Math 150: Introduction to Calculus

Spring 2006

 

Text: Applied Calculus, Hughes-Hallett et. al., 2nd edition

 

Pre-requisites: One of the following – 580 Math SAT or 25 Math ACT score, or completion of Math 124, 126 or 129.  Students not satisfying one of these will be dropped from the course.  Please note that Math 150 is NOT a prerequisite for Math 155 and that in general it does NOT satisfy the same credit requirements as Math 155.  Math 150 covers both first and second semester calculus and is intended to prepare primarily business, economics, pharmacy, and forestry majors for their major courses.

 

Technology:  This course will rely on the use of a graphing utility for problem solving and exploration.  Suggested tools are:  TI-83, 86 or HP48 or the online graphing tool found at http://iml.math.wvu.edu/grapher/grapher.html.   You are not required to have one but your instructor may use one and you may find one helpful during the lectures.  The online graphing tool will be the only graphing utility available in the computer lab during exams and gateways.  There will be an online calculator available during exams as well as the Windows calculator.  If you prefer a handheld calculator, only non-graphing, scientific calculators such as the TI-30II are allowed.    Graphing calculators and Derive are not allowed on any exam or gateway.

 

Exams and quizzes will be given in Vista as explained below.  You will need your MiX account ID and password to access the VISTA-WebCT site for the course.  If you are enrolled in 150 you may go to http://vista.wvu.edu and log on to the site or access the VISTA-WebCT site from http://www.mix.wvu.edu/.  You will see Math 150-Vista listed in myWebCT if you are enrolled in the course.  This applies to all sections of the course.  If you don’t see the course listed, you are no longer enrolled or have been locked out by the registrar for some reason.  You will also see a listing for your section and lab which will not be used.  Please contact your instructor if you see any of these removed or unavailable during the semester as this may mean that you have been dropped for fee related issues.

 

Contacts:    

 

Instructor:

 

Email:

 

Office:

 

Office Hours:

 

Phone:

 

 

For other assistance and information, you may also contact Dr. Ali Ikiz, the co-coordinator at ikizali@math.wvu.edu  or the course coordinator, Dr. Eddie Fuller who has a homepage at http://www.math.wvu.edu/~ef/ and the home page of the course is with more information can be found at http://vista.wvu.edu/ .  His office is 307G Armstrong Hall and his phone number is 293-2011 x2345.  Please check his web page for office hours.

 

Evaluation: Multiple forms of assessment will be used to measure your understanding of the concepts, skills, and problem solving.  The distribution of these assessments is:

                                                                                                    

Assessment

Number

Total Points

Percent of Grade

Quizzes and Weekly Problems

9-12

100

10%

Attendance/Participation/Classroom Activities

 

50

5%

Laboratory Activities        

7

200

20%

Gateways

3

150

15%

Exams

3

300

30%

Comprehensive Final

1

200

20%

Total

 

1000

100%

 

Grading Scale (by points): 

 

1000 – 950

A+

894 – 870

B+

794 – 770

C+

694 – 670

D+

949 – 915

A

869 – 815

B

769 – 715

C

669 – 615

D

914 – 895

A-

814 – 795

B-

714 – 695

C-

614 – 595

D-

 

 

 

 

 

 

       <595

F

 

 

 

 

 

Attendance/Participation/Activities:  Your instructor will determine the attendance/participation/activities portion that counts as 5% of your overall grade. 

 

Quizzes:  In addition to this, online quizzes will count another 10% of your grade.  These assessments will be administered as Vista quizzes taken outside of class time from any computer connected to the web. You will be allowed to take each quiz administered using Vista up to three times.  The highest score for each quiz will count as part of your grade.  There is a practice quiz for you to familiarize yourself with quizzes/exams in Vista prior to taking one for credit.  It does not count in your grade. 

 

Laboratory Exercises:  All sections of Math 150 will meet in the IML computer lab in 215 Armstrong Hall on Wednesdays during the same time as your lecture.  On these days, classes will work in groups or individually on a series of projects and activities that focus on applied topics related to the majors you have chosen.  Each lab activity will be preceded by an online lab preview.  These lab previews will require students to read ahead in the text and answer a few questions in an effort to be prepared for the lab activity.  These lab previews will be taken from any computer with web access and will only be available on Monday and Tuesdays.

The total of these activities will constitute 20% of your grade.

 

Gateways:  Three gateway exams will be given in the lab during the semester.  They will each count 5% of your grade.  These exams will consist of skill and computational exercises on algebra, differentiation and integration which you will be required to answer using only the online calculator, a NON-graphing calculator, and/or paper calculations.  You will be able to take these exams a maximum of two times.  Your first attempt will be a good indication of how prepared you are for major exams.  The second attempt will be a chance for you to answer questions correctly that you were challenged by on the first try.  The higher of the two grades will be used in your course average.

