NASSAU COMMUNITY COLLEGE
DEPARTMENT OF MATHEMATICS/COMPUTER SCIENCE/INFORMATION TECHNOLOGY
Course Syllabus for
Course Information
· Title Calculus II
· Credit Hours 4 Credits
· Number MAT 123
· Section/CRN ______
· Semester/Term ______
· Meeting time ______
· Location ______
Instructor/Contact Information
· Name ______
· Office location ______
· Office hours ______
· Office telephone and fax numbers ______
· Email address ______
· Blackboard link ______
· Website ______
· Other ______
Course Description
PREREQUISITE
Students must have satisfied all MAT, ENG, and RDG 001 remediation requirements. The student must have achieved at least a C in Calculus I (MAT l22). It is strongly advised that the student should have taken Calculus I not more than two semesters ago.
CATALOG DESCRIPTION
Techniques of integration including substitution, parts, partial fractions, trigonometric substitution; tables of integrals; improper integrals; applications including areas, volumes of solids of revolution, arc length, density and center of mass, work, hydrostatic force, and present and future value of an income stream; sequences; Taylor series, convergence of series, radius and interval of convergence, producing new series from old (substitution, integration, differentiation), errors in Taylor approximations; introduction to differential equations, particularly separation of variables and modeling.
OBJECTIVES
General
The course is meant to extend the student's understanding of calculus by providing appropriate techniques, necessary drill and useful applications.
Specific
This course is an extension of Calculus I (MAT l22), and treats techniques of integration and its applications, with emphasis on the meaning of the symbols used and the interpretation of results. Sequences and series are covered, including power series. Modeling using differential equations whose variables are separable are discussed.
DETAILED TOPICS OUTLINE
TOPICS
· Integration
The purpose of this chapter is to acquaint the student with several techniques of integration including substitution, parts, partial fractions (including quadratic factors), and trigonometric substitution (including completing the square). The rewriting of a given integral as a standard form that can be found in a table of integrals is also covered. Improper integrals are discussed.
Class lectures and exams: 5.5 weeks*
· Using the definite integral
The Riemann sum concept is once again treated and is used as a basis for solving problems of total change. Applications include areas, volumes of solids of revolution, arc length, density and center of mass, work, hydrostatic force, present and future value of an income stream, and probability.
Class lectures and exams: 3.5 weeks*
· Sequences and series
Introduction to the notion of sequences and infinite series, and tests for convergence are covered. Power series are introduced.
Class lectures and exams: 1.5 weeks*
· Approximating functions using series
Functions are approximated by polynomials using series. Topics include Taylor polynomials, Taylor series, convergence of series, radius and intervals of convergence, producing new series from old (substitution, integration, and differentiation), errors in Taylor approximations are briefly discussed.
Class lectures and exams: 2 weeks*
· Differential equations
This chapter begins with equations that involve derivatives and develops the idea that differential equations often provide a reasonable model for physical events. Topics include What are differential equations?, separation of variables, growth and decay, modeling, population growth.
Class lectures and exams: 2.5 weeks*
CHAPTERS AND SECTIONS
Topic Chapter Sections
Integration 7 1, 2, 3, 4, 5, 6, 7
Using the definite integral 8 1, 2, 4, 5, 6, 7*, 8*
Sequences and series 9 1, 2, 3, 4, 5
Approximating functions using series 10 1, 2, 3, 4*
Differential equations 11 1, 2*, 3*, 4, 5, 6, 7*
Note: The sections indicated by ‘*’ are optional. In addition, since there are a number of topics in chapter 8, instructors should focus on applications involving area, volume, arc length, work, density and interest theory. Less emphasis should be put on supply/demand, centroids, hydrostatic force and probability theory.
Course Learning Goals and Outcomes
1. Draw Inferences from Mathematical Models
Students will demonstrate the ability to and draw inferences from mathematical models such as formulas, graphs, tables, and schematics.
Learning Outcome / Mapping1.1 Mathematical Interpretation / SUNY General Education Learning Goals: 5.1. Demonstrate
Interpret variables, parameters, and other specific information within / ability to interpret/draw references.
a mathematical model .
1.2 Draw Inferences / SUNY General Education Learning Goals: 5.1. Demonstrate
Draw inferences about the situation being modeled mathematically. / ability to interpret/draw references.
1.3 Verbal Interpretation / SUNY General Education Learning Goals: 5.1. Demonstrate
Verbally interpret the results of their analysis of the mathematical / ability to interpret/draw references.
model.
2. Represent Mathematical Information
Students will demonstrate the ability to represent mathematical information symbolically, visually, numerically and verbally.
Learning Outcome / Mapping2.1 Mathematical Information / SUNY General Education Learning Goals: 5.2. Demonstrate
Employ the appropriate representation to display the mathematical / ability to represent mathematical info.
information.
2.2 Mathematical Terminology / SUNY General Education Learning Goals: 5.2. Demonstrate
Clearly define variables; draw, scale and label graphs; use correct / ability to represent mathematical info.
mathematical terminology and/or language.
3. Employ Quantitative Methods
Students will demonstrate the ability to employ quantitative methods such as arithmetic, geometry, or statistics to solve problems.
Learning Outcome / Mapping3.1 Identify Quantitative Methods / SUNY General Education Learning Goals: 5.3. Demonstrates
Identify a specific numeric, algebraic, or statistical method(s) / ability, employ quantitative methods
needed to solve a problem .
3.2 Applying Quantitative Methods / SUNY General Education Learning Goals: 5.3. Demonstrates
Apply the method identified, and correctly solve the problem. / ability, employ quantitative methods
4. Check Mathematical Results for Reasonableness
Students will demonstrate the ability to estimate and check mathematical results for reasonableness.
Learning Outcome / Mapping4.1 Estimation / SUNY General Education Learning Goals: 5.4. Demonstrate
Estimate and justify a mathematical result to a problem. / ability to estim & check math results
4.2 Reasonableness / SUNY General Education Learning Goals: 5.4. Demonstrate
Articulate a justification for the estimate using a clearly defined / ability to estim & check math results
logical plan.
5. Recognize Limits
Students will demonstrate the ability to recognize the limits of mathematical and statistical methods.
Learning Outcome / Mapping5.1 Real Life Comparison / SUNY General Education Learning Goals: 5.5. Demonstrate
Describe how the results of the mathematical model may differ from / ability to recognize limits
the real life situation it is modeling.
5.2 Mathematical Assumptions / SUNY General Education Learning Goals: 5.5. Demonstrate
Articulate the assumptions made in developing a / ability to recognize limits
mathematical/statistical model.
Instructional Methods
This course is taught using a variety of instructional methods including lecture, class discussion, and small group work when applicable.
Textbook and Materials
· Required textbook: Calculus, 6th ed. by Hughes-Hallett et al., published by Wiley
Student Responsibilities /Course Policies
Instructors need to complete the following for their specific policies. It is recommended that in class exams are required.
· Participation ______
· Homework ______
· Online discussions ______
· Projects ______
· Group work (include information on effective group procedures)
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· Exams/quizzes ______
· Attendance/lateness policy
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· Missed exams/ quizzes policy
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· Extra credit ______
· Academic Dishonesty & Plagiarism
Academic dishonesty, which includes plagiarism and cheating, will result in some form of disciplinary action that may lead to suspension or expulsion under the rules of the Student Code of Conduct. Cheating can take many forms including but not limited to copying from another
student on an examination, using improper forms of assistance, or receiving unauthorized aid when preparing an independent item of work to be submitted for a grade, be it in written, verbal or electronic form. Anyone who assists or conspires to assist another in an act of plagiarism or any
other form of academic dishonesty may also be subject to disciplinary action.
Plagiarism is a particular type of academic dishonesty that involves taking the words, phrases or ideas of another person and presenting them as one's own. This can include using whole papers and paragraphs or even sentences or phrases. Plagiarized work may also involve statistics, lab
assignments, art work, graphics, photographs, computer programs and other materials. The sources of plagiarized materials include but are not limited to books, magazines, encyclopedias or journals; electronic retrieval sources such as materials on the Internet; other individuals; or paper writing services.
A student may be judged guilty of plagiarism if the student:
(a) Submits as one's own an assignment produced by another, in whole or in part.
(b) Submits the exact words of another, paraphrases the words of another or presents statistics, lab assignments, art work, graphics, photographs, computer programs and other materials without attributing the work to the source, suggesting that this work is the student's own.
