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• Week 1: Three-Dimensional Coordinate Systems, Vectors, The Dot Product.
• Week 2: The Cross Product, Lines and Planes in Space, Cylinders and Quadric Surfaces
• Week 3: Vector functions, Modeling projectile motion, Arc length and the unit tangent vector T.
• Week 4: Curvature and the unit normal vector N, Torsion and the unit binormal vector B, Planetary motion and satellites
• Week 5: Functions of several variables, Limits and continuity in higher dimensions, Partial derivatives,
• Week 6: The chain rule, Directional derivatives and gradient vectors, Tangent planes and differentials
• Week 7: Extreme values and Saddle points, Lagrange multipliers,
• Week 8: Partial derivatives with constrained variables, Taylor's formula for two variables
• Week 9: Double integrals, Areas, Moments and centers of mass, Double integrals in polar form
• Week 10: Mid Term, December 14 - 18,2020 Week 11: Winter Break, December 21 - 24, 2020
• Week 12: Triple integrals in rectangular coordinates, Masses and moments in three dimensions, Triple integrals in cylindrical and spherical coordinates.
• Week 13: Substitution in multiple integrals, Line integrals, Vector fields, Work, Circulation and Flux,
• Week 14: Path independence, Potential functions and conservative fields, Green's theorem in the plane
• Week 15: Surface area and surface Integrals, Parameterized surfaces.
• Week 16: Stokes' Theorem, The Divergence theorem and a unified theory