College of Dupage Math 2232-002: Calculus and Analytic Geometry

I have this page of the syllabus and understand these are the course policies.

_________________________ (Signature)

College of Dupage

Math 2232-002: Calculus and Analytic Geometry II

Contact Information:

Dr. Matt Wechter

Office: BIC 3530A

Email: [email protected]du

Phone: (630) 942-4405

Course Objectives and Topic Outline:

Course description to appear in catalog: Applications of the definite integral, techniques of integration,

indeterminate forms, improper integrals, sequences and series, Taylor and Maclaurin expansions, power

series, conics, parametric equations, and polar coordinates.

Credit Hours: 5 Lecture Hours: 5 Lab Hours: 0

Prerequisite: MATH 2231 Calculus and Analytic Geometry I with a grade of "C" or better, or

equivalent

A. General Course Objectives:

Upon successful completion of the course the student should be able to do the following:

1. Use definite integrals to determine the area enclosed by graphs

2. Use the disc, shell, and slicing methods to determine volumes of solids

3. Use definite integrals to determine arc length and the surface area of a solid of revolution

4. Use definite integrals to perform work and fluid force calculations

5. Evaluate integrals using the following methods: integration by parts, partial fractions, and trigo-

nometric substitution

6. Determine integrals involving powers of trigonometric functions

7. Estimate a definite integral using the trapezoidal rule and Simpson's rule

8. Define hyperbolic functions

9. Graph hyperbolic functions

10. Verify identities involving hyperbolic functions

11. Differentiate functions involving hyperbolic functions

12. Integrate functions involving hyperbolic functions

13. Differentiate functions involving inverse hyperbolic functions

14. Determine the convergence or divergence of improper integrals and evaluate a convergent inte-

gral

15. Demonstrate the ability to write the terms of a sequence and an expression for the nth term of a

sequence

16. Demonstrate the ability to determine if a given geometric or telescoping series converges or di-

verges, and find its sum if it converges

17. Demonstrate the ability to determine whether a given sequence is monotonic and/or bounded

18. List the terms of the sequence of partial sums of a series

19. Apply the nth term test for divergence of a series

20. Demonstrate the ability to determine whether a p-series converges or diverges

21. Estimate the sum of a series of positive constants and estimate the error bound

I have this page of the syllabus and understand these are the course policies.

_________________________ (Signature)

22. Demonstrate the ability to determine the convergence or divergence of a series of constants us-

ing the following: integral test, comparison test, limit comparison test, alternating series test,

ratio test, and root test

23. Demonstrate the ability to determine if a series of constants is absolutely convergent, condition-

ally convergent, or divergent

24. Estimate the sum of an alternating series and approximate the error bound

25. Develop a Taylor or Maclaurin polynomial of given degree for a given function

26. Use Taylor or Maclaurin polynomials to approximate a given function and estimate the error

bound

27. Locate the interval of convergence of a power series and check for convergence at the endpoints

of the interval

28. Differentiate and integrate a power series and find the intervals of convergence for the new

power series obtained

29. Develop a power series to represent a function and determine its interval of convergence

30. Use a truncated power series to approximate functions and integrals

31. Demonstrate the ability to graph and analyze parabolas, ellipses, and hyperbolas

32. Demonstrate the ability to rotate the coordinate axes

33. Demonstrate the ability to sketch a curve represented by parametric equations and to write the

corresponding rectangular equation

34. Demonstrate the ability to find a set of parametric equations given the rectangular equation

35. Demonstrate the ability to find dy/dx and d

y/dx

given parametric equations

36. Demonstrate the ability to find the area of a surface generated by the rotation of a plane curve

37. Demonstrate the ability to find the area of a region enclosed by, and the arc length of, a plane

curve given in parametric form

38. Demonstrate the ability to plot points in polar coordinates and convert between polar and rec-

tangular coordinates

39. Convert rectangular equations to polar and vice-versa

40. Demonstrate the ability to graph polar equations and their tangents

41. Demonstrate the ability to find the area of a polar region and the arc length of a polar curve

42. Demonstrate the ability to find points of intersections of polar graphs

43. Demonstrate the ability to find the area of a surface of revolution of a polar curve

44. Demonstrate the ability to find polar equations of the conic sections

Topical Outline:

1) Applications of the definite integral

a) Areas between curves

b) Volumes

i) Disc method

ii) Shell method

iii) Slicing

c) Work done by a moving force

d) Fluid pressure on a vertical submerged surface

e) Arc length

f) Surface area of revolution

I have this page of the syllabus and understand these are the course policies.

