MAT 251 GENERIC COURSE SYLLABUS

Effective Date: Fall 2000

Instructor:

Campus:

Room:

Office Hours:

Phone:

I.

Course Prefix

Course Number

Course Name

Credit

Lecture

Lab

MAT

251

Calculus II

4

4

0

II.

Prerequisites:

MAT 250 with a grade of C or better.

III.

Course 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:

A. Evaluate definite integrals by using substitution, integration by parts, and tables.

B. Evaluate improper integrals.

C. Use integrals to find area, volume and arc length; application to physics and engineering.

D. Evaluating differential equations by Euler's method and the separation of variables.

E. Evaluating infinite sequences and series.

F. Using convergence tests and estimating series.

G. Using power series and representing functions by power series.

H. Using Taylor and Maclaurin series.

I. Understand two dimentional vector functions and their applications.

J. Understand polar equations and their application to differentiation and integration.

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

V.

Academic Integrity:

Students, Faculty and administration 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,
• making unauthorized changes in official documents,
• pretending to be someone else or having someone else to 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 with a fair hearing if a complaint is made. 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:

A. Techniques of Integration

1. Integration by parts
2. Integration by substitution
       a) Partial fractions
       b) Trigonometric substitutions
3. Integration using tables

B. Improper Integrals

1. L'Hopital's rule
2. Infinite limits of integration
3. Integration over discontinuities

C. Applications of the Definite Integral

1. Volumes using the cross-sectional area
2. Volumes of solids of revolution
3. Arc length
4. Work, hydrostatic pressure and force, moments,
and center of mass

D. Modeling and Differential Equations

1. Exponential growth and decay
2. Separable differential equations
3. Logistic models

E. Infinite sequences and series

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
7. Taylor and Maclaurin series
8. Applications including binomial series and solution to differential equations

F. Polar coordinates

1. Graphing with polar coordinates
2. Integration and differentiation using polar coordinates
3. Applications including area and arclength and surface area

G. Vectors and vector functions

1. Two-dimentional vectors and dot products
2. Vector-valued functions
3. Projectile motion

H. Recommended Technology

1. Use of technology to evaluate integrals
2. Use of technology to investigate improper integrals
3. Use Euler's method and technology to evaluate differential equations
4. Use technology for graphing, integrating, and differentiating parametric and polar equations

VII.

Methods of Instruction:

(To be completed by instructor)

Methods of presentation can include lectures, discussion, demonstration, experimentation, audiovisual aids, 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:

Custom -- Wier - Thomas' Calculus Early Transendantals 11/e
ISBN: 0-536-52919-1
Publisher: Addison Wesley

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

X.

Methods of Evaluating Student Progress:

(To be determined and announced by the instructor)

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

XI.

Other Course Information:

Individual instructors will establish and announce specific policies regarding attendance, due dates and make-up work, incomplete grades, etc.

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 Instructional Support Services. 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	2000	Ending Term:
	(term)	(year)		(term)	(year)
Prepared by:	R. Diprizio & R. Sompolski			Date: Fall 1999
Reviewed by Department/ Program Chair	Rudy Maglio			Date:
Approved by Dean:	Edward Garcia			Date: