NASSAU COMMUNITY COLLEGEDEPARTMENT 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

MAT 123Calculus II

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 OUTLINETOPICS

IntegrationThe 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 integralThe 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 seriesIntroduction 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 seriesFunctions 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 equationsThis 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 SectionsIntegration 7 1, 2, 3, 4, 5, 6, 7Using the definite integral 8 1, 2, 4, 5, 6, 7*, 8*Sequences and series 9 1, 2, 3, 4, 5Approximating 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.

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 OutcomeMapping

1.1 Mathematical InterpretationSUNY General Education Learning Goals: 5.1. Demonstrate

Interpret variables, parameters, and other specific information withinability to interpret/draw references.

a mathematical model .

1.2 Draw InferencesSUNY General Education Learning Goals: 5.1. Demonstrate

Draw inferences about the situation being modeled mathematically.ability to interpret/draw references.

1.3 Verbal InterpretationSUNY General Education Learning Goals: 5.1. Demonstrate

Verbally interpret the results of their analysis of the mathematicalability to interpret/draw references.

model.

2. Represent Mathematical Information

Students will demonstrate the ability to represent mathematical information symbolically, visually, numerically and verbally.

Learning OutcomeMapping

2.1 Mathematical InformationSUNY General Education Learning Goals: 5.2. Demonstrate

Employ the appropriate representation to display the mathematicalability to represent mathematical info.

information.

2.2 Mathematical TerminologySUNY General Education Learning Goals: 5.2. Demonstrate

Clearly define variables; draw, scale and label graphs; use correctability 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 OutcomeMapping

3.1 Identify Quantitative MethodsSUNY 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 MethodsSUNY 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 OutcomeMapping

4.1 EstimationSUNY General Education Learning Goals: 5.4. Demonstrate

Estimate and justify a mathematical result to a problem.ability to estim & check math results

4.2 ReasonablenessSUNY General Education Learning Goals: 5.4. Demonstrate

Articulate a justification for the estimate using a clearly definedability 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 OutcomeMapping

5.1 Real Life ComparisonSUNY General Education Learning Goals: 5.5. Demonstrate

Describe how the results of the mathematical model may differ fromability to recognize limits

the real life situation it is modeling.

5.2 Mathematical AssumptionsSUNY General Education Learning Goals: 5.5. Demonstrate

Articulate the assumptions made in developing aability 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 PoliciesInstructors 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)

____________________________________________________________ Exams/quizzes ____________________________________________________________ Attendance/lateness policy

____________________________________________________________ Missed exams/ quizzes policy

____________________________________________________________ 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 anotherstudent 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 anyother 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, labassignments, 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 disciplinaryaction 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 rightto 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. ________________________________________________________________________________

________________________________________________________________________________

Americans with Disabilities Statement & Non-Discrimination Statement (NCC Required) "If you have a physical, psychological, medical, or learning disability that may have an impact on

your ability to carry out the assigned coursework, I urge you to contact 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 Numbe

r Date Topic1/2/3 Orientation/Chapter 7: Integration4/5/6 Chapter 7: Integration7/8/9 Chapter 7: Integration

10/11/12 Chapter 7: Integration13/14/1

5 Chapter 7: Integration / Test #1 on Chapter 716/17/1

8 Chapter 8: Using the Definite Integral19/20/2

1 Chapter 8: Using the Definite Integral22/23/2

4 Chapter 8: Using the Definite Integral / Test #2 on Chapter 825/26/2

7 Chapter 9: Sequences & Series28/29/3

0 Chapter 9: Sequences & Series31/32/3

3 Chapter10: Taylor Series34/35/3

6 Chapter10: Taylor Series37/38/3

9 Test #3 on Chapters 9 & 10 / Chapter 11: Differential Equations40/41/4

2 Chapter 11: Differential Equations43/44/4

5 Chapter 11: Differential Equations / Cumulative Final Exam

EXAMSA 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. Examinations are to be constructed using word processing applications (such as Microsoft Word) and software designed to render mathematical notation (such as MathType) and graphs (such as GraphingAdvantage, Maple, or Web Works). Hand-written exams and those that are physically cut and pasted are strongly discouraged.

Math 123 Faculty Only!Sample Final Exam Questions

The questions below have been culled from previous final examinations. They are not meant to be all inclusive nor exclusive. Rather, they represent a minimum knowledge level for final examination questions. The questions may not have had the same point counts.

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10. A pyramid has a height of 100 ft. and a square base 200 ft. on a side. It is made of stone whose density

is lb/ft3. Set up the integral to find the total work done in building the pyramid. You need not solve the integral.

