12/12/03: Review of
integration. [Chapter 7]
12/10/03: Spherical coordinates. Review
of integration by parts. [Sections 12.7 and 7.1]
12/08/03: How to recognize a quadric
surface. Cylindrical surfaces. Cylindrical coordinates. [Sections
12.6-7 (spherical coordinates left for Wednesday)]
12/05/03: Planes in space. Quadric
surfaces. [Sections 12.5-6 (no cylindrical surfaces yet)]
12/03/03: Review: power series,
Maclaurin and Taylor series. [Sections 11.8-10]
12/01/03: Another geometric
interpretation of the cross product: the volume of a
parallelepiped. Lines in space. Vector, parametric, and symmetric
equations of lines. Skew lines. [Sections 12.4 and 12.5 (not covering
planes yet)]
11/26/03: The cross product. The
determinant of a 3x3 matrix. The right-hand rule. The geometric
interpretation of the cross product: the area of a
parallelogram. Orthogonal and parallel vectors in terms of the cross
product. [Section 12.4]
11/24/03: The dot product. The angle
between two vectors. Orthogonal and parallel vectors. Direction
angles. Projections. [Section 12.3]
11/21/03: Vectors in the plane and
space. Vector addition and multiplcation by a scalar. [Section
12.2]
11/19/03: Space geometry. 3d coordinate
system. The distance formula. Spheres and their equations. Regions in
space. [Section 12.1]
11/17/03: Applications of Taylor series
and polynomials: approximate computations based on Taylor series,
Taylor's Inequality. [Sections 11.10 and 11.12, omitting Applications
to Physics]
11/14/03: Taylor and Maclaurin
series. Expanding a function into its Taylor series. Approximate
computations based on Taylor series. [Section 11.10]
11/12/03: Representation of functions
as power series. Differentiation and integration of power
series. [Section 11.9]
11/10/03: Power series. The radius and
interval of convergence. Examples. [Section 11.8]
11/07/03: The ratio and root
tests. Examples. [Section 11.6, omitting "Rearrangements"]
11/05/03: The limit comparison
Test. Absolute and conditional convergence. The alternating series
test. The ratio test. Examples. [The Limit Comparison Test from
Section 11.4, omitting "Estimating Sums"; The Alternating Series Test
on p. 727 from Section 11.5; Section 11.6, leaving the Ratio Test for
Friday and omitting "Rearrangements"]
11/03/03: Examples on the Integral Test
for convergence. The Comparison Test. Examples. [Sections 11.3,
omitting subsections "Estimating the Sum of a Series" and "Proof of
the Integral Test," and 11.4, leaving the Limit Comparison Test for
Wednesday and omitting "Estimating Sums"]
10/31/03: Series, convergence, the
geometric series, the nth term divergence test, the Integral Test for
convergence, convergence of p-series. [Sections 11.2 and 11.3,
omitting subsections "Estimating the Sum of a Series" and "Proof of
the Integral Test"]
10/29/03: Review [Problems 7 and 11 of
the Sample Midterm II; graphing polar curves]
10/27/03: Limits of sequences. Series
and their limits [Sections 11.1 and 11.2]
10/24/03: Hyperbolas. Limits and
sequences. [Sections 10.6 and 11.1]
10/22/03: Conic sections: parabolas and
ellipses. (Hyperbolas to be finished Friday). [Section 10.6]
10/20/03: Tangents to polar
curves. Areas and lengths in polar coordinates. [Sections 10.4
(subsection on Tangents to Polar Curves) and 10.5]
10/17/03: Polar coordinates (tangents
to polar curves to be done Monday). [Section 10.4, omitting the
section on Graphing Polar Curves with Graphing Devices]
10/15/03: Arc length and surface of
revolution area. [Section 10.3]
10/13/03: Tangents and areas. [Section
10.2, omitting the section on Graphing Calculators and Computers]
10/10/03: Curves defined by parametric
equations. [Section 10.1]
10/08/03: Exponential growth and
decay. Popoulation growth. Radioactive decay. Radioactive dating: a
story. [Section 9.4]
10/06/03: Separable differential
equations. Mixing problems.[Section 9.3, omitting the section on
Orthogonal Trajectories]
10/03/03: Direction fields and Euler's
method. [Section 9.2]
10/01/03: Modeling with differential
equations. Population
growth, exponential growth and decay. Hooke's Law. Initial value
problems. [Section 9.1]
09/29/03: Applications of integration:
the moments, the center of mass, the centroid. [Section 8.3, omitting
the section on Hydrostatic Pressure and Force]
09/26/03: The area of a surface of
revolution. [Section
8.2]
09/24/03: The arc length (continued).
Review of improper
integrals. [Sections 8.1 and 7.8]
09/22/03: Improper integrals (comparison
test). The arc
length. [Sections 7.8 (pp. 529-531) and 8.1]
09/19/03: Approximate integration,
continued. Improper
integrals (Types 1 and 2) [Sections 7.7 and 7.8 through p. 529]
09/17/03: Approximate integration.
[Section 7.7]
09/15/03: Strategy for integration.
[Section 7.5]
09/12/03:
Integration by partial fractions. [Section 7.4]
09/10/03: Trigonometric substitution (continued). Partial fractions. [Section 7.3 and p. 490]
09/08/03: Trigonometric substitution. [Section 7.3]
09/05/03: Trigonometric integrals. [Section 7.2, omitting techniques involving the addition formulas, starting at the bottom of page 481]
09/03/03: Introduction. Integration by parts. [Section 7.1]