_________________________ (Signature)

g) Simpson's rule and the trapezoid rule

h) Moments and centers of mass (optional)

2) Integration techniques

a) Integration by parts

b) Trigonometric integrals

c) Trigonometric substitution

d) Partial fractions

e) Rational functions of sines and cosines

f) Tables (optional, but note cards, textbooks, tables of formulas and integrals, etc. will not be

permitted on tests given in the classroom for Mathematics 2232)

3) Improper integrals

4) Sequences and series

a) Sequences

b) Taylor polynomials

c) Series of positive terms

i) Direct comparison test

ii) Limit comparison test

iii) Integral test

d) Alternating series test

e) Ratio test

f) Root test

g) Power series

i) Maclaurin and Taylor series

ii) Binomial series

iii) Geometric series

iv) Series created by substitution

v) Differentiation and integration of power series

5) Conic sections

a) Parabolas, ellipses, and hyperbolas

b) Rotation of axes

c) Tangent and normal lines

6) Polar coordinates and parametric equations

a) Parametric equations

i) Smooth curves

ii) Derivatives

iii) Arc lengths

iv) Areas

v) Graphs

vi) Parametrization from graphs

b) Polar equations

i) Graphs

ii) Equations from graphs

iii) Conics

iv) Slope of tangent lines

v) The angle psi

vi) Area and arc length

I have this page of the syllabus and understand these are the course policies.

_________________________ (Signature)

7) Hyperbolic functions

a) Definitions and graphs

b) Derivatives and integrals

c) Inverse hyperbolic functions and their functions

Course Materials:

• Thomas' Calculus: Early Transcendentals, 14th Ed. by Hass, Heil, Weir (ISBN

9780134768496)

This textbook may come bundled with a MyMathLab access code. This code is not required

(see next item).

Classtime:

Students are expected to attend class and PARTICIPATE. Students are responsible for all material

covered in each class, even if they missed that day. Quizzes and exams will be held during class time.

While in class, students should be respectful of other students as well as the instructor. All

students are welcome to share their thoughts and the classroom will be an inclusive space.

Students should not distract others with their computers or cell phones. Any distractible cell

phone use should be done outside the classroom. All communication between instructor and students

will be conducted either through Blackboard or via a COD email account. Make sure you check your

COD email regularly.

Homework:

Homework will be assigned for every lecture from the textbook. Students need to spend time and

attempt every assigned homework problem to master the material and be prepared for quizzes and

exams.

Solution guides and online step-by-step solutions should not be overused when doing homework.

Students who rely on these resources are not self-sufficient and will underperform on exams. When

stuck on a problem, take the time to read class notes and the textbook for related examples. Set aside

time for contacting the instructor or the Math Assistance Area for help.

On the last day of the semester, every student should bring in all their completed homework. The

instructor will choose one section of homework that each student will turn in. Evidence of completion

of this homework (with work shown) will earn the student homework credit for the semester.

Quizzes:

Quizzes will be taken during class time according to the course calendar.

Formula sheets are not allowed on any quiz. Quizzes will usually cover a few sections in-depth.

The material covered on a quiz will be announced beforehand.

I have this page of the syllabus and understand these are the course policies.

_________________________ (Signature)

Work must be shown for credit to be awarded for quiz questions. Questions must be answered

according to the quiz or question instructions to receive full credit.

Every student may have one 24-hour extension on a quiz. The quiz will then be placed in the

COD Testing Center and the student must complete the quiz there (on their own time).

The lowest quiz grade will be dropped before calculation of the final grade.

Exams:

There will be three (3) unit exams. Every exam will be comprehensive and questions might cover any

material from earlier in the semester. See the calendar at the end of the syllabus for the weeks that the

exams and quizzes will be given.

