MATH 110 - Techniques of Calculus I

Penn State University Spring Semester 2017

Dr. James Hager (Coordinator)

Office: 211 McAllister Building

Phone: (814) 441-4550

eMail: jah14@psu.edu

Office Hours: T: 1:00-3:00, Th: 1:00-3:00 and By Appointment

Course Description TECHNIQUES OF CALCULUS I (4) Functions, graphs, derivatives, integrals, techniques of differentiation and integration, exponentials, improper integrals, applications. Students may take only one course for credit from MATH 110, 140, 140A, and 140B. Prerequisite: MATH 022 or satisfactory performance on the mathematics proficiency examination.

Course Coverage The goal for the course is to cover the chapters/sections detailed in the tentative class schedule below. Chapter 1 is considered review material for the students. Each student should confirm that they understand the material in Chapter 1 during the first week of the course.

Course Materials

1. Textbook:

One of the following textbook options:

a) Bundle: Applied Calculus for the Managerial, Life, and Social Sciences, 9th + Enhanced WebAssign, 1 term (6 months) Printed Access Card for Calculus, Physics, Chemistry, Single-Term Courses, Author: Tan, ISBN-10: 1-305-61888-2, ISBN-13: 978-1-305-61888-6 (about $141)

or (but not both) b) Enhanced WebAssign Instant Access for Applied Math, Single-Term Courses, 1st Edition, AUTHORS: WebAssign , ISBN-10: 1-285-85761-5, ISBN-13: 978-1-285-85761-9 (about $82)

A link for these textbook options is provided under your Angel Lessons tab.

It is important that you choose one of these options, since these choices come bundled with the WebAssign technologies. Purchasing a used textbook, renting a textbook, or purchasing a different edition/version of the textbook will not allow access to the required WebAssign technologies.

As part of your overall course grade, you will use WebAssign to regularly complete weekly-required homework assignments. Your overall WebAssign scores will be uploaded to your ANGEL grade-books on a regular basis. Although you will be assigned significantly more than three hundred (300) WebAssign problems throughout the semester, your overall WebAssign score will be normalized to a maximum of 70. However, it is important that you complete all your WebAssign assignments if you wish to attain this maximum score. It is important that you begin the WebAssign assignments early, and complete them by the due date – since students are given more than a week to complete the assignments, extensions to the due dates are rarely given.

Note: The WebAssign materials include: 1) a significant number of required homework/exercise problems from the chapters covered during the lectures, 2) instructional videos, 3) practice exam problems, and 4) step-by-step tutorials.

Access to these materials is granted by the license/key included in your textbook/eBook, or emailed directly to you if you purchase your textbook at

the link provided under your Angel accounts and below. It is important that you do not delete this important information from your email accounts (check Spam!) – it contains the alphanumeric key necessary to register your book, and gain access to the WebAssign materials. Note: There is no classroom/course key.

Further instructions for connecting to the unique PSU WebAssign server will be provided in a separate email, and discussed during the first week of classes. A helpful link containing information on using WebAssign is provided under your Angel Lessons tab. It is important that you read these materials before starting your first WebAssign assignment.

2. Clickers (Required):

An i>clicker is REQUIRED for the course. Valid models are the i>clicker, i>clicker+, and i>clicker 2. You may purchase yours from the bookstore, Amazon, the iclicker.com website, or some other retailer/reseller. Obtaining a used i>clicker is fine, but you may not share your i>clicker with another student.

Once you have obtained an i>clicker, you must REGISTER it with Angel. If you are using your clicker in another course that requires Canvas, you will need to register with both Canvas and Angel.

A link is provided in ANGEL to help with this process. If you do not register your clicker, your answers and participation will never be properly associated with the correct username.

In order to use your clicker in class, you must Hold down the power button until the light is blinking. Then, type in the classroom frequency code provided by your instructor. The light should flash green to indicate that you have connected. If the light does not flash green, you may need to replace the batteries.

If you have the original i>clicker, or if you are using your clicker in another class, you will need to reconnect at the beginning of EVERY CLASS. However, if you are using an i>clicker+ or an i>clicker 2, it will recall the last frequency code that was used.

Clicker totals will be updated frequently and posted to your Angel grade books. It is your responsibility to review your scores frequently to verify their accuracy, and discuss any issues with your instructors early.

