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.
Date First Offered:
Total Hours: 60
Lecture Hours: 3
Laboratory Hours: 1
This course is offered online:
MATH 101 Calculus or equivalent
- 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,
- Strategy for Testing Series, Power Series, Taylor and Maclaurin Series, approximation by Taylor Polynomials. (12.7, 12.8,
1. To formulate in terms of limits, the idea of the integral.
2. To establish one connection between differential calculus and integral calculus with one Fundamental Theorem of Calculus
3. To illustrate some applications of the definite integral
4. To develop techniques for using basic integration formulas to obtain indefinite integrals of more complicated functions
5. To investigate some additional applications of integration.
6. To develop two new methods of describing curves: (Parametric equations and polar coordinates)
7. To find ways of writing any function as a series so as to be able to integrate functions that were formerly non integrable
Final Exam: 45 %
Midterm Exam: 40 %
Quizzes and Tests: 15 %
Percentage of Individual Work:
Course Offered in Other Programs:
Associate of Arts Diploma - Fine Arts, Associate of Arts Degree, Associate of Arts - Criminology Specialization, Academic Elementary Education, Academic Engineering, Academic Pre-Medicine, Academic Social Sciences.