**Textbook:**

Stewart: *Calculus: Early Trancendentals,* 8th Edition, Brooks/Cole(Cengage), 2015

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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 Parametric 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 Double Integrals over General Regions

10.3 Polar Coordinates

15.3 Double Integrals in Polar Coordinates

15.4 Applications of Double Integrals

[15.5 Surface Area (optional)]

15.6 Triple Integrals

15.7 Triple Integrals in Cylindrical Coordinates

15.8 Triple Integrals in Spherical 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 & Their 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.

**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 spherical 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.