Math 222 — Second Semester Calculus

Lecture Schedule

We will go through the following subjects. Each subject will take about one lecture, although some of them will spill over into the next lecture.

1. Integration by parts; examples
2. Reduction formulas; examples
   Problems : 16, 17, 18, 19, 20, 21, 22, 23
3. Brief review of the inverse trigonometric functions. (We won't do this in lecture as this was already done in 221, but if you feel uncomfortable with the ArcSine or ArcTangent you should do these problems.)
   Problems : 9, 10, 11, 12
4. Partial fraction expansion; examples
   Problems : 26, 27(typo: read polynomials were it says rational functions), 28, 29, 30, 31 (skip 31(v))
5. Taylor Polynomials: definition, motivation and examples
   Problems : 46, 50, 51, 52, 53
6. Lagrange's remainder term and “little oh”
   Problems : 54, 55, 56, 57, 58
7. Computations with Taylor polynomials, using “little oh”
   Problems : 59, 60, 61, 62, 63
8. Sequences and their limits
   Problems : 64, 65, 66
9. Convergence of Taylor series
   Problems : 67, 68, 69, 70. I will do problem 71 in lecture.
10. Leibniz’ series for π/4 and ln 2
    Problems :
11. Complex numbers: definitions, absolute value, argument, argument of product
    Problems :
12. DeMoivre's formula and the complex exponential function
    Problems :
13. Applications of the complex exponential
    Problems :
14. Differential Equations: First order separable; examples
    Problems :93, 94(some)
15. Linear 1st order diffeqs; two methods, examples
    Problems : 94(the others), 95
    Note that some of the differential equations in 94 are linear first order, some are separable, and some are both.
16. Higher order equations: differential operators, linearity, the superposition principle
    Problems : 96, 97, 98, 99
17. Characteristic roots, special case of second order equations in detail
    Problems : 100
18. The inhomogeneous equation (undetermined coefficients)
    Problems : 101, 102, 103
19. Applications
    Problems : 105, 106, 107, 109, 110
20. Vectors: addition & scalar multiplication; Parametric equations for lines and planes
    Problems : 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132 .
21. The dot product, orthogonality; Orthogonal decomposition; defining equation for lines & planes
    Problems : 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144.
22. Cross product: definition and properties; The triple product and determinants; applications of the cross product
    Problems : 145, 146, 147, 148,149, 150, 151.
23. Vector functions, a.k.a. “parametrized curves”: circle, cycloid, helix; Derivative of a vector function; velocity vector; product rules; Tangents, unit tangent vector; Sketching a parametric curve
    Problems : 153, 154 (i, ii), 160(i, ii, ii, viii, ix)
24. Length of a curve, arclength function.
    Problems : 161, 162.
25. Graphs in Cartesian and Polar coordinates
    Problems : 163, 164.