MATH 110 - Techniques of Calculus I

Penn State University
  Fall Semester 2008

General Information

Dr. James Hager  (Coordinator)
405 McAllister Building
(814) 863-9096
hager@math.psu.edu


Office Hours: TTH: 4:00-5:30
and By Appointment

Dr. David Little

403 McAllister Building
(814) 865-3329
dlittle@psu.edu


Office Hours: WF: 10:00-11:00, TTh: 2:00-4:00
and By Appointment




                

 

Textbook: Applied Calculus for the Managerial, Life, and Social Sciences, 7th Edition, by S.T. Tan (Brooks/Cole, 2007)

Note: Hardcopies, electronic copies, and electronic copies of individual chapters of the textbook and supporting materials are available for purchase at reduced cost by visiting the www.ichapters.com website.

Note:  Brooks/Cole also maintains a companion website for the text. 

Course Description (from the Penn State University Blue Book)
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 Chapters 2-6 from the text. Note that 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.

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

        Examination 1:  Monday, October 6, 2008, 6:30 - 7:45 pm
        Examination 2:  Thursday, November 6, 2008, 6:30 - 7:45 pm

Information on the locations of these exams will be distributed at a future date. In addition, the math department schedules a conflict exam for each of the midterms from 5:05 - 6:20 on the same night as the regularly scheduled exam and a makeup exam scheduled on an evening different from the regularly scheduled exam night. Sign-up sheets for the conflict exam or the makeup exam will be available from your lecturers approximately one week before the exam. 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, December 15-19, 2008.  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.  Hence, the above note regarding a 25% deduction will be enforced in the event that a student's travel plans conflict with the university's designated final examination period for this course.

In-Class Quizzes
Several short quizzes will be given throughout the course of the semester during the recitation hour. The quiz questions will be similar to the assigned homework problems and the reading done in preparation for class, which is a good motivation for you to complete the suggested homework problems noted below. The purpose of the quizzes is to encourage you to keep up with your preparation (and reward you for doing so). Each quiz will consist of problems based on the materials presented during the previous week's lectures. During the first week, your first quiz score will be based on the Readiness Test to be taken through Angel. Since the purpose of the Readiness Test is to test the basic algebraic skills required to be successful in Math 110, it is critical that everyone take the test during the first week of classes.  Students who score poorly on this test should work the Chapter 1 self-assessment exercises also included on Angel and, if still finding difficulty with the preparatory materials, strongly consider taking Math 22 before proceeding with Calculus. Minimally, all students should review the basic algebraic concepts covered by the test questions during the first week of the semester in preparation for the related Calculus materials.

Any student who takes the Readiness Test will have a 10 recorded for the first quiz score. A student who does not take the Readiness Test will have a 0 score assigned.

Thirteen quizzes are planned for the semester (approximately one per week and the Readiness Test).  A student's quiz grade will be determined by summing each student's highest ten quiz scores and dropping the remaining ones. Each quiz will be worth 10 points.

Suggested Homework

A list of suggested homework problems 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 quizzes and exams. Since much of this material builds upon previous material, you are encouraged to do all of the suggested homework and keep up with the suggested homework, even though it will not be handed in.

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.

Grading:  your course grade will be determined by your exam scores and your quiz scores.
Total possible points follow:   

 Examination I

100

 Examination II

100

 Quizzes

100

 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, A-

90-100

405-450

B+, B, B-

80-89

360-404

C+, C

70-79

315-359

D

60-69

270-314

F

0-59

0-269

 

After the second exam and before the late-drop deadline, the grade-line cutoffs for the major grades (A, B, C, D, F) will be provided to facilitate your planning for the remainder of the semester. The +/- 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, and quiz scores. There is no “extra credit” work.

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.

Class Attendance
Although regular classroom attendance will not figure into your grade in a tangible way, you are strongly encouraged to regularly attend class. Attending all classes is extremely beneficial to you. Seeing the material presented in a lecture is extremely helpful as the presentation will often be different than the text in order to clarify and enhance the reading assignments. Having questions answered in class (as well as hearing other students' questions) is also a benefit. Material not present in the text may be presented in class; you will be held accountable for this material on quizzes and exams. Finally, regular attendance demonstrates good stewardship of your time and money.

Classroom Protocol
Please turn off all cell phones and put away all electronic devices  (iPods, etc.) and 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 instructor at the beginning of class and sit near an exit to minimize classroom disturbance.

Calculator Usage
A graphics calculator is recommended, but any calculator that can compute "x to the power y" is sufficient. It may be used, as appropriate, in the lectures and homework, but will not be allowed on the in-class quizzes, two midterms and final examination.

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

 

Hopefully Helpful Hints

 

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 of life.

