MAT 2500 Syllabus

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

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)]

This material is covered over a 14 week (56 class hours) semester.

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.


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

Dr. Douglas Norton

Christine Gadonas 610.519.4809