Allegations of student plagiarism and academic dishonesty will be dealt with by the appropriate academic department personnel. It is the policy of Nassau Community College that, at the discretion of the faculty member, serious acts will be reported in writing to the Office of the Dean of Students, where such records will be kept for a period of five years beyond the student's last semester of attendance at the College. These records will remain internal to the College and will not be used in any evaluation made for an outside individual or agency unless there is a disciplinary
action determined by a formal ruling under the Student Code of Conduct, in which case only those records pertaining to the disciplinary action may apply. A student whose alleged action is reported to the Office of the Dean of Students will be notified by that office and will have the right
to submit a letter of denial or explanation. The Dean will use his/her discretion in determining whether the alleged violation(s) could warrant disciplinary action under the Student Code of Conduct. In that case the procedures governing the Code of Conduct will be initiated.
· Copyright statement: The Higher Education Opportunity Act of 2008 (HEOA) requires the College to address unauthorized distribution of copyrighted materials, including unauthorized peer-to-peer file sharing. Thus, the College strictly prohibits the users of its networks from engaging in unauthorized distribution of copyrighted materials, including unauthorized peer-to-peer file sharing. Anyone who engages in such illegal file sharing is violating the United States Copyright law, and may be subject to criminal and civil penalties. Under federal law, a person found to have infringed upon a copyrighted work may be liable for actual damages and lost profits attributable to the infringement, and statutory damages of up to $150,000. The copyright owner also has the right to permanently enjoin an infringer from further infringing activities, and the infringing copies and equipment used in the infringement can be impounded and destroyed. If a copyright owner elected to bring a civil lawsuit against the copyright infringer and ultimately prevailed in the claim, the infringer may also become liable to the copyright owner for their attorney's fees and court costs. Finally, criminal penalties may be assessed against the infringer and could include jail time, depending upon the severity of the violation. Students should be aware that unauthorized or illegal use of College computers (such as engaging in illegal file sharing and distribution of copyrighted materials), is an infraction of the Student Code of Conduct and may subject them to disciplinary measures. To explore legal alternatives to unauthorized downloading, please consult the following website: http://www.educause.edu/legalcontent.
· Course Resources
· Web sites ______
· Library services ______
· Labs and learning centers: MATH CENTER REQUIREMENT
If needed, students are encouraged to avail themselves of further study and/or educational assistance available in the Mathematics Center located in B-l30. These activities and use of the resources provided are designed to help the student master necessary knowledge and skills.
· Study groups ______
· Extra help options ______
Assessments and Grading Methods
· Provide a clear explanation of evaluation, including a clear statement on the assessment process and measurements. Be explicit! Include format, number, weight for quizzes and exam, descriptions of papers and projects as well as how they will be assessed and the overall grading scale and standards.
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Americans with Disabilities Statement & Non-Discrimination Statement (NCC Required)
· "If you have a physical, psychological, medical, or learning disability that mayhave an impact on your ability to carry out the assigned coursework, I urge you tocontact the staff at the Center for Students with Disabilities (CSD), Building U,(516)572-7241, TTY (516)572-7617. The counselors at CSD will review your concerns and determine to what reasonable accommodations you are entitled as covered by the Americans with Disabilities Act and section 504 of the Rehabilitation Act of 1973. All information and documentation pertaining to personal disabilities will be kept confidential.”
Course Schedule and Important Dates
Class Number / Date / Topic1/2/3 / Orientation/Chapter 7: Integration
4/5/6 / Chapter 7: Integration
7/8/9 / Chapter 7: Integration
10/11/12 / Chapter 7: Integration
13/14/15 / Chapter 7: Integration / Test #1 on Chapter 7
16/17/18 / Chapter 8: Using the Definite Integral
19/20/21 / Chapter 8: Using the Definite Integral
22/23/24 / Chapter 8: Using the Definite Integral / Test #2 on Chapter 8
25/26/27 / Chapter 9: Sequences & Series
28/29/30 / Chapter 9: Sequences & Series
31/32/33 / Chapter10: Taylor Series
34/35/36 / Chapter10: Taylor Series
37/38/39 / Test #3 on Chapters 9 & 10 / Chapter 11: Differential Equations
40/41/42 / Chapter 11: Differential Equations
43/44/45 / Chapter 11: Differential Equations / Cumulative Final Exam
EXAMS
A minimum of two full-length (i.e. approximately 75 minute) examinations must be administered, as well as a cumulative final examination. Due to the depth and volume of material presented in this course, at least 115 minutes of class time should be allocated to the administration of this final examination. Multiple choice exams are strongly discouraged.