**Textbook:**

Stewart: *Calculus: Early Trancendentals,* 7th Edition, Brooks/Cole(Cengage), 2012. The Math Department orders a custom Villanova Edition of this book* ISBN: 9781133273226.

Coordinators: Marilyn Belkin and Joyce Longman

**Chapter 12: Vectors and the Geometry of Space
**12.1 Three Dimensional Coordinate Systems

12.2 Vectors

12.3 The Dot Product

12.4 Cross Products

10.1 Curves Defined by Parameteric Equations

12.5 Equations of Lines and Planes

**Chapter 13: Vector Functions**

13.1 Vector Functions and Space Curves

13.2 Derivatives and Integrals of Vector Functions

13.3 Arc Length and Curvature

13.4 Motion in Space: Velocity and Acceleration

**Chapter 14: Partial Derivatives
**14.1 Functions of Several Variables

14.3 Limits (14.2), Partial Derivatives

14.4 Tangent Planes and Linear Approximations

14.5 The Chain Rule

14.6 Directional Derivatives and the Gradient

14.7 Maximum and Minimum Values

**Chapter 15: Multiple Integrals**

15.1 Double Integrals over Rectangles

15.2 Iterated Integrals

15.3 Double Integrals over General Regions

15.5 Applications of Double Integrals

15.6 Surface Area

10.3 Polar Coordinates

15.4 Double Integrals in Polar Coordinates

15.7 Triple Integrals in Cylindrical Coordinates

**Chapter 16: Vector Calculus**

16.1 Vector Fields

16.2 Line Integrals

16.3 Fundamental Theorem for Line Integrals

16.4 Green's Theorem

16.5 Curl and Divergence

16.6 Parametric Surfaces & Areas (Optional)

16.7 Surface Integrals (Optional)

16.8 Stokes' Theorem (Optional)

16.9 The Divergence Theorem (Optional)

A suggested schedule based on a 14 week (56 class hours) semester, is given below. It may be modified at the instructor's discretion.

Sections |
Approximate Time |
Comments |

12.1-12.5 | 10 class hours | Insert 10.1 between 12.4 and 12.5 |

13.1-13.4 | 6 class hours | |

14.1-14.7 | 9 class hours | Limits as needed for partial derivative def. |

15.1-15.8 | 15 class hours | Introduce polar, cylindrical, spherical coords. |

16.1-16.9 | 9 class hours | 16.6-16.9 are optional |

Exam Reviews | 4 class hours | Includes final exam review |

Exams | 3 class hours |

**Maple or Other Computer Software
**Maple discussions should be determined by each instructor. Each student shoud master the following topics: (1) graphing in polar coordinates, (2) graphing parametric equations, (3) three dimensional graphs in rectangular, cylindrical, and sphyerical coordinates, (4) graphing spacecurves, (5) partial derivatives, and (6) multiple integration.

*The Villanova Edition can be bought new or used through our bookstore. You also have the option to rent the full version of the textbook through any online vendor.