SYLLABUS

 

Course:       MATH 217  Calculus I                 Term:   Winter 2007-08                    Meets:   MTWF 10:40 – 11:50

 

Instructor:   Craig Kalicki         Office:   HH-284        E-mail:   craig.kalicki@briarcliff.edu       Phone:   279-5541

 

Text:           Stewart, Essential Calculus Early Transcendentals, First Edition, Thomson Brooks/Cole, ã2007
                     ISBN 0-495-01428-1

 

Prerequisites:

           

Students in this course should have had at least three years of high school mathematics including some
trigonometry, but four years is highly recommended.  Anyone who does not meet these prerequisites is
advised to take MATH 112 Elementary Functions or an equivalent course as additional preparation.

 

Goals of course:

 

MATH 217 is a survey of topics in beginning calculus and is intended for students in mathematics, the
physical sciences, and pre-engineering.  Students in this course should expect to

   1)  gain an appreciation of calculus as an organized body of mathematical tools with numerous applications
           in the sciences.

   2)  develop some of the mathematical skills necessary to understand and apply models involving the
           concepts of calculus.

   3)  learn to discover mathematical results by experimentation, examining evidence, and formulating and
           testing conjectures.
   4)  become competent in the use of technology as a tool for discovering, learning, and applying
           mathematics.

 

General education:

 

MATH 217 is designated as a basic quantitative literacy (QL) course.  Quantitative literacy at Briar Cliff is
defined as “a collection of acquired skills, knowledge, and dispositions that enable a person to deal with
quantitative issues and problems that arise in academic study, in the workplace, and in daily life.” 
After successfully completing this course, students will be able to do the following at a basic level:

   -  read and understand quantitative information.
   -  use algebraic and graphical methods to solve problems in context.
   -  interpret mathematical models and draw inferences from them.
   -  compare and assess solutions of quantitative problems.
   -  effectively communicate results of quantitative investigations.
   -  recognize limitations of mathematical methods.
   -  use appropriate technology as an aid for solving problems.

Grading procedure:
          

Three exams @ 15%

45%

 

A   = 100 - 93

C+ =  76 - 74

Final exam

25%

 

A-  =  92 - 90

C   =  73 - 67

Text assignments

20%

 

B+ =  89 - 87

D+ =  66 - 64

Computer lab reports

10%

 

B   =  86 - 80

D   =  63 - 55

Total

100%

 

B-  =  79 - 77

 

 

Grading rubric:

 

The grading rubric below will be used to assess written work, including text assignments and exam questions.

A separate rubric will be distributed for lab reports.

 

        Level

              Characteristics

 4     Superior

Solution is correct and clearly stated.
All essential steps are shown, are readable, and are in logical order.
Appropriate graphical displays are included and are informative.

 3     Good

Method of solution is substantially correct.
Minor algebraic or arithmetic errors occur.
Most essential steps are shown.
Appropriate graphical displays are included.

 2     Adequate

Method of solution is flawed but some elements are correct.
Mathematical tools are appropriate but incorrectly applied.
Some essential steps are not clearly stated or are omitted.
Graphical displays are poorly constructed or inappropriate.

 1     Minimal

Solution is attempted but significant errors occur.
Mathematical tools are inappropriate or incorrectly applied.
Some essential steps are omitted.
Graphical displays are inappropriate or omitted.

 0     Unacceptable

Solution is omitted or an answer is given with no supporting evidence.

 

Expectations of students:

 

1)  Attend class and computer lab on a regular basis.  Three or more unexcused absences should be considered

        excessive.  If you miss a lab, you will need to make it up on your own time.

2)  Read and review the text as needed, paying particular attention to terminology and examples.  There will be
        no specific reading assignments, but it will be assumed that you are reading the material in the text that is
        relevant to lectures and discussions in class.
3)  You may want to take some notes in class, but trying to transcribe lectures is highly inadvisable.  Most of the

        material presented in class is also in the textbook.  The most important activities in class are listening and
        asking questions.

