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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