• 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
• 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