Anne Arundel Community College

MAT 201: Calculus & Analytic Geometry 3


CATALOG DESCRIPTION:
A third course in calculus. Topics include solid analytic geometry; vectors and vector functions; partial differentiation; gradients; directional derivatives and tangent planes; maximum/minimum applications; Lagrange multipliers; multiple integration with applications; line and surface integrals; and the classical theorems of Green, Gauss and Stokes.

Prerequisite: MAT 192 or equivalent.

LEARNING OBJECTIVES:
Upon completion of this course, the student will be able to:
  1. Analyze surfaces using partial differentiation and the gradient operator.
  2. Analyze space curves including their curvature, arc length, velocity, and acceleration.
  3. Find areas, volumes, and moments using multiple integrals.
  4. Solve optimization problems in several variables.
  5. Combine the concepts of surfaces, space curves and vector fields into multiple integrals and surface integrals.
  6. Calculate the circulation of a vector field around a plane region with and without Green's theorem.
  7. Calculate the circulation of a vector field around the edge of a surface with and without Stoke's theorem.
  8. Calculate the flux of a vector field through a closed surface with and without Gauss, divergence theorem.

COURSE OUTLINE:
Vectors and Geometry of Space:
  • Three Dimensional Coordinate Systems
  • Vectors
  • The Dot Product
  • The Cross Product
  • Equations of Lines and Planes
  • Cylinders and Quadric Surfaces

Vector Functions:
  • Vector Functions and Space Curves
  • Derivatives and Integrals of Vector Functions
  • Arc Length and Curvature
  • Motion in Space: Velocity and Acceleration

Partial Derivatives:
  • Functions of Several Variables
  • Limits and Continuity
  • Partial Derivatives
  • Tangent Planes and Linear Approximations
  • Chain Rule
  • Directional Derivatives and the Gradient Vector
  • Maximum and Minimum Values
  • Lagrange Multipliers

Multiple Integrals:
  • Double Integrals over Rectangles
  • Iterated Integrals
  • Double Integrals over General Regions
  • Double Integrals in Polar Coordinates
  • Applications of Double Integrals
  • Triple Integrals
  • Triple Integrals in Cylindrical Coordinates
  • Triple Integrals in Spherical Coordinates
  • Change of Variables in Multiple Integrals (optional)

Vector Calculus:
  • Vector Fields
  • Line Integrals
  • Fundamental Theorem for Line Integrals
  • Green's Theorem
  • Curl and Divergence
  • Parametric Surfaces and Surface Areas
  • Surface Integrals
  • Stokes' Theorem
  • The Divergence Theorem

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