Math 222, Course Plan

Sequences and convergence, Basic techniques for computing limits. Boundedness. Monotone convergence. Telescoping series. Geometric and harmonic series. Alternating series. Absolute convergence. Comparison and limit comparison tests. Ratio test. Root test. Integral test. p-test. Power series. Taylor and Maclaurin series.Jan 9 thru Feb 6
Review of vector geometry. Dot and cross products. Parametric curves. Velocity. Tangent vectors. Arclength. Vector integrals. Arclength parameterization. Acceleration. Normal and binormal. Curvature formulas. Osculating circle. Components of acceleration. Ellipse. Archimedean spiral. The fundamental equations for plane curves. Torsion. Frenet-Serret equations. Torsion formula.Feb 8 thru Feb 22
Reading week, no classes.Mar 5 thru Mar 9
Multivariate functions. Limits. Continuity. Partial derivatives. Directional derivatives. Gradient. Chain rule. Higher order derivatives. Extremals and their classification. The Hessian. Lagrange multipliers.Feb 27 thru Mar 20
Double integrals. Fubini's theorem. Change of coordinates. Variable substitution. Polar coordinates. Surface area. Triple integrals, cylindrical and spherical coordinates.Mar 22 thru Apr 5
Revision.Apr 10, 12
Important dates 
Written quiz.TBA
Add/drop deadline.Jan 23
Withdrawal deadline.Mar 13