OAKTON COMMUNITY COLLEGE

GENERIC COURSE SYLLABUS

I. Course Course Course

Prefix Number Name Credit Lecture Lab

MAT 251 Calculus II 4 4 0

II. Prerequisite:

MAT 250 with a grade of C or better.

III. Course (Catalog) Description:

Course is second in calculus and analytic geometry. Content focuses on differentiation and integration of transcendental functions such as inverse trigonometric functions; hyperbolic functions and inverse hyperbolic functions; applications of the definite integral; polar coordinates; techniques of integration and improper integral; vectors operations and vectors functions. Calculators/computers used when appropriate.

IV. Course Objectives:

1. Demonstrate an understanding of L’Hopital’s rule by using it to calculating limits.

2. Apply integration to find surface area, volume, and arc length, and use it to solve physics and

engineering applications, including finding moments, centroids, and total work.

3. Evaluate integrals by various techniques including integration by parts, partial fractions, substitutions, and tables.

4. Use hyperbolic functions in modeling, differentiation, and integration.

5. Evaluate and interpret improper integrals.

6. Solve separable and first order linear differential equations in abstract and applied contexts.

7. Graph, differentiate, and integrate polar equations in abstract and applied contexts.

8. Evaluate infinite sequences and series.

9. Use convergence tests and estimate series.

10. Demonstrate and apply an understanding of power series and Taylor and Maclaurin series by using them to represent, differentiate, and integrate functions.

11. Use technology for evaluating integrals, series, and polar and parametric equations.

V. Academic Integrity:

Students and employees at Oakton Community College are required to demonstrate academic integrity and follow Oakton’s Code of Academic Conduct. This code prohibits:

· cheating,

· plagiarism (turning in work not written by you, or lacking proper citation),

· falsification and fabrication (lying or distorting the truth),

· helping others to cheat,

· unauthorized changes on official documents,

· pretending to be someone else or having someone else pretend to be you,

· making or accepting bribes, special favors, or threats, and

· any other behavior that violates academic integrity.

There are serious consequences to violations of the academic integrity policy. Oakton’s policies and procedures provide students a fair hearing if a complaint is made against you. If you are found to have violated the policy, the minimum penalty is failure on the assignment and, a disciplinary record will be established and kept on file in the office of the Vice President for Student Affairs for a period of 3 years.

Details of the Code of Academic Conduct can be found in the Student Handbook.

VI. Outline of Topics (ICCB AAT Codes, see Section IX): (Textbook Sections Referenced)

A. L’Hopital’s Rule and Review of Differentiation and Integration (Sections 4.6 and 5.6)

1. L’Hopital’s Rule (and review of rules of differentiation)

2. Using basic integrals and substitutions to find the area between curves

B. Applications of the Definite Integral (Sections 6.1 through 6.7)

1. Volumes using cross-sectional areas

2. Volumes of solids of revolution using discs, washers, and shells

3. Arc length and Surface Area of Revolution

4. Work, hydrostatic pressure and force, moments, and center of mass

C. Hyperbolic Functions: Graphing, Differentiating, Integrating (Section 7.4)

D. Techniques of Integration (Sections 8.1 through 8.6)

1. Integration by parts

2. Integration of rational functions by partial fractions

3. Integration of trigonometric functions

4. Trigonometric substitutions

5. Integration using tables

E. Improper Integrals (Section 8.8)

1. Infinite limits of integration

2. Integration over discontinuities

F. Differential Equations and Their Applications (Sections 9.1, 9.2, and 9.5)

1. Separable differential equations

2. First order differential equations

3. Applications

G. Polar Coordinates (Sections 10.5, 10.6, and 10.7)

1. Graphing with polar coordinates

2. Integration and differentiation using polar coordinates

3. Applications including area, arc length and surface area

H. Infinite Sequences and Series (Sections 11.1 through 11.9)

1. Sequences and series

2. Geometric series

3. Tests for positive terms (integral, comparison, ratio, n'th root)

4. Alternating series

5. Absolute and conditional convergence

6. Power series, Taylor and Maclaurin series

7. Applications including binomial series and solution to differential equations

I. Recommended Technology

1. Use of technology to evaluate integrals

2. Use of technology to investigate improper integrals

3. Use of technology to investigate differential equations

4. Use of technology for graphing, integrating, and differentiating parametric and

polar equations

VII. Methods of Instruction (ICCB AAT Codes, see Section IX):

(To be completed by instructor).

Methods of presentation can include lectures, discussion, experimentation, audio-visual aids, small-group work and regularly assigned homework. Calculators/computers will be used when appropriate. Use of a computer algebra system is recommended. Mathematica is available for use at the College at no charge.

VIII. Course Practices Required:

(To be completed by instructor)

IX. Instructional Materials:

Required Textbook: http://www.oakton.edu/acad/dept/mcs/mat/textbooks.htm

Required Materials: A TI-83 graphics calculator (or an equivalent or more advanced model).

A graphics calculator is required. A TI-83 or higher numbered model will be used for instructional purposes.

X. Methods of Evaluating Student Progress (ICCB AAT Codes, see Section IX):

(To be determined and announced by the instructor).

Evaluation methods can include grading homework, chapter or major tests, quizzes, individual or group projects, calculator/computer projects and a final examination.

XI. Other Course Information:

If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services. To request accommodations or services, contact the ASSIST office in the Learning Center. All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.

Effective beginning term: __Fall 2009______________ Ending term: ___________

(term) (year) (term) (year)

Syllabus prepared by: J. Strehler, P. Boisvert, M. Farquhar, J. Kotowski, G. McCLarren,

K. Murashkina, S. Hamed Date _ May, 2009____

Reviewed by Dept/Program Chair: Julia Hassett Date __May 2009__

Approved by Dean: Robert Sompolski Date __May 2009__