MTH 1110-03  Term I  2009

MATHEMATICAL ANALYSIS I

 

12-12:50 pm      Room E 237

 

PREREQUISITES: Level of competency equivalent to MTH 101.  No reviewing of this material will take place in this class.

 

INSTRUCTOR: Dr. M. S. Skaff                             Office: E204    Telephone: (313) 993-3376       

                                                                                 E-Mail: skaffms@udmercy.edu

 

OFFICE HOURS:  10:30-11 am  MWF or  any time the office door is open, or by appointment.

 

TEXT BOOK: College Algebra: by Larson and Hostetler, 7th Edition, Houghton-Mifflin Publisher, 2007, ISBN: 0-618-64310-9   or  978-0-618-64310-3

     

COURSE DESCRIPTION.  This course presents the mathematics needed to understand and apply college algebra concepts in a real world setting. Students will learn these concepts in terms of how they apply to the business world. This includes both a theoretical understanding of algebra and practical examples illustrating the use of algebra in applications. 

 

COURSE OBJECTIVES.  The main objective of the course is to teach students to understand (and apply) algebra in terms of functions, solving equations and inequalities, and solving systems of equations. Properties of functions will be studied including continuity, domain, range, 1-1, inverses, even, odd, composition, and arithmetic operations. In addition, graphs of functions will be analyzed and asymptotic behavior studied. Exponential and logarithmic functions will also be studied, in addition to learning how to solve equations and inequalities.  Finally, system of equations is introduced and methods of solution are found. All of these algebraic tools are applied to real business problems.

 

To illustrate the practical use of college algebra, students will be asked to complete project assignments which involve analyzing data. This data represents information defined by some practical problem. One method which will be employed to study the behavior of the data is regression analysis.  Students will be shown how to set up the data and use regression tools.

 

COURSE OUTCOMES.  After taking this course, a student should be able to understand:

             1.  Functions, their main properties and graphs.

             2.  How to perform arithmetic operations such as addition, subtraction, multiplication, division, and

                  composition of functions.

             3.  Applications of functions when modeling real world problems.

             4.  Finding solutions of both equations and system of equations and know when solutions do not exist.

             5.  Finding solutions of both inequalities and system of inequalities.

             6.  What are matrices and how to use them to solve systems of equations and special applications such as

                  cryptography.

             7.  How to analyze data points using tools like curve fitting and regression analysis.

                         

EXAMINATIONS.  There will be three (3) closed book hour examinations and a final exam. These tests will be taken using BLUEBOOKS. These bluebooks (4 of them) can be purchased in the book store. Do so no later than Sept 21, 2009.  Put your name and MTH 111 on the cover. No books, computers, calculators or cell phones will be allowed on any examination. Students may bring a single 8.5x11 sheet of paper with notes for each exam. Exams will contain multiple choice questions.  All exams will be graded using a curve rather than straight scale.

 

SPECIAL EXAM RULES.  (1) Exams will start at the beginning of the designated class time. No additional time will be allowed especially if a student arrives late. Be on time. (2) Students are responsible for pencils or pens to take exams. None will be provided by the instructor. (3)  No test will be given to a student who has not turned in a bluebook. (4) Tests will begin only after all materials are removed from the desktop. Any loss of time (due to excess talking or delays in removing materials) will not be made up. (5)  One hour exam score or project score will be dropped from calculation of final grade but not the final exam score.  If any exam is missed or not submitted, that exam or project score is chosen as the “dropped” score. If more than two scores are missing, a grade of F will be given for the missing scores.  (6) NO MAKEUP EXAMS will be given.

 

 

 

 

 

MTH 1110-03  Term I  2009      p.2

MATHEMATICAL ANALYSIS I

 

 

DATES for EXAMS, HOMEWORK, and PROJECT ASSIGNMENTS

Dates for all graded assignments are listed on the attached class schedule.  Homework dates are in RED, Project dates are in GREEN, and Exam dates are in Orange. 

 

EXAM DATES.  Please mark your calendars.

               Exam 1.  Monday       Oct. 5, 2009

               Exam 2.  Monday       Nov. 2, 2009

               Exam 3.  Wednesday  Dec. 2, 2009

               Final Exam.   Wednesday 11-12:50pm  December 16, 2009

 

PROJECT DATES.

               Project 1.   Monday            Sept. 28, 2009

               Project 2.   Wednesday       Oct. 21, 2009

               Project 3.   Wednesday       Nov. 11, 2009

 

HOMEWORK DATES.   Sections for the homework (HW) assignments are in parentheses.

              HW 1   (1.1-1.3)   09/16/09     HW2    (1.4-1.5)           09/21/09       HW3    (1.6-1.8)    09/25/09

              HW4    (2.1-2.4)   10/02/09     HW5    (2.5-2.7)          10/14/09        HW6    (3.1-3.3)    10/19/09

              HW7    (3.4-3.5)   10/23/09     HW8    (4.1-4.2)          10/28/09        HW9    (5.1-5.3)    11/06/09

              HW10  (5.4-5.5)   11/13/09     HW11  (6.1-6.3)          11/18/09        HW12  (6.4-6.5)    11/23/09

              HW13  (7.1-7.4)   11/30/09     HW14  (7.5, 8.1-8.3)   12/11/09   

 

IMPORTANT NOTE FOR PROJECT AND HOMEWORK DUE DATES:

1)  Each day that an assignment is late will lose 25 points.

