# MAT 2500 Syllabus

Textbook:
Stewart: Calculus: Early Trancendentals, 8th Edition, Brooks/Cole(Cengage), 2015
[click link for format options]
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.

 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 [review 10.3 before 15.4]. 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 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.

### Contact Information

Department of Mathematics & Statistics
SAC Room 305
Villanova University
800 Lancaster Avenue
Villanova, PA 19085
Tel: 610.519.4850
Fax: 610.519.6928
Email: math@villanova.edu

Chair:
Dr. Douglas Norton

Staff:
Marie O'Brien, 610.519.4809