Participation in classroom clicker-based exercises is an important part of your understanding of the Math 110 curriculum, and preparation for the midterm exams. One (1) clicker point will be awarded for each day that you successfully respond to all clicker exercises presented in class. The maximum number of clicker points you can earn is 30, however, there will be more than 30 opportunities to earn clicker points. Offering more than 30 chances to earn clicker points will allow you to miss a couple of classes without the need to coordinate these absences. We will not be offering any makeups for missed clicker points except under longer-term extreme circumstances that have been fully documented, and coordinated with your instructor. Since there are no accommodations for missed points due to user operator-error, be sure to follow the directions on correct usage of your clickers discussed during the first week of classes.

Exams

Two evening examinations (midterms) will be given. The dates and times of these exams will be as follows:

Examination 1: Wednesday, February 22, 2017, 7:45 – 9:00 pm Examination 2: Monday, April 3, 2017, 7:45 – 9:00 pm

Information on the locations and content of these exams will be distributed at a future date.

Conflict/Makeup Exams

In addition to the regularly scheduled exam, the math department schedules two additional options: a conflict exam for each of the midterms from 6:30 - 7:45 on the same night as the regularly scheduled exam and a makeup exam scheduled on an evening different from the regularly scheduled exam night. Students who attend the conflict exam will not be permitted to leave before

7:45. Sign-up sheets for both the conflict exam and the makeup exam will be distributed by your instructor during class. If you need to schedule the conflict exam, you must sign up at least one full week ahead of the scheduled exam date. A valid conflict/makeup reason is required to sign up for either of these exams.

NOTE: If you miss an exam without an official excuse (such as illness or official university business), then you may be allowed to take a makeup exam, but with an automatic 25% deduction from the grade. To avoid this deduction, you must notify your lecturer, with your official excuse, before the date and time of the exam. This notification may be performed in person, via e-mail, or by telephone.

Final Exam

The final examination in the course will be comprehensive. It will be given during the university's final examination week, May 1 - 5, 2017. Do not make plans to leave the university before the end of this week. Travel plans do not constitute an official university excuse for missing an examination or for obtaining a conflict or makeup examination. Conflicts for the final exam are determined by scheduling - any student with a potential final exam conflict situation should apply online before the final exam conflict application period expires. The math department does not offer a makeup exam option for the final exam.

Practice Exams and WebAssign Practice Exam Problems Models of previous Math 110 exams are included in a folder under the Lessons tab in your Math 110 Angel website. Additionally, practice exam questions will be bundled as specific WebAssign assignments to be completed but not submitted in preparation for the exams. The practice WebAssign exam problems are an integral part of your exam preparation – there is a strong correlation between effort on these problem sets, and overall exam performance.

Care should be taken in the usage of these models during the preparation for each exam, i.e., students should understand that the exams for this semester are not based strictly on the practice exams. Good study/preparation habits include the review of lecture notes, completion of assigned homework problems, review of clicker exercises, and where appropriate, attendance at

Guided Study Group weekly work sessions. Your lecturer will provide specific guidance prior to each exam on the specific topics included/excluded. Suggested Homework

A list of suggested homework problems from the back of each section of your online textbook appears at the end of this syllabus. These homework problems will not be turned in for a grade. The purpose of doing the homework is to better understand the material discussed in the lectures, and to prepare oneself for the WebAssign problems and exams. Since much of this material builds upon previous material, you are encouraged to complete many of the suggested homework and keep up with the suggested homework, even though it will not be collected.

Piazza Collaboration Board

A link is provided under the Lessons tab of your Angel site for a Math 110 collaboration board. The collaboration board provides a framework for you to post and respond to questions about any Math 110 content, including homework, WebAssign problems, classroom examples, practice exams, and course logistics. Periodically, your instructors will use the site to post classroom materials, make announcements, and respond to student questions. You should make a habit of visiting the collaboration board frequently to monitor and participate in the discussions. Your lecturer will discuss the Piazza board in more detail during the first week of classes.

Academic Integrity Academic integrity is the pursuit of scholarly activity in an open, honest and responsible manner. Academic integrity is a basic guiding principle for all academic activity at The Pennsylvania State University, and all members of the University community are expected to act in accordance with this principle. Consistent with this expectation, the University's Code of Conduct states that all students should act with personal integrity, respect other students' dignity, rights and property, and help create and maintain an environment in which all can succeed through the fruits of their efforts.

Academic integrity includes a commitment not to engage in or tolerate acts of falsification, misrepresentation or deception. Such acts of dishonesty

violate the fundamental ethical principles of the University community and compromise the worth of work completed by others.

