MATH 2110 Calculus III Syllabus

Course Description, Textbook, Topics

Course Description:
This is a 4-credit hour course.  Topics include vector functions, three-dimensional space, partial derivatives, multiple integrals, line integrals, and applications.

Required Textbook:
 Calculus: Early Transcendentals by Stewart, Clegg, and Watson, 9th edition

Chapter 12: Vectors and the Geometry of Space

Section 12.1: Three-Dimensional Coordinate Systems
Section 12.2: Vectors
Section 12.3: The Dot Product
Section 12.4: The Cross Product
Section 12.5: Equations of Lines and Planes

Chapter 13: Vector Functions

Section 13.1: Vector Functions and Space Curves
Section 13.2: Derivatives and Integrals of Vector Functions
Section 13.3: Arc Length and Curvature

Chapter 14: Partial Derivatives

Section 14.1: Functions of Several Variables
Section 14.2: Limits and Continuity
Section 14.3: Partial Derivatives
Section 14.4: Tangent Planes and Linear Approximations
Section 14.5: The Chain Rule
Section 14.6: Directional Derivatives and the Gradient Vector
Section 14.7: Maximum and Minimum Values
Section 14.8: Lagrange Multipliers

Chapter 15: Multiple Integrals

Section 15.1: Double Integrals over Rectangles
Section 15.2: Double Integrals over General Regions
Section 15.3: Double Integrals in Polar Coordinates
Section 15.4: Applications of Double Integrals (Mass, Center of Mass)
Section 15.5: Surface Area
Section 15.6: Triple Integrals
Section 15.7: Triple Integrals in Cylindrical Coordinates
Section 15.8: Triple Integrals in Spherical Coordinates
Section 15.9: Change of Variables in Multiple Integrals

Chapter 16: Vector Calculus

Section 16.1: Vector Fields
Section 16.2: Line Integrals
Section 16.3: The Fundamental Theorem for Line Integrals
Section 16.4: Green’s Theorem
Section 16.5: Curl and Divergence
Section 16.7: Surface Integrals
Section 16.8: Stokes’ Theorem
Section 16.9: The Divergence Theorem