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RARITAN VALLEY COMMUNITY COLLEGE
ACADEMIC COURSE OUTLINE
MATH 152 CALCULUS II
I. Basic Course Information
A. Course Number and Title: MATH 152 Calculus II
B. New or Modified Course: Modified Course
C. Date of Proposal: Spring 2009
D. Sponsoring Department: Mathematics
E. Semester Credit Hours: 4
F. Weekly Contact Hours: 5 Lecture: 3 Laboratory: 2
G. Prerequisite: MATH 151 Calculus I
H. Laboratory Fees: None
I. Name and Telephone Number or E-Mail Address of Department Chair: Patricia Hulsen (908) 526-1200 extension 8542 phulsen@raritanval.edu
II. Catalog Description
Prerequisite: MATH 151 Calculus I. The second semester of a three-semester sequence of introductory calculus with a technology-based computer laboratory. Topics include integration techniques, integration applications in various coordinate systems, indeterminate forms, improper integrals, and infinite series. The Honors Option is available for this course.
III. Statement of Course Need
This course is a prerequisite for MATH 251 Calculus III. This course also serves as a math requirement for programs in Chemistry, Computer Science, Engineering Science, General Science, and Mathematics.
IV. Place of Course in College Curriculum
A. This course is a free elective and a Mathematics elective for all programs. B. This course serves as a General Education requirement in Mathematics. C. This course meets a program requirement in Chemistry, Computer Science, Engineering Science, General Science, and Mathematics. D. This course transfers as a second semester calculus course. Course transferability; for New Jersey schools go to the NJ Transfer website, www.njtransfer.org. For all other colleges and universities go their individual websites.
V. Outline of Course Content
A. Applications of Integration
- Area of a region between two curves
- Volume, disk method and shell method
B. Integration Techniques, L'Hôpital's Rule, and Improper Integrals
- Basic integration rules, integration by parts, trigonometric substitution
- Partial fractions; tables
- Indeterminate forms and L'Hôpital's Rule
- Improper integrals
C. Infinite Series
- Sequences, series, and convergence
- Integral test, p-series, comparison test
- Alternating series, ratio test, root test
- Taylor polynomials and approximations; power series
- Representation of functions by power series; Taylor and Maclaurin series
D. Conics, Parametric Equations, and Polar Coordinates
- Conics and calculus
- Plane curves and parametric equations; parametric equations and calculus
- Polar coordinates and polar graphs
- Area and arc length in polar coordinates
- Polar equations of conics and Kepler's Laws
VI. Educational Goals and Learning Outcomes
A. General Education Goals
Students will:
- apply mathematical arguments to problems. (G. E. 1)
- solve problems quantitatively and symbolically. (G. E. 7)
Please Note: The course outline is intended only as a guide to course content and resources. Do not purchase textbooks based on this outline. The RVCC Bookstore is the sole resource for the most up-to-date information about textbooks.
XI. Resources
This course is held in a computer lab for two hours a week. The computers need to be installed with the math software currently licensed to the math department. Contact the math department to determine which software to install.
XII. Honors Option
Definition
Students pursuing the Honors Option in Calculus II will be required to demonstrate a higher level of knowledge and skill in the theory, techniques, and applications of integration, as well as in polar coordinates conic sections and Infinite Series. In addition to learning how to apply integration to many problems in geometry and physics they are required to derive the formulas they use, generalize results and construct some proofs in infinite series. They are also required to solve advanced and challenging application problems.
A. Educational Goals and Learning Outcomes
In addition to the education goals and learning outcomes in Roman numeral VI. A and B listed above, students should be able to:
- Demonstrate how formulas are derived
- Provide proofs of theorems appropriate to the Calculus II level
- Solve challenging and advanced application problems
B. Honors Option Content
Students, who participate in the Calculus II Honors Option, must complete three additional assignments. For the third assignment the student is given a choice to select one of three mathematical activities described in item 3 below.
- Students must present two proofs assigned by the instructor that are relevant to the main theorems of the course or are an enrichment of them. The instructor will assign a time for the presentation and students in the class will be invited and encouraged to attend.
- Students must complete two extra Lab assignments. These Honors Lab Assignments will be on the theory portion of the course or on application problems.
- Students must choose and complete one of the following three mathematical activities:
a. Investigate and solve two assigned advanced problems.
b. Write a report on a project that begins with a problem, state the theoretical foundation of the problem and its solution and apply calculus II tools such as techniques of integration, or infinite series to solve the problem
c. Submit a poster on a topic or an application problem in Calculus II and present it at the Mathematical Association of America Spring or Fall Student Poster Session.
C. Assessment Instruments for Honors Option Work
Honors Option students will be assessed for their ability to deliver the additional required assignments. In particular they must:
- Make a clear and in depth presentation of two proofs
- Hand in two additional lab assignments
- Complete one of the following: design a Poster, complete a written project that requires investigating and solving a problem, or solve two advanced application problems
D. Grade Determinants for Honors Option Work
In addition to quizzes, labs, tests and final exam, the final grade for students in the Honors Option will be based upon students completing the three additional assignments described above.
E. Extra Resource Materials for the Honors Option
In addition to the suggested textbook above, students may need to use:
a. Computer lab with Maple software b. Selected articles appropriate to the Calculus II level from the College Mathematics Journal, a publication of the Mathematical Association of America