2)  Once an assignment is returned to the class with answers, no late assignment will be accepted.

             

GRADING.  The final grade for the course is determined by the following percentages:

               Hour exams:                                     40%

               Graded Homework:                          15%

               Projects:                                            15%

               Class attendance and participation:   5%

               Final Exam:                                      25%

 

Note: Class participation includes attendance, attention, no late arrivals or early departures, no miscellaneous talking not related to the class lecture, and general interest in the class. Use of cell phones during class lectures and exams

are prohibited.

 

 

 IMPORTANT FACTS.   Last day to drop class:  Sept. 26, 2009

                                          No class Days: Nov 26-29, 2009

                                          Last day to withdraw with “W”: Nov 23, 2009

                                         

ACADEMIC INTEGRITY.  Everything submitted for grading is expected to be a student’s own work. Anything suspected as being otherwise the case will be dealt with according to University and College policies.

 

CHAPTER MATERIAL.  The following sections will be covered (as time allows).

 

Chapter        Sections

     P              None.  Assumed as prerequisite Mth 101 material

     1              1.1 to 1.8

     2              2.1 to 2.7

     3              3.1 to 3.5

     4              4.1 to 4.2

     5              5.1 to 5.5

     6              6.1 to 6.5

     7              7.1 to 7.5

     8              8.1 to 8.3    

 

MATH 111-03     CLASS SCHEDULE DATES      Homework

12-12:50 pm MWF     rm 237                                Projects

                                                                                                          Exams

SEPT          MONDAY             WEDNESDAY               FRIDAY

                                                              9  (1.1)                      11 (1.2)

 

                     14   (1.3)                       16  (1.4)                       18 (1.5)

                                                           HW1 (1.1-1.3)

                     

                     21   (1.6)                       23  (1.7-1.8)                 25 (2.1)

                     HW2 (1.4-1.5)                                                  HW3 ( 1.6-1.8)

 

                    28   (2.2)                        30  (2.3)

                    Project 1

OCT                                                                                       2 (2.3,2.4)

                                                                                               HW4 (2.1-2.4)

 

                      5  EXAM 1                 7  (2.5)                          9  (2.6)

 

                     12  (2.7)                       14  (3.1)                        16 (3.2-3.3)

                                                          HW5 (2.5-2.7)

 

                     19  (3.4)                       21  (3.5)                        23 (4.1)

                     HW6 (3.1-3.3)                                                  HW7 (3.4-3.5)

 

                     26  (4.2)                       28  (5.1)                        30 (5.2)

                     Project 2                     HW8 (4.1-4.2)

NOV

                     2  EXAM 2                   4 (5.2-5.3)                     6  (5.4)

                                                                                                 HW9 (5.1-5.3)

 

                     9  (5.5)                          11  (5.4-5.5)                  13  (6.1)

                                                                                                HW10 (5.4-5.5)

                     16  (6.2-6.3)                  18   (6.4)                       20  (6.5)

                     Project 3                      HW11 (6.1-6.3)

                     23  (7.1)                         25  (7.2)                       27 (no school)

                     HW12 (6.4-6.5)

                     30  (7.3-7.4)              

                     HW13 (7.1-7.4)

DEC                                                    2  EXAM 3                 4 (7.5, 8.1)

 

                     7  (8.2)                            9   (8.3)                       11 Review Final

                                                                                                 HW14 ( 7.5, 8.1-8.3)

                                                              16  Final Exam                                          

 

 

MATH 111    PROJECT 1

Due Sept 28, 2009

                            Name _________________________________________

    

Suppose in anthropology, the relationship between the length of an adult’s femur (thigh bone from hip to knee) and the height of the adult can be approximated by the linear equations

                             y  =  0.410 x  - 10       female

                             y  =  0.465 x  - 12       male

where y is the length of the femur in inches and x is the height of the adult in inches.

 

(A)  From the foot bones of an adult human male, an anthropologist estimates that the person’s height was 65 inches. A few feet away from the site where the foot bones were discovered, the anthropologist discovers a male adult femur is 18 inches long. Is it likely that both the foot bones and the thigh bone came from the same person?       

 

(B)  Complete the following table to determine if there is a height of an adult for which an anthropologist would not be able to determine whether the femur belonged to a male or female.

                    Height x         Female Femur length, y       Male Femur length, y

                         60       

                         70

                         80

                         90

                       100

                       110

 

(C)  Solve part (C) algebraically by setting the two equations equal to each other and solving for x.  Compare your solutions. Do you believe an anthropologist would ever have the problem of not being able to determine whether a femur belonged to a male or a female?   Why?

