Course Objectives:

1.         Use advanced integration techniques such as integration by parts and trigonometric substitutions and to evaluate complicated integrals.
2.         Apply integration techniques to determine the area between curves and the volume and surface area of solids of revolution.
3.         Determine whether sequences and series converge or diverge and to be able to find a power series approximation for a function.
4.         Know the equations and properties of conic sections.
5.         Know formulas to make conversions between polar coordinate systems and rectangular coordinate systems and to recognize the shapes of several polar coordinate curves.
 

Topical Outline:

1.         Demonstrate knowledge of hyperbolic functions.
2.         Integrate functions using the method by parts.
3.         Use methods of integration by partial fractions.
4.         Evaluate improper Integrals.
5.         Evaluate Trigonometric Integrals
6.         Use the method of integration by Trigonometric Substitutions.
7.         Apply integration to calculate an area between curves.
8.         Calculate a volume of a solid of revolution.
9.         Solve problems about arc length of plane curves.
10.       Illustrate applications of integrals to find surface area of solids of revolution.
11.       Express and calculate a work by using integration.
12.       Define variety of sequences and calculate their limits.
13        Demonstrate knowledge of geometric series, telescoping series, p-series.
14.       Apply divergence test (nth term test), convergence tests: comparison, integral, for infinite series.
15.       Use convergence tests to prove Absolute or Conditional Convergence of Alternating Series.
16.       Prove convergence of series by using Ratio and Root Tests.
17.       Find a Radius of Convergence of Power Series.
18.       Demonstrate knowledge about the Taylor and Maclaurin Polynomial Series and about the Algebra and Calculus of Power Series.
19.       Identify Polar Coordinates.
20.       Illustrate Special Curves in Polar Coordinates.
21.       Evaluate Derivatives, Tangent Lines and arc length for Parametric and Polar Curves.
22.       Analyze Area in polar coordinates.
23.       Recognize Conic Sections with center at the origin.
24.       Practice with Conics with vertex or center not in the origin.
25.       Represent conic sections in Polar Coordinates.