Calculus Multivariable, 2nd Edition

Supplementary Resources.

Acknowledgments.

About the Authors.

C H A P T E R 9 Vectors.

Preview.

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.

Preview.

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.

Preview.

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.

Preview.

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.

Preview.

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.

Index.