No cell phones or computers will be allowed at all at a student's desk during the exam.

Calculators will NOT be allowed. If a student cannot complete the problems asked without a calculator

or referring to the textbook, then they should do the best they can while maintaining their academic

honesty. Decimal approximations of numerical solutions on exams are not expected and will be

penalized.

Exams will be graded not only on the correct answer, but correct work. Correct final answers

without the appropriate work that leads to that answer will receive little or no credit. If a prompt asks

for a problem to be completed using a certain method or formula, then using a different method of

formula will not receive full credit.

Any submitted work that is not clearly visible or legible will be graded as if it was not

completed.

Attendance Policy:

There is a constant stream of new material, homework, and other assessments in this course. Students

should be working every day to master the material and complete the assigned work. Taking an

occasional day off each week is recommended to not become over-stressed, but doing no work for

more than a day will usually cause students to fall behind and never catch up.

Exams CANNOT be made up after their due date under any circumstances except as an

accommodation required by the Center for Access and Accommodations. Quizzes cannot be made up

after their due date unless an extension request is made in a timely manner.

Grade Calculation:

Graded Assessment

Percentage of Final Grade

Homework (1 section, turned in on the last day)

Quizzes (lowest quiz is dropped)

23%

Three Unit Exams

25% Each

Letter Grade

Percentage

90% and Up

80% - 89%

70% - 79%

60% - 69%

Below 60%

I have this page of the syllabus and understand these are the course policies.

_________________________ (Signature)

Written Style:

Student should practice and use good style when answering problems to receive any partial credit. If a

student writes down a correct answer without sufficient work, they will receive no credit and may have

to defend the academic integrity of their submission.

Any answer which requires an explanation should be written in complete sentences, all

mathematical notation should be consistent and make sense, and anybody reading the solutions for the

first time (namely, the grader) should have no confusion as to both the final answer and the work

involved to get there. For example, “1 + 1 =2” is a complete sentence. It has a subject (1+1), a verb

(=) and an object (2). Sloppy writing gets no credit. Professors are not mind-readers; Only the written

work matters.

Academic Integrity:

Students should be aware of the Code of Academic Conduct and know the consequences should the

code be violated. The document can be found at

Code of Academic Conduct

If a student is caught violating the Code they will receive grade penalty and will be reported through

COD's academic integrity reporting system.

Student academic dishonesty includes but is not limited to:

· Dishonest use of course materials, such as student papers, examinations, reports and ma-

terial posted on the Internet.

· Knowingly posting course materials of any kind on Internet sites such as (but not limited

to) Course Hero and Chegg without the consent of the instructor.

· Knowingly assisting others in the dishonest use of course materials such as student pa-

pers, examinations and reports.

· Knowingly providing course materials such as papers, lab data, reports and/or electronic

files to be used by another student as that student’s own work.

· Plagiarizing, i.e., using language or ideas from materials without acknowledgement

and/or copying work from other sources and submitting it as one’s own.

· Examples of plagiarism include but are not limited to:

§ Copying a phrase, a sentence, or a longer passage from a source (including an Internet

source) and submitting it as one’s own.

I have this page of the syllabus and understand these are the course policies.

_________________________ (Signature)

§ Summarizing or paraphrasing someone else’s ideas without acknowledging the source.

§ Submitting group assignments individually as one’s own independent work.

§ Copying or taking pictures of course materials such as videos, exams, quizzes or assign-

ments and posting the copied items and/or pictures on the Internet or sharing these

copied items and/or pictures with other students who have not yet completed the as-

signments.

§ Taking pictures or copying course materials that are considered confidential by the in-

structor such as exams or quizzes.

If an exam is being proctored, students should comply with the proctor’s instructions. If a

proctor accuses a student of violating the Code of Academic Conduct or not conforming to the

assessment’s instructions, and the student does not agree with the accusation, the student should

provide countervailing written or video evidence to support their case.

Covid-19 Information and Exposure Reporting

Students should adhere to COD’s Covid-19 safety protocols throughout the semester if visiting campus.