Based on the University's Faculty Senate Policy 49-20, a range of academic sanctions may be taken against a student who engages in academic dishonesty. Please see the Eberly College of Science Academic Integrity homepage for additional information and procedures.

Disability Services

Penn State welcomes students with disabilities into the University's educational programs. Every Penn State campus has an office for students with disabilities. The Office for Disability Services (ODS) Web site provides contact information for every Penn State campus: http://equity.psu.edu/ods/dcl. For further information, please visit the Office for Disability Services Web site: http://equity.psu.edu/ods. In order to receive consideration for reasonable accommodations, you must contact the appropriate disability services office at the campus where you are officially enrolled, participate in an intake interview, and provide documentation: http://equity.psu.edu/ods/doc-guidelines. If the documentation supports your request for reasonable accommodations, your campus’s disability services office will provide you with an accommodation letter. Please share this letter with your instructors and discuss the accommodations with them as early in your courses as possible. You must follow this process for every semester that you request accommodations.

Grading

Your course grade will be determined by your exam scores, your WebAssign score, and your clicker score. Total possible points follow:

Examination I 100 Examination II 100 WebAssign 70 Clicker 30

Final Examination 150 Total 450

The exact point requirements for each letter grade will be decided at the end of the course. General University guidelines follow:

Grade %-Score Points A 93 - 100 417 - 450 A - 90 - 92 403 - 416 B + 87 - 89 390 - 402 B 83 - 86 372 - 389 B - 80 - 82 358 - 371 C + 77 - 79 345 - 357 C 70 - 76 313 - 344 D 60 - 69 268 - 312 F 0 - 59 0 - 267

After the second exam and before the late-drop deadline, if required, the grade-line cutoffs for the major grades (A, B, C, D, F) will be updated to facilitate your planning for the remainder of the semester. The exact +/- grade-lines will be assigned after the final exam. The unavoidable consequence is that some students are just a point away from a higher grade. For reasons of fairness, the policy in this course is to NOT adjust individual grades in such circumstances.

Note: Your grade will be based exclusively on the midterm examinations, final examination, WebAssign problems, and clicker exercises. There is no extra credit work. Students are encouraged to discuss their performance with their lecturers regularly during the semester, and if appropriate, work out strategies to improve overall study, problem solving, and knowledge retention skills.

Deferred Grades: Students who are unable to complete the course because of illness or emergency may be granted a deferred grade, which will allow the student to complete the course within the first six weeks of the following semester. Note that deferred grades are limited to those students who can verify and document a valid reason for not being able to take the final examination. For more information, see DF grade.

Classroom Protocol Please turn off all cell phones and put away all materials not directly related to the course (e.g. newspapers). Since noises are greatly amplified in the lecture halls, it is important that non-essential conversations are minimized. Finally, if you must leave early, please notify your lecturer at the beginning of class and sit near an exit to minimize classroom disturbance.

Note: Keep in mind, that if you leave early, you are at risk of missing an important clicker exercise.

Calculator Usage

A graphics-business calculator is highly recommended, but any calculator that can compute "x to the power y" is sufficient. It may be used, as appropriate, in the lectures, WebAssign exercises, self-assessment tests, and homework, but will not be allowed on the two midterms and final examination.

Obtaining Assistance There are various avenues for obtaining assistance for this course:

• Your lecturer - office hours appear above • The Math Tutoring Center (part of Penn State Learning located on the

2nd floor Boucke building) • Guided Study Group (part of Penn State Learning - Times TBA

later)

Hopefully Helpful Hints

o Learn for the long term. Strive to retain the knowledge that you acquire. Do not simply try to learn material a couple of days before an exam with the goal of forgetting it right after finals. View the learning of the material as an active

process, not a passive one. (You are here to learn, not to receive grades.) Learning is a process, not an event.

o Strive to know the material, to understand it at a very deep level, rather than a superficial one.

o Do the homework with as little help (solutions manuals, friends, etc.) as possible. Balance the use of group learning with individual study so you actually know the material.

o Ask questions, either in class or during office hours. o Read the textbook before the planned lecture. The tentative

schedule of classes gives you a guide as to what to read in advance.

o Carefully study and rework the examples in the text. o Re-read and rewrite your notes. o Study for exams progressively, over a long period of time.

Begin the studying process at least one week prior to the date of the exam.

o Manage your time wisely. Plan to spend at least two hours outside of class for every hour in class, if not more!

o Take responsibility for your education. Work the self-assessment tests and learn from the objective feedback.

