## MATH 102 - Calculus II

Calculus II: The definite integral, area, volume, work, techniques of integration, arc length, area of surface of revolution, moments, parametric equations, polar coordinated, Taylor series and approximation by Taylor polynomials.

Credits: 3

Hours: 60 (Lecture Hours: 3; Laboratory Hours: 1)

Total Weeks: 15

Prerequisites:

MATH 101 Calculus
OR equivalent

Non-Course Prerequisites:

None

Co-requisites:

None

Course Content:
- Sigma Notation, Area, The Definite Integral, Properties of the Definite Integral. (5.1, 5.2, 5.3)
- Properties of the Definite Integral, The Fundamental Theorem of Calculus, The Substitution Rule. (5.4, 5.5)
- Areas between Curves, Volume, Volumes by Cylindrical Shells. (6.1, 6.2, 6.3)
- Work, Average Value of a Function. (6.4, 6.5)
- Integration by Parts, Trigonometric Integrals, Trigonometric Substitution. (8.1, 8.2, 8.3)
- Integration of Rational Functions by Partial Fractions, Rationalizing Substitutions, Strategy for Integration. (8.4, 8.5, 8.6)
- Approximate Integration, Improper Integrals. (8.7, 8.8)
- Separable Differential Equations, Arc Length, Area of a Surface of Revolution (10.3, 9.1, 9.2, 9.3)
- Curves Defined by Parametric Equations, Tangents and Areas, Arc Length and Surface Area, Polar Coordinates. (11.1, 11.2, 11.3)
- Areas and Lengths in Polar Coordinates, Sequences, Series. (11.5, 12.1, 12.2)
- The Integral Test, The Comparison Tests, Alternating Series, Absolute Convergence and the Ratio and Root Tests. (12.3, 12.4, 12.5, 12.6)
- Strategy for Testing Series, Power Series, Taylor and Maclaurin Series, approximation by Taylor Polynomials. (12.7, 12.8, 2.9,12.10,12.12)

Learning Outcomes:
- To formulate in terms of limits, the idea of the integral.
- To establish one connection between differential calculus and integral calculus with one Fundamental Theorem of Calculus
- To illustrate some applications of the definite integral
- To develop techniques for using basic integration formulas to obtain indefinite integrals of more complicated functions
- To investigate some additional applications of integration.
- To develop two new methods of describing curves: (Parametric equations and polar coordinates)

- To find ways of writing any function as a series so as to be able to integrate functions that were formerly non integrable