Note: This is a fall or spring schedule. In summer, this schedule is accelerated by 50% in order to accommodate a 10-week session.
Text: Calculus, with Early Vectors, Preliminary Edition, by James Stewart. Individual sections may vary somewhat from this schedule.
Week 1 3D vectors, dot and cross product, lines and planes Sections 11.1, 11.2, 11.3, 11.4.
Week 2 Quadric surfaces, vector functions and space
curves, arclength, motion in space. Sections 11.5, 11.6, 11.7,
11.8.
Note: if instructor is pressed for time, curvature,
normal, and binormal vectors from 11.7 and all of 11.8 can be
skipped
Week 3 Functions of several variables, limits and continuity (optional), Partial derivatives, tangent planes, differentials. Sections 12.1, (12.2), 12.3, 12.4.
Week 4 Chain rule, directional derivatives, gradients, max/min problems Sections 12.5, 12.6, 12.7.
Week 5 Lagrange multipliers. Sections 12.8.
Exam
I (covering 11.1 - 12.7)
Week 6 Double integrals, iterated integrals, double integrals over general regions. Sections 13.1, 13.2, 13.3.
Week 7 Polar coordinates (rapidly), integrals in polar coordinates, applications of double integrals, triple integrals. Sections 13.4, 13.5, 13.6, 13.8.
Week 8 Cylindrical and spherical coordinates,
integrals in cylindrical and spherical coordinates, change of
variables in multiple integrals. Sections 13.9, 13.10. 13.11
Note: if instructor is pressed for time, section 13.11 may be
skipped
Week 9 Vector fields, line integrals. Section
14.1, 14.2.
Exam II (covering 12.7 - 13.11)
Week 10 Fundamental theorem for line integrals, Green's Theorem. Sections 14.3, 14.4.
Week 11 Curl and divergence, parametric surfaces and their areas Sections 14.5, 14.6.
Week 12 Surface integrals, Stokes' Theorem. Sections 14.7, 14.8.
Week 13 Divergence Theorem (Thanksgiving falls on this week in the fall). Section 14.9.
Week 14 Review
Exam III (covering 14.1 - 14.9)
Week 15 Review for Final Exam. Last Day of class is Tuesday of this week.