11. The region bounded by the graphs of is rotated about the line whose equation is y = 3. Set up the integral necessary to compute the volume of the resulting solid. You need not solve the integral.

12. The territory of an ant colony can be roughly approximated by a circle of radius 100 inches. Moving

away from the center, the population density is given by ants per square inch. Set up the integral necessary to find the total population of the colony. You need not solve the integral.

13. A right conical container (with its apex downward) is 10 feet high and has a radius is 2 feet. It is buried 6 feet below the ground. It is half-full of liquid whose density is 15 lbs/ft3. Set up the integral necessary to find the work done to pump the water into a second tank located 3 feet above the ground. You need not solve the integral.

14. A 20 lb weight that is attached to a 15 ft chain with weight density is 3 lb/ft is hanging over the roof of a building. How much work is done lifting the system to the roof?

15. Consider the fish tank shown below.

If the tank is full, and if the water in the tank has a weight density of 62.4 lb/ft3, find the hydrostatic force on the front pane of the tank.

16. Suppose Find u. You need not find u explicitly.

17. Solve the differential equation given that 18. Test each of the following series for convergence. Be sure to state the test you used and the decision

you have come to.

127

5

a. b. c. d. e.

19. Find the radius of convergence for each of the following power series.

a. b. c. d.

20. a. Find a series for b. Find the interval of convergence for the series in part (a).

21. a. Find a series for b. Find the interval of convergence for the series in part (a).

22. a. Find the 2nd degree Taylor polynomial for centered at

b. Use the Taylor polynomial found in part (a) to approximate .

23. a. Construct a Taylor series for b. Find the interval of convergence for the series found in part (a).

c. Use the series found in part (a) to find 24. A calculus student was working on a calculus problem and got for her answer. The problem asked

the student to give her answer to 4 decimal places. Unfortunately, she forgot her calculator. However, she did remember that there is a Taylor series for

She then used the first 4 terms of this series to approximate her answer by letting x = 2 and substituting as follows:

Use a few sentences to explain why her logic is or is not correct.

25. a. A bank account earns 7% annual interest compounded continuously. Suppose you wish to withdraw $48,000 a year for 15 years beginning at age 62, and still have $100,000 left at the end of that time to give to your spouse. What should your initial balance be when you retire at age 62 to meet this goal?

b. What is the annual continuous cash flow contribution (compounded continuously at 10% per year) over 40 years to achieve a balance of $500,000?

26. Suppose an adult male needs 20 calories per pound of body weight per day to maintain his weight. If more or fewer calories are consumed, his weight changes at a rate proportional to the difference between the number of calories consumed and the number need to maintain body weight. The constant

of proportionality is pounds per calorie. Assume the person had a constant caloric intake of I calories per day. Let W(t) be the person’s weight in pounds at time t, measured in days.

a. Write the differential equation that you can use to find W(t). b. Solve the equation in part (a). c. If the person began the diet weighing 160 pounds and consumed 3000 calories per day, and all

else remained the same, what weight could the dieter hope to attain?

27. An apple pie whose temperature is 200°F is removed from a 350°F oven at 1:00 pm and placed on the kitchen table where the air temperature is a constant 70°F. I love warm apple pie with ice cream, but if the pie is warmer than 150°F, I will burn my mouth. After thirty minutes, the temperature of the pie was 185°F. When is the earliest I will be able to enjoy the treat?

28. Test each entity that follows for convergence:

a. The sequence b. The sequence

c. The series d. The series e.

29. Upon graduation from college, you have been offered two positions. The table below shows the salary offer proposed by each company. If the prevailing interest rate is 5% compounded continuously, and all other things are equal, which offer would you accept? You must support your answer with appropriate mathematical concepts.

Signing bonus Year 1 Year 2 Year 3

Company A 10,000 40,000 45,000 50,000

Company B 2,000 45,000 47,000 53,000

30. Suppose we invest $500 per month (on a continuous basis), for 10 years, in an account which pays 5% annual interest rate compounded continuously.

a. Determine the present and future values of this investment.b. What is the mathematical relationship between the present and future values?

c. How long will it take, in years and months, for the balance to reach $50,000?

31. When I was hired at the College, my desk was clean, but papers accumulate on my desk at the rate of 2g./ft.2 per week. I manage to remove 80% of the papers per week. I have been at the college for 43 years. Find the condition of the papers on my desk.

32.. Match each of the following slope fields with its differential equation. a. b. c.

d. e.