||March 31, 2011
General Course Description
A second course in differential and integral calculus of a single variable: integration; techniques of integration; infinite sequences and series; polar and parametric equations; applications of integration. Primarily for Science, Technology, Engineering & Math Majors.
Any rationale or comments
Single Variable Calculus I Early Transcendentals (Math 210, CAN 18).
- Areas between curves;
- Volume, volume of a solid of revolution;
- Additional techniques of integration including integration by parts and trigonometric substitution;
- Numerical integration; trapezoidal and Simpson's rule;
- Improper integrals;
- Applications of integration to areas and volumes;
- Additional applications such as work, arc length, area of a surface of revolution, moments and centers of mass, separable differential equations, growth and decay;
- Introduction to sequences and series;
- Multiple tests for convergence of sequences and series;
- Power series, radius of convergence, interval of convergence;
- Differentiation and integration of power series;
- Taylor series expansion of functions;
- Parametric equations and calculus with parametric curves; and
- Polar curves and calculus in polar coordinates;
Upon successful completion of the course, students will be able to:
Evaluate definite and indefinite integrals using a variety of integration formulas and techniques;
Apply integration to areas and volumes, and other applications such as work or length of a curve;
Evaluate improper integrals;
Apply convergence tests to sequences and series;
Represent functions as power series; and
Graph, differentiate and integrate functions in polar and parametric form.
Methods of Evaluation
Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems.
A college level textbook designed for science, technology, engineering and math majors, and supporting the learning objectives of this course.