 

(D)   Plot the data points (x, y) from (B) on the following graph (Men use Male data and women use Female data).  Draw the “best” regression line on the graph using a ruler only.  Do not run software.

                                  y

                             40

                             35                

                             30

                             25

                             20

                             15

                ______ 10_____________________________________   x

                                       60       70      80      90      100      110

 

 

 

MATH 111    PROJECT 1  Answers

Due Sept 28, 2009

                            Name _________________________________________

    

(A)     Yes ___      No ____

           Why? _________________________________________________

                      _________________________________________________

                      _________________________________________________

 

(B)              Height x         Female Femur length, y       Male Femur length, y

                         60       

                       

                         70

                        

                         80

                       

                         90

                      

                       100

                      

                       110

          Yes ____    No _____

           Why? ________________________________________________

                      ________________________________________________

(C)    Yes ____     No _____

          Why or why not? _______________________________________

           ______________________________________________________

           ______________________________________________________

           ______________________________________________________

 

(D)  

                                  y

                              40

                              35

                              30

                              25

                              20

                              10

                ___________________________________________   x

                                        60     70     80     90     100     110

 

 

 

 

 

 

 

MATH 111    PROJECT 2

Due Oct. 26, 2009

Name ______________________________________________

 

The total revenue (in millions of dollars) for Outback Steakhouse from 1995 to 2003 are listed below.

              1995     664                     2000    1906

              1996     937                     2001    2127

              1997    1151                    2002    2362

              1998    1358                    2003    2744

              1999    1646

 

(A)  Sketch a scatter plot of the data. Let y represent the total revenue (in millions of dollars) and let t = 5 represent 1995.

(B)  Use a straightedge to sketch the best-fitting line through the points and find an equation of the line.

(C)  Find the least squares regression line that fits the data. How good is the model?

(D)  Compare the models from (B) and (C). Which is better? worse? Why?

(E)   Using the models in (B) and (C), estimate the revenues for 2005. Which is better?  Why?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MATH 111    PROJECT 2 Answers

Due Oct. 26, 2009

Name ______________________________________________

 

(A)                            y

                     

                        3000

                     

                        2500

                     

                        2000

                     

                        1500

                     

                        1000

                     

                          500

                    ___________________________________________________  t

                                       5     6      7       8       9      10      11      12       13

 

(B)  Put sketch of best fitting line (in RED) on graph in (A)

       Equation of line   y = ______  t   +  _______

 

(C)   Put the regression line (in GREEN) on the graph in (A) .

         Equation of the regression line is   y = ________  t  +  ________.

         The regression line is good _____ or poor _____. 

         Why? __________________________

              

 

(D)   Model (B) is better____, worse ______ or the same ______ as Model (C).

         Why?  _______________________________________________

                     _______________________________________________

                     _______________________________________________

 

(E)    Model (B) estimates revenue for 2005 to be ________________.

         Model (C) estimates revenue for 2005 to be ________________.

         Which answer is a better estimate? ________

         Why? ____________________________________________

                    ____________________________________________

                    ____________________________________________

 

 

 

 

 

 

MATH 111   PROJECT 3

Due Nov. 16, 2009

Name __________________________________________________

 

The following table shows the time t (in seconds) required to attain a speed of s miles per hour from a standing start for a car.

 

                      Speed, s                 Time, t

                           30                         3.4

                           40                         5.0

                           50                         7.0

                           60                         9.3

                           70                       12.0

                           80                       15.8

                           90                       20.0

 

(A)  Draw a scatter diagram for the table data above. Then find the regression least squares line  t = as + b and draw the line on the scatter graph.

 

(B)  Repeat (A) using s  in place of s.  Find  the regression line  t  =  as  + b.

 

(C)  Complete the following chart and determine which model (A) or (B) is better. Why?

 

  Speed, s          model A                                    Speed, s           model B

                        t         t          t  -  t                                             t            t            t  -  t   

       30                                                                      900

       40                                                                    1600

       50                                                                    2500

       60                                                                    3600

       70                                                                    4900

       80                                                                    6400

       90                                                                    8100

   Sum

   Avg     

 

 

 

 

 

 

 

 

 

 

 

MATH 111   PROJECT 3 Answers

Due Nov. 16, 2009

Name __________________________________________________

 

(A)                     t

     

 

 

 

 

 

 

                  ___________________________________________   s

 

Regression line:  a ____________ ,   b ______________

 

(B)                    t

 

 

 

 

 

 

 

                ____________________________________________  s

 

Plot s  not s on the graph.

Regression line:  a ____________ ,   b ______________

 

 

(C) 

  Speed, s          model A                                    Speed, s           model B

                        t         t          t  -  t                                             t            t            t  -  t   

       30                                                                      900

       40                                                                    1600

       50                                                                    2500

       60                                                                    3600

       70                                                                    4900

       80                                                                    6400

       90                                                                    8100

   Sum

   Avg

 

The better model is   A ________   or  B _________

Why?  _______________________________________________

            _______________________________________________