MATH 2432This is an archive of the Common Course Outlines prior to fall 2011. The current Common Course Outlines can be found at http://www.gpc.edu/programs/Common-Course-Outlines.
Credit Hours 4
Course Title Calculus II
Prerequisite(s) MATH 2431 with a "C" or better
Corequisite(s) None Specified
This course includes the study of techniques of integration, applications of the definite integral, an introduction to differential equations, polar graphs, and power series.
Expected Educational Results
As a result of completing this course, the student will be able to:
1. Evaluate integrals using techniques of integration.
2. Use integrals to solve application problems.
3. Solve separable differential equations and apply to elementary applications.
4. Investigate the convergence of series and apply series to approximate functions and definite integrals.
5. Apply polar representations including graphs, derivatives, and areas.
General Education Outcomes
I. This course addresses the general education outcome relating to communication by providing additional support as follows:
A. Students improve their listening skills by taking part in general class discussions and in small group activities.
B. Students improve their reading skills by reading and discussing the text and other materials. Reading mathematics requires skills somewhat different from those used in reading materials for other courses in that students are expected to read highly technical material.
C. Unit tests, examinations, and other assignments provide opportunities for students to practice and improve mathematical writing skills. Mathematics has a specialized vocabulary that students are expected to use correctly.
II. This course addresses the general education outcome of demonstrating effective individual and group problem-solving and critical-thinking skills as follows:
A. Students must apply mathematical concepts to non-template problems and situations.
B. In applications, students must analyze problems, often through the use of multiple representations, develop or select an appropriate mathematical model, utilize the model, and interpret results.
III. This course addresses the general education outcome of using mathematical concepts to interpret, understand, and communicate quantitative data as follows:
A. Students must demonstrate proficiency in problem-solving skills by using the definite integral to solve application problems.
B. Students must be able to solve applied problems that can be modeled by differential equations.
C. Students must use power series techniques to approximate function values to a specified degree of accuracy.
IV. This course addresses the general education outcome of locating, organizing, and analyzing information through appropriate computer applications (including hand-held graphing calculators). As a result of taking this course, the student should be able to use technology to:
A. Approximate definite integrals using Simpson's rule or a built-in integration feature.
B. Approximate points of intersection of curves for use in determining approximate limits of integration in application problems.
C. Investigate series representations of functions, their graphs, and the convergence or divergence of series.
D. Approximate values of functions and definite integrals using Taylor series.
V. This course addresses the general education outcome of using scientific inquiry by using techniques of Calculus including integration or differentiation to apply scientific inquiry to problem solving.
1. Techniques of Integration
2. Applications of the Definite Integral
3. Differential Equations
5. Polar representations
ENTRY LEVEL COMPETENCIES
Upon entering this course the student should be able to do the following:
1. Investigate limits using algebraic, graphical, and numerical techniques.
2. Investigate derivatives using the definition, differentiation techniques, and graphs. The classes of functions studied include algebraic, trigonometric, inverse trigonometric, exponential, logarithmic, and implicit.
3. Apply the derivative as a rate of change, optimize functions, use Newton's Method, and sketch curves.
4. Define the definite integral and approximate definite integrals using Riemann sums.
5. State and apply the Fundamental Theorem of Calculus.
6. Graph and use parametric equations.
Assessment of Outcome Objectives
The Calculus Committee or a special assessment committee appointed by the Chair of the Math, Computer Science, and Engineering Executive Committee, will accumulate and analyze the results of the assessment and determine implications for curriculum changes. The committee will prepare a report for the Academic Group summarizing its finding.
Last Revised: Aug. 10, 2011Return to all courses