Further topics in differential and integral calculus, including sequences and series, Taylor polynomials, polar coordinates, methods of integration, and applications of the integral. Prerequisite: MATH 110 or 111. (Offered each semester.)

Larson, Hostetler and Edwards, Calculus with Analytic Geometry, 8^th edition, D. C. Heath, 2006.

Douglas C. Phillippy, Ph.D., Associate Professor of Mathematics

Students majoring in computer science, engineering, mathematics, physics, or chemistry.

1. To acquire a comparative knowledge of standard coordinate systems and the ability to choose the most efficient system for any specific problem.
2. To develop a rigorous understanding of sequences and series with ability to determine their convergence or divergence.
3. To understand applications of the definite integral to problems such as area, volume, arc length, work and centers of mass.
4. To enhance learning by examining geometric, numerical and algebraic aspects of each topic.
5. To develop an ability to recognize calculus concepts in the context of applications in a wide variety of scientific fields and implement the corresponding processes.
6. To use the tools of calculus to formulate and solve multi-step problems and to interpret the numerical results.
7. To enhance the ability to communicate mathematical concepts through a series of written laboratory assignments and classroom discussions.
8. To select and use technology when appropriate in problem solving.

1. Ability to graph functions and identify extrema and asymptotes
2. Understand the use of Riemann sums in finding areas and volumes.
3. Understand and use the fundamental theorem of calculus.
4. Familiarity with the method of substitution for evaluating an integral.

1. Techniques of integration: a) integration by parts, b) trig functions and products of trig functions c) partial fraction representation of rational functions, d)trig substitutions.
2. L’Hopital’s Rule and improper integration
3. Infinite sequences: a) arithmetic and geometric, b) limits of sequences.
4. Infinite series: a) tests for convergence, b) alternating series, c) absolute and conditional convergence, d) power series, e) Taylor and Maclaurin Series.
5. Polar coordinates and parametric equations: a) study of coordinate system, b) graphing, c) areas and arc lengths.
6. Conic sections: a) representation in both rectangular and polar form, b) graphs with emphasis on applications.

1. The mathematics and engineering reading room (Frey 351).
2. Student math assistants available Monday through Thursday evening 7:00 p.m. to 9:00 p.m. in Frey 349 and 351.
3. Messiah College welcomes students with disabilities. AMERICANS WITH DISABILITIES ACT: Any student whose disability falls within ADA guidelines should inform the instructor within the first two weeks of any special accommodations or equipment needs necessary to complete with the Office of Disability Services (Hoffman 101). If you have questions, call extension 5387.

1. This class is a lecture and discussion oriented class.
2. There will be a minimum of six laboratory projects that include written reports.