Math 283 (Section 1007), Fall 2023
Below is the plan for the semester. I will try my best to stick to this schedule, but it may be modified as necessary. Take this as a rough outline for the semester; if a topic is not explicitly mentioned here, this does not mean it is or is not covered.
Week 1: Overview, 10.1-10.5
Dates: Aug. 28-Sept. 1
Topics: Overview of Calculus III, 3D-geometry, vectors, dot products and projections, cross products, lines & planes, distance from line to plane.
Skipped: Physics applications, torque.
Week 2: 10.7-10.9
Dates: Sept. 6 - Sept. 8 (No class Sept. 4)
Topics: Vector-valued functions, parameterized curves, coordinatewise differentiation and integration, arc-length, velocity and acceleration.
Skipped: Section 10.6, using computers to draw space curves, curvature, normal and binormal vectors, tangent and normal components of acceleration, Kepler's laws.
Week 3: 11.1, 11.2
Dates: Sept. 11 - Sept. 15
Topics: Functions of several variables, graphs, level curves, limits, continuity.
Skipped: The δ-ε definition of limits.
Week 4: 11.3, 11.5, 11.6
Dates: Sept. 18 - Sept. 22
Topics: Partial derivatives, higher order derivatives, equality of mixed partial derivatives, chain rule, implicit differentiation, directional derivatives, gradient, tangent plane.
Skipped: Linear approximation, differentials, partial differential equations.
Week 5: 11.7, 11.8
Dates: Sept. 25- Sept. 29
Topics: Local and absolute minimum and maximum, second derivative test, Lagrange multipliers with one constraint.
Skipped: Lagrange multipliers with more than one constraint.
Week 6: Review, Exam 1, 12.1
Dates: Oct. 2 - Oct. 6 (Discussion on Oct. 6 replaced by a lecture)
Topics: Review and catch up. Exam 1 on Wednesday. Iterated integrals, Fubini's theorem.
Skipped: Riemann sums, midpoint rule.
Week 7: 12.2, 12.3
Dates: Oct. 9 - Oct. 13
Topics: Double integrals over non-rectangular regions, double integrals in polar coordinates.
Skipped: Applications of double integrals (12.4)
Note: We will cover triple integrals in Week 13.
Week 8: 13.1, 13.2
Dates: Oct. 16 - Oct. 20
Topics: Vector fields, gradient fields, line integrals of vector fields.
Skipped: Line integrals of scalar fields.
Week 9: 13.3, 13.4
Dates: Oct. 23 - Oct. 25 (No discussion Oct. 27)
Topics: Fundamental theorem of line integrals, independence of path for line integrals of gradient fields, Green's theorem.
Skipped: Conservation of energy, simply connected regions.
Week 10: 13.4, 13.5
Dates: Oct. 30 - Nov. 3
Topics: more Green's theorem, curl and divergence.
Week 11: 13.6, 13.7
Dates: Nov. 6 - Nov. 8 (No discussion Nov. 11)
Topics: Parametric surfaces, surface area, surface integrals of vector fields.
Skipped: Surface integrals of functions.
Week 12: Review, Exam 2, 13.8
Dates: Nov. 13 - Nov. 17 (Discussion on Nov. 17 replaced by a lecture)
Topics: Review and catch-up, Exam 2 on Wednesday. Stokes' theorem.
Week 13: 13.8, 12.5-12.6
Dates: Nov. 20 - Nov. 22 (No discussion Nov. 24)
Topics: More Stokes' theorem, triple integrals, iterated integrals and Fubini's theorem, volume, triple integrals in cylindrical coordinates.
Skipped: Riemann sums.
Week 14: 12.7, 13.9, Conclusion
Dates: Nov. 27 - Dec. 1
Topics: Triple integrals in spherical coordinates, divergence theorem, concluding remarks.
Skipped: general change of variables formula (12.8)
Week 15: Study week
Review of problem solving following student suggestions.