Course Schedule

Week 1

Quiz 1

Session 1: Calculus review; Cartesian coordinates; distance; spheres (12.1)

Session 2: Cylindrical and spherical coordinates (15.7)

Session 3: Vectors; magnitude; unit vectors; midpoint (12.2)

Week 2

Quiz 2

Session 4: Dot product; angle between vectors; projection; work (12.3)

Session 5: Cross product; areas; volume (12.4)

Session 6: Lines; planes; normal vectors; distances (12.5)

Week 3

Quiz 3

(No class)

Session 7: Quadric surfaces (12.6)

Session 8: Parametric curves; motion; derivatives of vector valued functions; tangent lines (13.1)

Week 4

Quiz 4

Session 9: Integrals of vector functions (13.2)

Session 10: Arc length; cumulative arc length (13.3)

Session 11: Decomposing motion; unit tangent; unit normal; unit binormal; osculating plane (13.5)

Week 5

Exam 1 (Covers 12.1-13.5)

Session 12: Curvature (13.4)

Review for Exam 1

Exam 1

(Exam on Thursday evening; no class on Friday)

Week 6

Quiz 5

Session 13: Functions of several variables; level curves; level surfaces; contour diagrams (14.1)

Session 14: Limits; continuity (14.2)

Session 15: Partial derivatives; higher order partial derivatives (14.3)

Week 7

Quiz 6

Session 16: Differentiability; tangent plane; chain rule; implicit differentiation (14.4)

Session 17: Gradient; directional derivatives (14.5)

Session 18: Tangent planes; properties of gradient; linear approximation (14.6)

Week 8

Quiz 7

Session 19: Taylor polynomials for multi-variable functions (14.9)

Session 20: Optimization; critical points; classification with second partials test (14.7)

Session 21: Optimization for a closed and bounded region (14.7)

Week 9

Exam 2 (Covers 14.1-14.9)

Session 22: Optimization using method of Lagrange multipliers (14.8)

Review for Exam 2

Exam 2

(Exam on Thursday evening; no class on Friday)

Week 10

Quiz 8

Session 23: Multivariable integration; iterated integrals over rectangles and regions (15.1, 15.2)

Session 24: Changing order of integration (15.2)

Session 25: Integration in polar coordinates (15.4)

Week 11

Quiz 9

Session 26: Triple integration in Cartesian coordinates; changing order of integration (15.5)

Session 27: Geometrical applications of multivariable integration(15.3, 16.5)

Session 28: Physics applications of multivariable integration (15.6)

Week 12

Quiz 10

Session 29: Integration in Cylindrical and Spherical (15.7)

Session 30: Jacobian; substitution in multiple integrals (15.8)

Session 31: Line integrals; work (16.1, 16.2)

Week 13

Quiz 11

Session 32: Vector fields; curl; divergence (16.2)

Session 33: Line integrals of conservative functions (16.3)

Session 34: Green's Theorem (16.4)

Week 14

Exam 3 (Covers 15.1-16.6)

Session 35: Surface integrals (16.5, 16.6)

Review for Exam 3

Exam 3

(Exam on Thursday evening; no class on Friday)

Week 15

Quiz 12 (not administered)

Session 36: Stokes' Theorem (16.7)

Session 37: Gauss's Divergence Theorem (16.8)

Review for the Final