H A P T E R 1 1 Functions of Several Variables.


1 Functions of Several Variables.

2 Cylinders and Quadric Surfaces.

3 Limits and Continuity.

4 Partial Derivatives.

5 Differentiability and the Chain Rule.

6 Gradients and Directional Derivatives.

7 Tangent Planes.

8 Maximum-Minimum Problems.

9 Lagrange Multipliers.

Summary of Key Topics.

Review Exercises.

Genesis & Development 11.

C H A P T E R 1 2 Multiple Integrals.


1 Double Integrals Over Rectangular Regions.

2 Integration Over More General Regions.

3 Calculation of Volumes of Solids.

4 Polar Coordinates.

5 Integrating in Polar Coordinates.

6 Triple Integrals.

7 Physical Applications.

8 Other Coordinate Systems.

Summary of Key Topics.

Review Exercises.

Genesis & Development 12.

C H A P T E R 1 3 Vector Calculus.


1 Vector Fields.

2 Line Integrals.

3 Conservative Vector Fields and Path Independence.

4 Divergence, Gradient, and Curl.

5 Green’s Theorem.

6 Surface Integrals.

7 Stokes’s Theorem.

8 The Divergence Theorem.

Summary of Key Topics.

Review Exercises.

Genesis & Development 13.

Table of Integrals.

Formulas from Calculus: Single Variable.

Answers to Selected Exercises.


ü Major reorganisation of topics: Table of contents has been reorganised to be more in line with standard syllabi

ü Chapter Review Exercises: This edition now includes chapter review exercises

ü Exercises:More exercises added throughout, especially drill and medium-level exercises

ü Readable rigor: The writing of this text is cogent, clear, and compelling; while carefully maintaining mathematical precision.

ü Depth of Exercises: Exercise sets have real depth and are organised  into three parts; skills exercises (Problems for Practice), more challenging and thought-provoking exercises (Further Theory and Practice), and technology exercises (Calculator/Computer Sciences)

ü Pedagogical Features: These include: Insight, A Look Back, A Look Forward, Quick Quiz, Preview, Key/Basic Steps, Summary of Key Topics, Genesis and Development

ü 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”)

ü 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.

ü 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.

ü Sequences: These are introduced early and used throughout to motivate key ideas like limits, exponentials and series.