 

Exams:  Major exams will also be given in the IML computer lab on Wednesdays as indicated in the course outline.  Exams will be completed and submitted on the computers in this lab.  You will need to present your WVU ID on exam days and keep it out during the test.  The final exam will also be in the lab on Wednesday during finals week.  You may sign up for a final exam time via the Vista site for the course after the drop date.  Exam material will be based on homework exercises, lab activities, and quiz material.  Exams will count as 30% of your grade and the final counts another 20%.  Graphing calculators and Derive are NOT allowed on any exam.  An online graphing utility is provided as well as an online calculator.  If you wish to use a handheld calculator, it must be a non-graphing scientific calculator similar to the TI-30II (roughly $10-15).

 

An additional review “super quiz” will be offered at the end of the semester that will allow students who have missed questions on exams to show that they know the material and make up for the lack of partial credit on these exams.  In large section courses such as this, partial credit is impossible to administer and this quiz serves as a way to offset minor errors in your problem solutions.

 

Objectives: The general goals of the Introduction to Calculus course are:

·        APPLICATIONS:  use math to model and solve real world problems

·        CONCEPTUAL UNDERSTANDING:  explore and understand central concepts in algebra and calculus, rather than just rote memorization of algorithms

·        COMPUTATIONAL SKILLS: develop proficiency in manipulating algebraic expressions and the computation of derivatives and integrals

·        PROBLEM SOLVING:  gain experience as a problem solver, to use a heuristic to analyze problems in an organized manner

·        MULTIPLE APPROACHES:  to examine problems from analytical, geometric and numeric perspectives, to make decisions about the appropriateness of the choice of formal or approximate methods of solution

·        TECHNOLOGY AS A TOOL:  use technology as an integral part of the process of formulation, solution, and communication, to gain experience in selecting the proper tool for a given problem

·        ACTIVE STUDENT LEARNING:  to engage in the exploration and discovery of concepts and to learn to work cooperatively to solve problems

·        COMMUNICATION OF IDEAS:  to demonstrate understanding by explaining in written or oral form the meanings and applications of concepts

 

The specific goals of this course will be to stress an algebraic, graphic, and numeric approach to the study of:

 

  • the concept of function, using functions as models and modeling techniques used in solving real world problems
  • using the derivative as a tool to solve problems; using the definite integral and area to solve problems

 

To accomplish these goals requires active student learning, not passive participation.  Attendance is required and you will be required to engage in class activities as determined by your instructor.  Most of these will be based on exercises from the text.  These are intended to promote discussion of mathematical concepts and modeling and you are encouraged to share your ideas.

 

West Virginia University is committed to social justice.  I concur with that commitment and expect to foster a nurturing learning environment based upon open communication, mutual respect, and non-discrimination.  Our University does not discriminate on the basis of race, sex, age, disability, veteran status, religion, sexual orientation, color or national origin.  Any suggestions as to how to further such a positive and open environment in this class will be appreciated and given serious consideration.

 

If you are a person with a disability and anticipate needing any type of accommodation in order to participate in this class, please advise me and make appropriate arrangements with Disability Services (293-6700).

Math 150

Spring 2006 Course Outline

Date

Topic

Section

Exercises

1

M

1/9

Functions; Linear Functions

1.1, 1.2

1.1  1,2,3,5,7,12,15,17 1.2 1,3,5,7,9,17,18

W

1/11

Intro to Vista, Rates of Change

1.3

1.3 1,3,5,6,9,11,13,17,27

F

1/13

Applications of Functions

1.4

1.4 1,2,3,5,7,9,11,13,19,27

2

M

1/16

Martin Luther King Day (NO CLASSES)

 

 

W

1/18

Exponential Growth and Decay (1)

1.7

1.7 1,3,5,7,9,11,13,15,19,25,33

F

1/20

Exponential and Logarithm Functions

1.5,1.6

1.5 1,3,5,6,11,15,19,24; 1.6 1,3,5,7,9,13,17,19,23,25,27,31,37

3

M

1/23

Functions and Proportions

1.8,1.9

1.8 1,4,5,9,13,19,21,25; 1.9 1,3,4,13,17,21,23,27,35,37

W

1/25

Algebra Gateway

 

 

F

1/27

Instantaneous Rates of Change

2.1

2.1 1,3,4,5,11,19,21

4

M

1/30

The Derivative

2.2

2.2 1,2,3,4,5,7,9,11,19,21,27,31

W

2/1

Exam 1 (Chapter 1 and 2.1-2.2)

 

 

F

2/3

Interpretations of the Derivative

2.3

2.3 1,3,5,9,11,15,17,21

5

M

2/6

The Second Derivative

2.4

2.4 1,3,5,7,9,11,13,17,19,25

W

2/8

Marginal Cost and Revenue (2)

2.5

2.5 1,3,5,7,9,11,13

F

2/10

Derivatives:  Powers and Polynomials

3.1

3.1 1,3,5,7,9,11,13,15,17,19,21,27,29,30,35

6

M

2/13

Derivatives:  Exponents and Logs

3.2

3.2 1,3,5,7,15,17,19,25,27

W

2/15

Rates of Change and Tangents (3)