4)  Come to class prepared to ask questions and present solutions of assigned problems.  Due to time
        constraints, not all assigned problems will be discussed in class.  Solutions of selected problems will be
        placed in a reserve folder in the main library.  Doing text assignments and studying for exams with others
        in the course is encouraged. 

5)  Make use of your instructor's office hours.  Ask for help whenever difficulties arise or when you feel the need
        for advice or encouragement.

6)  Hand in reasonably complete text assignments.  Credit will be given for handing in assignments and selected
        problems will be graded.  Answers to odd-numbered problems are in the back of the text.  Assignments are
        to be handed in at the beginning of class on the date due.  No late work will be accepted except in cases
        of serious illness or family emergency. 
7)  Do all lab exercises and be prepared to discuss results obtained and any problems encountered at the next
        class meeting.  Labs are intended to be cooperative learning experiences; working with a lab partner is
        expected.  The report for each lab is due at the next lab meeting.  Carelessly written lab reports may be
        returned for resubmission.

8)  Show evidence of learning on exams.  Exams will be thorough and sufficient study time must be allotted.
        Exams will require understanding of concepts as well as ability to perform computational procedures. 
        Unexcused absence from an exam will result in an automatic grade of zero for that exam.

 

Technology:

 

Each student should have a graphing calculator available for use during class and exams.  Keep the manual
supplied with the calculator and learn to use the calculator effectively.  Recommended models are the TI 84+,
86, or 89.  The software Derive 6 is installed on the Briar Cliff network and will be used in all lab sessions. 
Derive is very user-friendly, and students should expect to become reasonably proficient in its use by the end
of the term.

 

Student learning outcomes:

 

The specific expected learning outcomes for this course are listed below.  Assessment of the degrees to which
these outcomes have been achieved will be done via written exams, homework assignments, and lab reports.

 

Students who have completed MATH 217 will be able to

   1)   define and understand the concept of a function of one variable.
   2)   represent and interpret functions using formulas, tables, and graphs.

   3)   apply functions as mathematical models.

   4)   perform algebraic operations on functions.

   5)   understand the concept of limit of a function.

   6)   use technology to approximate limits.

   7)   define and understand the concept of continuity.

   8)   define and understand the concept of the derivative of a function.

   9)   find derivatives analytically using basic rules.

   10)  use the process of implicit differentiation.

   11)  apply the derivative to problems involving rates of change.          
   12)  compute and apply linear approximations of functions.

   13)  find and apply derivatives of common transcendental functions.  

   14)  find absolute and local extreme values of functions.

   15)  analyze the graphical behavior of functions.
   16)  solve applied optimization problems.

   17)  find antiderivatives analytically using basic rules. 
   18)  understand the concept of definite integral.

   19)  approximate the values of definite integrals using technology.

   20)  understand and apply the Fundamental Theorem of Calculus.

  

Course outline:

 

Ch 1  Functions and Limits   [7 classes]

   Representations of functions /  functions as models /  catalog of basic functions /  transformations of
   functions /  composition of functions  /  limit of a function /  properties of limits /  continuity /  limits
   involving infinity.

 

Ch 2  Derivatives   [9 classes]

   The tangent line problem /  the instantaneous velocity problem / average rate of change /  derivative of a
   function / basic differentiation rules /  Chain Rule /  implicit differentiation /  related rates / linear
   approximations /  differentials.

                         

Ch 3  Inverse Functions   [7 classes]

   Exponential functions /  inverse functions / logarithmic functions /  derivatives of exponential and logarithmic
   functions /  growth and decay models /  inverse trig functions /  hyperbolic functions /  indeterminate forms. 

 

Ch 4  Applications of Differentiation   [8 classes]

   Extreme values of a function /  Extreme and Mean Value Theorems /  monotonicity and concavity / 
   analyzing graphs /  optimizations problems /  Newton’s method /  antiderivatives /  rules for antiderivatives.  

                  

Ch 5  Integrals   [6 classes]

   The area problem / displacement and distance /  the definite integral / approximating definite integrals /
   Fundamental Theorem of Calculus /  substitution rule.

 

 

Ó2007 by  Craig Kalicki PhD,  Briar Cliff University,  Sioux City  IA  51104