All relevant policies regarding masking, vaccinations, reporting can be found on the COD website at

https://www.cod.edu/coronavirus/index.aspx

If you have been exposed to Covid-19 or have been diagnosed with Covid-19, please fill out the

Student Self-Reporting form at

https://cm.maxient.com/reportingform.php?CollegeofDuPage&layout_id=9

Covid Vaccination or Testing Requirement

College of Dupage follows the statewide mandate for students, faculty, and staff to show a proof of

vaccination or a weekly negative COVID test result.

If you are vaccinated, you must submit your vaccination card using the steps located here:

https://cod.edu/coronavirus/vaccine-verification.aspx

If you are not vaccinated, you must follow the testing requirements located here:

https://cod.edu/coronavirus/covid-testing.aspx

If you have followed the instructions above and receive an email from me and/or the college

indicating that you are NOT CLEARED to attend class, please contact the Dean of Student Affairs

[email protected] immediately. If you are not cleared to come to class, the college may

automatically drop you from the course.

I have this page of the syllabus and understand these are the course policies.

_________________________ (Signature)

Center for Access and Accommodations:

The College of DuPage is committed to the equitable access of educational opportunities for students

with disabilities in accordance with The Americans with Disabilities Act, As Amended and Section 504

of the Rehabilitation Act of 1973. Any student who feels they may need an accommodation on the basis

of an illness, injury, medical condition, or disability should contact the Center for Access and

Accommodations to determine eligibility for accommodations and to obtain an official Letter of

Accommodation. The Center for Access and Accommodations can be reached via email at

[email protected]. Students may also initiate a request for services by going to www.cod.edu/access and

clicking on the green box labeled “complete form to request accommodations.” If you are already

registered with the Center for Access and Accommodations, please email me your Letter of

Accommodation as soon as possible. Please DO NOT send any private health documentation or

Doctor’s notes to the course instructor.

Withdrawal Policy:

The final day for a student to withdraw from any course will be equal to 75% of the time for the

respective academic session (see the Registration Calendar) through myACCESS

https://myaccess.cod.edu or in person at the Registration office, Student Services Center (SSC), Room

2221.

After the deadline, students will be required to appeal for late withdrawal and provide

appropriate documentation to the Student Registration Services Office for all requests. Students who

are granted approval to withdraw by petition will not be eligible for refunds of tuition or fees and will

receive a 'W' grade on their transcript. Appeals must be submitted prior to the designated final exam

period for 16-week classes and before the last class meeting for all other session classes

Course Schedule:

Semester Week (Monday)

New Material Available

Assignments Due

I have this page of the syllabus and understand these are the course policies.

_________________________ (Signature)

Week 1 (June 13, 2022)

Calculus I review, hyperbolic

functions, area between curves,

volume of solids of revolution,

disc and washer method

Quiz 1 (Thursday): Calculus I

Review, 7.3, 5.6

Week 2 (June 20)

Arc length, surface area of

volumes of revolution, work

and fluid pressure, basic

integration rules

Quiz 2 (Thursday): 6.1-6.4

Week 3 (June 27)

Integration by parts,

trigonometric integrals,

trigonometric substitution

Exam 1 (Wednesday): 5.6, 7.3,

Chapter 6, 8.1

Week 4 (Tuesday, July 5)

No classes on Monday, July 4

Partial fractions, numerical

integration method, improper

integral, sequences

Quiz 3 (Wednesday): 8.1-8.4

Week 5 (July 11)

Series, integral test, p-series,

comparison tests, alternating

series, ratio and root tests

Quiz 4 (Tuesday): 8.5, 8.7-8.8,

10.1

Week 6 (July 18)

Last Day to Withdraw is

Sunday, July 24

Power series, Taylor and

Maclaurin series, convergence

of power series, applications of

Taylor series

Exam 2 (Tuesday): Chapter 8,

10.1

Week 7 (July 25)

Parametric equations, calculus

of parametric equations, polar

coordinates, graphing with

polar coordinates

Quiz 5 (Thursday): 10.2-10.6

Week 8 (August 1)

Polar area and arc length, polar

conics, rotation of axes

Exam 3 (Tuesday): Chapter 10

Quiz 6 (Thursday): 11.1-11.7,

Rotation of Axes

One homework section chosen

at random (Thursday)