This Solutions Manual was written completely by the Authors. This means that it has the same problem- solving format as the textbook and, unlike other solutions manuals, provides more details, more steps toward the solutions, and more commentary and background. The figures and graphics are first-rate. Multivariable Solutions Manual covers Chapters 9-14.

Preface

**Chapter 9 Plane Curves and Polar Coordinates**

9.1 Parametric Equations

9.2 Parametric Calculus - Derivatives

9.3 Parametric Calculus - Integrals

9.4 Polar Coordinates

9.5 Polar Coordinate Calculus

9.6 Conic Sections

**Chapter 10 Vectors and Geometry**

10.1 Three Dimensional Coordinate Systems

10.2 Vectors

10.3 The Dot Product

10.4 The Cross Product

10.5 Lines and Planes in Space

10.6 Cylinders and Quadric Surfaces

**Chapter 11 Partial Derivatives**

11.1 Functions of Two or More Variables

11.2 Multivariable Limits and Continuity

11.3 Partial Derivatives

11.4 The Chain Rule

11.5 Directional Derivatives - The Gradient

11.6 Tangent Planes

11.7 Local Extrema and Saddle Points

**Chapter 12 Multiple Integrals**

12.1 Double Integrals and Iterated Integrals

12.2 Double Integrals over General Regions

12.3 Double Integrals in Polar Coordinates

12.4 Applications of Double Integrals

12.5 Triple Integrals

12.6 Triple Integrals in Cylindrical and Spherical Coordinates

**Chapter 13 Geometry of Curves and Surfaces**

13.1 Space Curves and Arc Length

13.2 Surfaces and Surface Area

**Chapter 14 Vector Analysis**

14.1 Vector Fields and Differential Operators

14.2 Line Integrals

14.3 The Fundamental Theorem of Line Integrals

14.4 Surface Integrals

14.5 Stokes’ Theorem - Green’s Theorem

14.6 The Divergence Theorem

**Mylan Redfern Betounes**

Mylan Redfern received her BS in mathematics from Augusta College and her PhD in mathematics from Louisiana State University. She has authored numerous refereed publications in stochastic analysis and has published two books on Mathematical Computing and Calculus. She has taught all levels of mathematics at the University of Southern Mississippi, Valdosta State University, and the University of Texas, Permian Basin.

**David Betounes**

David Betounes received his BArch in architecture from the University of Southern California and his PhD in mathematics from Florida State University. He has authored numerous refereed publications in differential geometry and mathematical physics and has published four books on DEs, PDEs, Mathematical Computing, and Calculus. He has taught all levels of mathematics at the University of Southern Mississippi, Valdosta State University, and the University of Texas, Permian Basin.