Final Comments It is our hope that your appreciation for mathematics will grow during this semester. Although the applications we cover are limited in scope, the application of mathematics extends to many areas in your chosen careers. The Calculus skills developed in this class provide a solid foundation for addressing many of the questions that surface during the introduction of standard business models in your future coursework.

Tentative Class Schedule (Lectures)

Day Date Material Covered Other Information

M 1/9 Course Overview First Day of Classes

T 1/10 2.1 Functions

W 1/11 2.2 Algebra of Functions

Th 1/12

F 1/13 2.3 Functions and Mathematical Models

Regular Drop Deadline

Saturday, 1/14

Regular Add Deadline

Sunday, 1/15

M 1/16 No Class

MLK Holiday

T 1/17 2.3 Functions and Mathematical Models

W 1/18 2.4 Limits

Th 1/19

F 1/20 2.4 Limits

M 1/23 2.5 One-Sided Limits

T 1/24 2.5 Continuity

W 1/25 2.6 Definition of the Derivative

Th 1/26

F 1/27 2.6, 3.1 Basic Rules of Differentiation

M 1/30 3.1

T 1/31 3.2 Product / Quotient Rules

W 2/1 3.2

Th 2/2

F 2/3 3.3 Chain Rule

M 2/6 3.3

T 2/7 3.4 • Marginal Revenue, Cost, Profit • Marginal Average Revenue,

Cost, Profit • Price Elasticity of Demand • Elasticity and Revenue

W 2/8 3.4

Th 2/9

F 2/10 3.4

M 2/13 3.5 • Higher Order Derivatives

T 2/14 3.6 • Implicit Differentiation • Related Rates - Basic

Algebraic/Geometric Applications

• Related Rates - Business Applications

W 2/15 3.6

Th 2/16

F 2/17 4.1

Applications of First Derivative

M 2/20 4.1

T 2/21 4.2 Applications of Second Derivative

W 2/22 4.2 Evening Exam 1, 7:45 – 9:00

Location – posted by lecture class

Th 2/23

F 2/24 4.3 Curve Sketching

M 2/27 4.3

T 2/28 4.4 Absolute Extrema - Optimization

W 3/1 4.4

Th 3/2

F 3/3 4.5 • Optimization - Basic Algebraic / Geometric Applications

• Optimization - Business Applications

Spring Break

3/5 – 3/11

M 3/13 4.5

T 3/14 5.1 Exponential Functions

W 3/15 5.1, 5.2 Logarithmic Functions

Th 3/16

F 3/17 5.2

M 3/20 5.3 • Compound Interest • Continuous Interest • Effective Rates of Interest • Present Value