2.1-2.3

Review these sections for pre-lab

F

2/17

The Chain Rule

3.3

3.3 1,5,7,15,21,24,25,31,35,37

7

M

2/20

The Product and Quotient Rules

3.4

3.4 1,3,4,7,9,11,13,15,17,21,25,32,33,35,36

W

2/22

Derivatives Gateway

 

 

F

2/24

Local Maxima and Minima(mid term grades)

4.1

4.1 1,1,3,5,7,8,9,11,15,17,23

8

M

2/27

Inflections

4.2

4.2 1,3,5,7,9,13,15,17,24,25

W

3/1

Exam 2  (2.3-2.5, Chapter 3 and 4.1-4.2)

 

 

F

3/3

Global Maxima and Minima

4.3

4.3 1,3,5,7,9,11,19,21

9

M

3/6

Profit, Cost and Revenue

4.4

4.4 1,3,4,5,7,9,13

W

3/8

Surge Functions and Drug Concentration (4)

4.8

4.8 1,2,3,4,11

F

3/10

Elasticity of Demand

4.6

4.6 1,3,5,7,9,11

3/11 – 3/19 Spring Break (NO CLASSES)

10

M

3/20

Accumulating Change

5.1

5.1 1,3,5,7,9,11,13,15

W

3/22

The Definite Integral  (5)

5.2

5.2 1,3,5,7,9,13,15

F

3/24

 Area (last day to drop a class)

5.3

5.3 1,2,3,4,5,7,9,10,12,14,27

11

M

3/27

The Fundamental Theorem of Calculus

5.5

5.5 1,3,5,9,11,12

W

3/29

Interpretations of the Definite Integral (6)

5.4

5.4 1,3,6,11,16,19,23

F

3/31

Anti-derivatives

7.1

7.1 1,3,5,7,9,11,19,20,25 

12

M

4/3

Review

 

 

W

4/5

Exam 3 (4.3-4.6, 4.8, Chapter 5 and 7.1)

 

 

F

4/7

Average Value

6.1

6.1 1,3,4,5,9,15

13

M

4/10

Consumer and Producer Surplus

6.2

6.2 1,2,3,4,5,7

W

4/12

Present and Future Value (7)

6.3

6.3 1,2,3,7,9,11

F

4/14

Relative Growth

6.4

6.4 1,3,6,7,9,13

14

M

4/17

Anti-derivatives, Part II

7.1

 

W

4/19

Integration Gateway

 

 

F

4/21

Substitution

7.2

7.2 1,3,5,9,11,19

15

M

4/24

Using the Fundamental Theorem

7.3

7.3 1,3,5,7,9,11,13,15,25,27,32

W

4/26

Problem Workshop

 

 

F

4/28

Review

 

 

W

5/3

Final Exam in IML lab

 

Must sign up for time slot

**Note:  The Final Exam will be two hours long.  It will contain 12 problems from Chapters 6 and 7 with the remaining  12-14 problems coming from previous material.


Lab Schedule

Math 150 Spring 2006

 

 

Week

Activity

Topic

To Be Turned In

1

Intro to Vista and Practice Quiz

Lecture and Exercises on 1.3

 

2

Exponential Growth and Decay

Functions and Rates of Change

Worksheet

3

Algebra Gateway

Prerequisite Algebra Skills

 

4

Exam 1

Chapters 1 and 2

 

5

Marginal Cost and Revenue

Applications of Derivatives

Worksheet

6

Rates of Change and Tangents

Using Derivatives

Worksheet

7

Derivatives Gateway

Computing derivatives

 

8

Exam 2

Chapters 3 and 4

 

9

Surge Functions

Metabolism of Drugs and Modeling

Worksheet

10

The Definite Integral

Computing Integrals

Worksheet

11

Interpretations of the Definite Integral

Definite Integrals and Riemann Sums

Worksheet

12

Exam 3

Chapters 5 and 6

 

13

Future and Present Value

Future Value of an Income Stream

Worksheet

14

Integration Gateway

Computing integrals

 

15

Practice Problems

 

 

 

Getting Help:  You should expect to spend six to ten hours per week outside of class working on homework, quizzes and general studying.  If you are spending more, then you may need to seek help!  There are several excellent sources for such help.  First, seek help from your classmates.  Often they can explain the problem clearly since they have been working on it.  Second, seek assistance from your instructor.  A few questions may clarify the problem.  Third, seek help from the Math Learning Center in Armstrong 301.  Finally, the IML Computer Center will offer mentoring sessions during open lab times in which mentors can work with you individually on any material from the class.  These lab times can include both computer-based tutorials and human tutors.

 

Note:  Unless otherwise noted, all labs and second attemps on gateways are to be completed by Friday at 4pm following the Wednesday lab meeting.