• Learning Outcomes for 3450:223 Analytic Geometry and Calculus III 

    Students are expected to be able to

    • Communicate mathematical results through the proper use of mathematical notation and words
    • Describe the geometry of R^3 and use vector analysis to characterize motion along curves
    • Find partial derivatives, directional derivatives and gradient vectors
    • Solve optimization problems on a closed, bounded domain and on a constraint curve (Lagrange Multipliers)
    • Set up and evaluate line integrals, and double and triple integrals (in rectangular, polar, cylindrical and spherical coordinates)
    • Set up and evaluate integrals involving the main theorems of vector calculus
  • Topical Outline
    • 3-D Coordinate Systems
    • Vectors
    • Dot Product 
    • Cross Product 
    • Lines and Planes in Space
    • Quadratics Surfaces
    • Cylindrical and Spherical Coordinates
    • Vector Functions and Space Curves
    • Derivatives and Integrals of Vector Functions
    • Arc Length and Curvature
    • Velocity and Acceleration
    • Functions of Several Variables
    • Limits and Continuity
    • Partial Derivative
    • Tangent Planes and Linear Approx.
    • Chain Rule
    • Directional Derivative & Gradient Vectors
    • Maximum and Minimum Values
    • Lagrange Multipliers
    • Double Integrals over Rectangles
    • Iterated Integrals
    • Double Integrals over General Regions
    • Double Integrals in Polar Coordinates
    • Applications
    • Surface Area
    • Triple Integrals
    • Integrals in Spherical and Cylindrical Coordinates
    • Change of Variables
    • Vector Fields
    • Line Integrals
    • Fundamental Theorem for Line Integrals
    • Green's Theorem
    • Curl and Divergence
    • Parametric Surfaces and their Areas
    • Surface Integrals
    • Stoke's Theorem
    • Divergence Theorem