T 3/21 5.3

W 3/22 5.3

Th 3/23

F 3/24 5.4 Differentiation of Exponential Functions

M 3/27 5.4, 5.5 Differentiation of Logarithmic Functions

T 3/28 5.5

W 3/29 5.6 Logistical Growth Models

Th 3/30

F 3/31 5.6, 6.1 Antiderivatives and Rules of Integration

M 4/3 6.1, 6.2 Exam 2, 7:45 – 9:00

Location – posted by lecture class

Integration by Substitution

T 4/4 6.2

W 4/5 6.3 Area and the Definite Integral

Th 4/6

F 4/7 6.4 Fundamental Theorem of Calculus

Late Drop Deadline

M 4/10 6.4

T 4/11 6.5 Evaluating Definite Integrals

Average of a Continuous Function

W 4/12 6.6 Areas Between Curves

Th 4/13

F 4/14 6.6

M 4/17 6.7 • Consumer / Producer Surplus • Future/Present Value of

Continuous Income Stream • Annuity Amount and Present

Value

T 4/18 6.7

W 4/19 6.7

Th 4/20

F 4/21 6.7

M 4/24 7.1 Integration by Parts

Applications to Business Models

T 4/25 7.1

W 4/26 7.4 Improper Integrals

Future/Present Value of Perpetuities

Th 4/27

F 4/28 7.4

Last Day of Classes

Final Exam Period

May 1 - 5

Suggested Homework Problems

Section Problems

2.1 1-13 odd, 23-34, 39-50, 51-58

2.2 1-23 odd, 25-34, 43-52, 64, 65, 66

2.3 1-7 odd, 9-14, 17, 18, 51, 53, 55, 66-69, 72, 73 76

2.4 1-8, 17-22, 23-39 odd, 49-66, 73-80, 83

2.5 1-14, 15-20, 21-35, 39-44, 45-55, 57-60, 73, 74

2.6 9-21, 23, 24, 34, 35, 47-52

3.1 1-36, 37, 38, 41-46, 67

3.2 1-29, 35-41, 46, 48, 56

3.3 1-53 odd, 61-64, 85

3.4 3-17, 23-33

3.5 1-19 odd

3.6 1-8, 9-29 odd, 41-47

4.1 11, 12, 13-35 odd, 37-43, 45-48, 49-65 odd

4.2 1-8, 11-14, 25-59 odd, 61-75 odd, 94

4.3 1-10, 11-27 odd, 37-57 odd, 62

4.4 1-8, 9-27 odd, 40, 45-47

4.5 5, 8, 9, 10, 17

5.1 1-18 odd, 17-26

5.2 1-11 odd, 17-20, 21-28, 35-42

5.3 1-28

5.4 1-28, 33-40, 43-46, 63, 67

5.5 1-33 odd, 41-50, 51-58

6.1 9-48, 51-58, 67-70

6.2 1-46 odd, 59

6.3 3, 5, 7, 13, 15

6.4 5-16, 17-40, 41, 42, 43

6.5 1-27, 29-41 odd, 57, 61

6.6 1-16, 17-33 odd

6.7 1-18, 22

7.1 1-26, 27-32, 42, 43, 44, 46

7.4 1-13 odd, 19-37 odd, 47-50

Learning Objectives

Upon successful completion of Math 110, the student should be able to:

1. Identify polynomial, rational, power, exponential, and logarithmic functions.

2. Calculate the domains of polynomial, rational, power, exponential, and logarithmic functions.

3. Calculate the sums, differences, products, quotients, and compositions of functions.

4. Model cost, revenue, profit, supply, and demand business functions.

5. Calculate equilibrium points within supply/demand markets and interpret the results.

6. Calculate or estimate finite/infinite limits of functions given by formulas, graphs, or tables.

7. Calculate one-sided limits of functions.

8. Determine whether a function given by a graph or formula is continuous at a given point or on a given interval.

9. Determine whether a function given by a graph or formula is differentiable at a given point or on a given interval.

10. Distinguish between average and instantaneous rate of change and interpret the definition of the derivative graphically.

11. Determine derivatives of some functions using the definition of derivative of a function.

12. Calculate derivatives of polynomial, rational, power, exponential, and logarithmic functions, and combinations of these functions.

13. Calculate derivatives of implicitly defined functions.

14. Apply the ideas and techniques of derivatives to related rate problems to include basic algebraic/geometric models and cost/average cost, revenue/average revenue, profit/average profit, supply, and demand models

15. Apply the ideas and techniques of derivatives to perform marginal analysis of basic economics models.

16. Apply the ideas and techniques of derivatives to calculate elasticity of basic economics models.

17. Apply the ideas and techniques of derivatives to determine intervals where a models/graph is:

(a) Increasing/decreasing

(b) Concave up/down

18. Apply the ideas and techniques of derivatives to determine points in a model/graph that are:

(a) Relative extrema

(b) Absolute extrema

(c) Critical

(d) Inflection

19. Identify vertical and horizontal asymptotes

20. Apply the ideas and techniques of derivatives to graphing or recognizing the graphs of functions.

21. Apply the ideas and techniques of derivatives to optimization problems to include basic algebraic/geometric models and cost, revenue, profit, supply, and demand models.

22. Apply the ideas and techniques of derivatives to solve:

(a) Compound interest

(b) Continuous interest

(c) Effective interest rate

(d) Present value

business models.

23. Determine the point-of-diminishing returns for a model/function.

24. Calculate the derivatives of functions using logarithmic differentiation

25. Calculate the Riemann sum for a given function, partition and collection of evaluation points.

26. Describe a definite integral as the limit of a Riemann sum.

27. Determine anti-derivatives of basic algebraic functions.

28. Calculate values of definite integrals using anti-derivatives and areas.

29. Apply concepts of integration to solving basic business model applications

30. Apply substitution and integration by parts techniques to integrate basic functions.

31. Apply the ideas of definite integrals to solve problems of areas.

32. Calculate the average value of business models using the definite integral.

33. Apply the ideas and techniques of the definite integral to evaluate:

(a) Consumer/producer surplus

(b) Future/present value of income streams

(c) Future/present value of annuities business models.

34. Evaluate improper integrals and apply the ideas and techniques to evaluate Perpetuities.

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