Math 1272: Lecture Outlines

o12/12/03: Review of integration. [Chapter 7]

o12/10/03: Spherical coordinates. Review of integration by parts. [Sections 12.7 and 7.1]

o12/08/03: How to recognize a quadric surface. Cylindrical surfaces. Cylindrical coordinates. [Sections 12.6-7 (spherical coordinates left for Wednesday)]

o12/05/03: Planes in space. Quadric surfaces. [Sections 12.5-6 (no cylindrical surfaces yet)]

o12/03/03: Review: power series, Maclaurin and Taylor series. [Sections 11.8-10]

o12/01/03: 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)]

o11/26/03: 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]

o11/24/03: The dot product. The angle between two vectors. Orthogonal and parallel vectors. Direction angles. Projections. [Section 12.3]

o11/21/03: Vectors in the plane and space. Vector addition and multiplcation by a scalar. [Section 12.2]

o11/19/03: Space geometry. 3d coordinate system. The distance formula. Spheres and their equations. Regions in space. [Section 12.1]

o11/17/03: 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]

o11/14/03: Taylor and Maclaurin series. Expanding a function into its Taylor series. Approximate computations based on Taylor series. [Section 11.10]

o11/12/03: Representation of functions as power series. Differentiation and integration of power series. [Section 11.9]

o11/10/03: Power series. The radius and interval of convergence. Examples. [Section 11.8]

o11/07/03: The ratio and root tests. Examples. [Section 11.6, omitting "Rearrangements"]

o11/05/03: 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"]

o11/03/03: 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"]

o10/31/03: 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"]

o10/29/03: Review [Problems 7 and 11 of the Sample Midterm II; graphing polar curves]

o10/27/03: Limits of sequences. Series and their limits [Sections 11.1 and 11.2]

o10/24/03: Hyperbolas. Limits and sequences. [Sections 10.6 and 11.1]

o10/22/03: Conic sections: parabolas and ellipses. (Hyperbolas to be finished Friday). [Section 10.6]

o10/20/03: Tangents to polar curves. Areas and lengths in polar coordinates. [Sections 10.4 (subsection on Tangents to Polar Curves) and 10.5]

o10/17/03: Polar coordinates (tangents to polar curves to be done Monday). [Section 10.4, omitting the section on Graphing Polar Curves with Graphing Devices]

o10/15/03: Arc length and surface of revolution area. [Section 10.3]

o10/13/03: Tangents and areas. [Section 10.2, omitting the section on Graphing Calculators and Computers]

o10/10/03: Curves defined by parametric equations. [Section 10.1]

o10/08/03: Exponential growth and decay. Popoulation growth. Radioactive decay. Radioactive dating: a story. [Section 9.4]

o10/06/03: Separable differential equations. Mixing problems.[Section 9.3, omitting the section on Orthogonal Trajectories]

o10/03/03: Direction fields and Euler's method. [Section 9.2]

o10/01/03: Modeling with differential equations. Population growth, exponential growth and decay. Hooke's Law. Initial value problems. [Section 9.1]

o09/29/03: Applications of integration: the moments, the center of mass, the centroid. [Section 8.3, omitting the section on Hydrostatic Pressure and Force]

o09/26/03: The area of a surface of revolution. [Section 8.2]

o09/24/03: The arc length (continued). Review of improper integrals. [Sections 8.1 and 7.8]

o09/22/03: Improper integrals (comparison test). The arc length. [Sections 7.8 (pp. 529-531) and 8.1]

o09/19/03: Approximate integration, continued. Improper integrals (Types 1 and 2) [Sections 7.7 and 7.8 through p. 529]

o09/17/03: Approximate integration. [Section 7.7]

o09/15/03: Strategy for integration. [Section 7.5]

o09/12/03: Integration by partial fractions. [Section 7.4]

o09/10/03: Trigonometric substitution (continued). Partial fractions. [Section 7.3 and p. 490]

o09/08/03: Trigonometric substitution. [Section 7.3]

o09/05/03: Trigonometric integrals. [Section 7.2, omitting techniques involving the addition formulas, starting at the bottom of page 481]

o09/03/03: Introduction. Integration by parts. [Section 7.1]


Last modified: Fri Aug 29 12:31:18 CDT 2003