Prerequisites
MATH 226 (Calculus I) with a grade of C or better.Bulletin Description
The second semester of Calculus: integration, area between curves, volume, integration by parts, partial fractions, improper integrals, parametric equations, infinite sequences and series, an introduction to computer algebra systems.Course Objectives
The main objective of Calculus II is for students to continue learning the basics of the calculus of functions of one variable. They will study both the concepts and techniques of integration, parametric equations, and infinite sequences and series, culminating with Taylor series. They will also apply these ideas to a wide range of problems that include area between curves, volume, work, arc length and surface area. They will study approximate integration, a topic that will involve an introduction to a computer algebra system. The students should be able to interpret the concepts of Calculus algebraically, graphically and verbally. More generally, the students will improve their ability to think critically, to analyze a problem and solve it using a wide array of tools. These skills will be invaluable to them in whatever path they choose to follow, be it as a mathematics major or in pursuit of a career in one of the other sciences. Upon successful completion of the course, students should be able to- Evaluate definite, indefinite and improper integrals exactly using basic integration techniques such as substitution, integration by parts and partial fractions.
- Apply integration to problems such as volume, arc length, surface area, and work or hydrostatic force.
- Carry out numerical integration using Simpson's Rule, Taylor Series, and Mathematica.
- Correctly apply convergence tests to infinite series and determine the interval of convergence of a power series.
- Approximate functions by Taylor polynomials and provide error estimates.
Evaluation of Students
Students will be evaluated on their ability to devise, organize and present complete solutions to problems. While instructors may design their own methods of evaluating student performance, these methods must include in-class examinations, frequent homework assignments and a final exam.Course Outline
| Topics | Number of Weeks | Sections in Text |
| Techniques of Integration | 4 | 4.5-4.7, 5.1.5.2*.5.3*.5.4, 5.5 |
| Numerical Integration, Improper Integrals | 1 | 5.6-5.7 |
| Applications of Integration | 3 | 6.1-6.3, 6.5* |
| Infinite Series | 4 | 7.1-7.10 | Parametric Equations and Polar Coordinates | 2 | 8.1-8.3,8.4* |
| Mathematica | Lab |
Textbooks & Software
University Calculus Elements with Early Transcendentals by Hass, Weir, and Thomas Mathematica
Date: August 3 2008