 

Tentative Class Schedule (Lectures)
 

Day

Date

Material Covered

Other Information

M

8/25

Course Overview

First Day of Classes

W

8/27

 2.1

 

F

8/29

 2.2

 

 

M


9/1

 

Labor Day

Holiday
 No Classes

W

9/3

 2.3

 

F

9/5

 2.4

 

M

9/8

 2.4, 2.5

No Intermediate Value Theorem

W

9/10

 2.5

 

F

9/12

 2.6

 

M

9/15

 3.1

 

W

9/17

 3.2

 

F

9/19

 3.3

 

M

9/22

 3.4

·        Marginal Revenue, Cost, Profit

·        Marginal Average Revenue, Cost, Profit

·        Elasticity

·        Elasticity and Revenue

W

9/24

 3.4

 

F

9/26

 3.5

 

M

9/29

 3.6

·        Related Rates - Basic Algebraic/Geometric Applications

·        Related Rates - Business Applications

W

10/1

 3.6

 

F

10/3

 Review

 

M

10/6

 4.1

Exam 1

Monday, 10/6

6:30-7:45

W

10/8

 4.1, 4.2

 

F

10/10

 4.2

 

M

10/13

 4.3

 

W

10/15

 4.4

·        Absolute Extrema

·        Optimization - Business Applications

F

10/17

 4.5

·        Optimization - Basic Algebraic / Geometric Applications

·        Optimization - More Advanced Business Applications

M

10/20

 5.1

 

W

10/22

 5.2

 

F

10/24

 5.3

·        Compound Interest

·        Continuous Interest

·        Effective Rates of Interest

·        Present Value

M

10/27

 5.3

 

W

10/29

 5.4

·        Exponential Business Models

F

10/31

 5.4, 5.5

 

M

11/03

 5.5

 

W

11/5

 Review

Exam 2

Thursday, 11/06

6:30-7:45

F

11/7

 6.1

 

M

11/10

 6.1

 

W

11/12

 6.2

 

F

11/14

 6.2

Late Drop Deadline

M

11/17

 6.3

 

W

11/19

 6.4

 

F

11/21

 6.5

 

 

 

 

11/24 – 11/28

Thanksgiving Holiday

M

12/1

 6.6

 

W

12/3

 6.6

 

 

 F


 12/5


 6.7

·        Consumer / Producer Surplus

·        Future/Present Value

·        Annuity Amount and Present Value

 

 M


12/08 


 6.7

 

W

12/10

 Review

 

F

12/12

 Review

Last Day of Classes

 

As noted above, the university's final examination week for this semester is December 15-19, 2008.  Do not plan to leave the university before the completion of this week.

 

Suggested Homework Problems
 

Section

Problems

1.1

1-89 odd

1.2

1-93 odd

1.3

1-33 odd

1.4

1-10, 11-45 odd

2.1

1-13 odd, 21-33 odd, 49-55

2.2

1-23 odd, 25-34, 47, 51. 52

2.3

1-7 odd, 9-14, 51, 53, 56, 66, 67, 74, 75, 78

2.4

1-8, 17-22, 23-39 odd, 49-62, 73-80

2.5

1-6, 9-14, 21-35 odd, 39, 44, 51, 52

2.6

9-21 odd, 30, 34-36, 45-50

3.1

1-36 odd, 37, 38. 41-46

3.2

1-29 odd, 35-41 odd, 46

3.3

1-53 odd, 61-64

3.4

3-17 odd, 23-33 odd

3.5

1-14 odd, 30

3.6

1-17 odd, 31, 33, 41, 42, 56, 59, 60, 61

4.1

1-8, 11-33 odd, 35-41, 43-46, 47-63 odd

4.2

 1-12, 21-67 odd

4.3

 1-10, 11-27 odd, 37-43 odd, 49-53, 56, 62

4.4

 1-8, 9-27 odd, 40, 42, 46-51

4.5

 1, 3, 4, 5, 6, 7, 8, 10, 12, 28

5.1

 1-25 odd

5.2

 1-27 odd, 35-42 odd

5.3

 1-23 odd

5.4

 1-45 odd, 46, 60, 61

5.5

 1-55 odd

6.1

 1-57 odd, 67, 68

6.2

 1-43 odd, 51

6.3

 5, 7, 13, 15

6.4

 1-39 odd, 41-43

6.5

 1-27 odd, 29-37 odd, 53

6.6

 1-37 odd

6.7

 1-9, 11-13, 16-18

 

Practice Exams

Links are provided for the exams given during the Fall 2007 / Spring 2008 semesters. Although several of the questions contained on these exams provide useful examples, care must be taken since the course emphasis and syllabus have changed significantly with the Fall 2008 semester. Before each exam, your lecturer will point out the specific questions not relevant to this semester’s instruction.

 

Practice exams for the Math 110 Examination 1 can be found at the following link:

              1. Practice Math 110 Midterm 1

              2. Practice Math 110 Midterm 1

      
Practice exams for the Math 110 Examination 2 can be found at the following link:

             1. Practice Math 110 Midterm 2  

             2. Practice Math 110 Midterm 2 

 
Practice exams for the Math 110 Final Examination can be found at the following link:

             1. Practice Math 110 Final

             2. Practice Math 110 Final


Room locations for each of the exams will be posted as they become available.

Note: Students should understand the suggested homework problems from the relevant sections. They may also wish to study similar problems, which appear in the corresponding chapter review(s), but students should understand that the exams for this semester are not based strictly on the practice exams.
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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 finding extrema.

18.  Apply the ideas and techniques of derivatives to graphing functions.

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

20.  Apply the ideas and techniques of derivatives to solve compound interest, continuous interest, effective interest rate, and present value business models.

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

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

23.  Determine anti-derivatives of basic algebraic functions.

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

25.  Apply substitution techniques to integrate basic functions.

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

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

28.  Apply the ideas and techniques of the definite integral to evaluate consumer/producer surplus, future/present value of income streams, and annuity business models. 

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Course Announcements

Course announcements will be posted to this part of the syllabus.

 

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