Department of Mathematics and Computer Science
Spring Syllabus 2004
SECT 03 - MEETS TR 11:00-1:00 RUSSELL 327
MATH 240: Calculus I [4 CREDITS]
This is the first of three semesters of Calculus. There will be
a short review of precalculus functions with an emphasis on graphical,
numerical, and modeling applications. Calculus topics to be covered
will include:
limits, continuity, derivatives and their interpretations, tangent
line approximations, the definite integral as a limit of Riemann sums,
applications of the definite integral to area and average value, the Fundamental
Theorem of Calculus, rules of derivatives, formulas for derivatives of
precalculus functions, implicit functions, economics applications, optimization
and modeling, and Newton’s method.
The course requires that each student have a graphing calculator.
[recommend TI-83]. Students will be required to complete assignments
and/or projects using the computer algebra system, Mathematica, available
in all campus computer lab.
INSTRUCTOR: CANDACE H. TODD, PH.D OFFICE: RUSSELL 318
EMAIL: chtodd@samford.edu TELEPHONE: 726-4122
OFFICE HOURS: 10:30 – 11:15 MW; 2:15
– 2:30 MW; 10:00 - 11:00 TR
Other hours by appointment.
PREREQUISITE: Math 150: Precalculus, or Placement
Score
TEXTS (1) Calculus, by Hughes-Hallett, D., et.al, third ed.; Published
by John Wiley & sons, 1998, New York.
Chapter 1: A Library of Functions - review
Chapter 2: Key Concept: The Derivative
Chapter 3: Short-Cuts to Differentiation
Chapter 4: Using the Derivative
Chapter 5: Key Concept: The Definite Integral
(2) Optional Text Introduction to Mathematica for Calculus Students,
by Bruce W. Atkinson and David L. Foreman
IMPORTANT DATES
The final exam will be given Tuesday, May 18, 2004 from 10:30am - 12:30
pm.
ADDITIONAL REQUIREMENTS FOR COURSE:
(1) Separate Notebook for daily notes and handouts
(2) Black bound homework book
(3) Formatted IBM disk.
HOMEWORK:
Students are expected to DO their homework in a standard black composition
book and use Mathematica when necessary. READ ALL OF THE TEXTBOOK sections
assigned and keep the composition book organized from the first assignment
to the last homework problems in order. Always be prepared to discuss
these problems in class. A separate notebook for daily notes is important.
ATTENDANCE POLICY:
Absences dramatically affect your understanding of the material and
ultimately your grade. Hence, I will expect to see you each time
the class meets. You are permitted 6 absences without penalty for TR attendance
in this class. Thereafter, at the discretion of the instructor, a maximum
5% penalty off the final course grade from each class missed will be assessed.
There will be no distinction between "excused" or "unexcused" absences.
Students are encouraged to save their allowable absences for critical times.
ACADEMIC INTEGRITY IS EXPECTED AND THE CLASS WILL FOLLOW THE RULES OF THE STUDENT HANDBOOK.
"Samford University complies with Section 504 of the
Rehabilitation Act and the Americans with Disabilities Act. Students
with disabilities who seek accommodations must make their request through
the Advisor for Students with Disabilities in Disability Support Services.
This office is located in Counseling Services on the lower level of Pittman
Hall, or can be reached by calling 726-4078 or 726-2105. A faculty
member will grant reasonable accommodations only upon notification from
the Disability Support Services."
ASSIGNMENT OF EVALUATION OF POINTS:
75% 3 tests 25% each timed exams
20% Comprehensive Final Exam
5% Homework/Quizzes and Daily Work
[Black Composition Notebook of homework from entire semester]
Mathematica grades will be within the exams or under daily work.
The grading scale will follow the +/- process outlined in the catalog.
The scale is in percentages.
93-100 A 73-76 C
90-92 A- 70-72 C-
87-89 B+ 67-69 D+
83-86 B 63-66 D
80-82 B- 60-62 D-
77-79 C+ BELOW 60 F
MAKEUP POLICIES:
No makeup tests will be given. It is your responsibility to notify
the professor IN WRITING before a test date to explain the reason for missing
a test.
EXPECTED TIME INVESTMENT:
You should expect to spend 2 to 3 times the number of class hours per
week [8 - 12 hours for this course alone outside of class] “learning-preparing”
for class each week. Your effort in this course is expected to be of the
highest professional quality.
You are expected to attend all classes. If you miss
a class, you are responsible for the material during that class.
(THIS INCLUDES ASSIGNMENTS!)
OBJECTIVES
Calculus is one of greatest achievements of the human intellect. Thus
we will not study calculus as a collection of rules and procedures, but
instead learn the mathematical concepts and practical value of calculus.
The student will acquire clear intuitive pictures of the central ideas
of calculus. The student will reason with these ideas and explain the reasoning
clearly in plain English. As well, the student will examine some
of the theory of calculus thus developing a deeper, richer understanding
and appreciation for its beauty. Also, the student will study calculus
as a powerful tool for analyzing real world problems.
Students will gain a knowledge of integral and differential calculus. Students also will gain experience using appropriate technology: TI-83 graphing calculator and the computer algebra system, Mathematica. With these tools students will discover the role, nature, and limitations of calculators and computers as tools in solving problems and will have exposure to technological advances that affect the teaching of mathematics. Students will use technology in problem solving and in exploring mathematical concepts. Students will use approximation and estimation skills to assess the reasonableness of solutions. During the course students will develop concrete models of mathematics concepts; use concrete models to develop algorithms; select or create appropriate models to solve problems in mathematics and in other disciplines; integrate strategies learned in mathematics into solutions of the problems encountered in daily living.
This course will emphasize learning using many different techniques including lecture, graphing calculator, computer algebra system, individual and group problem solving and critical thinking skills which are needed in the workplace and must begin in the classroom.
FUNCTIONS:
Students will
• Identify functions from their graphs and numerical properties.
• Describe and contrast the different types of functions.
• Employ properties of functions in real world problem solving.
• Decide which type of function best fits a given problem.
• Derive the formula for the inverse of a given function and apply
to a real world problem.
• Define and apply the concept of continuity.
DERIVATIVES:
Students will
• Describe the derivative as a limit process.
• Give examples of failure of differentiability.
• Compare the analytical, graphical, and numerical interpretations
of the derivative and use these interpretations in real world problems.
• Derive formulas for derivatives by the limit process and by application
of derivative theorems.
• Classify critical points and summarize the properties of a graph
by analyzing the first and second derivatives.
• Break down an optimization problem by identifying the relevant variables,
functions, and intervals.
• Decide, in an optimization problem, which tests are appropriate.
• Justify the solution of word problems, interpret the results, and
validate them with examples.
• Decide when Newton’s method applies and use it to solve application
problems.
• Apply tangent line approximations.
INTEGRALS:
Students will
• Describe the definite integral as a limit of Riemann sums.
• Estimate a definite integral by using a table of function values
or a graph.
• Compare and contrast the Riemann sum method to the method of evaluation
using the Fundamental Theorem of Calculus.
• Decide which of the above two methods may be more useful in a given
application.
• Interpret the definite integral as it applies to velocity, distance,
area, and average function values.
• Formulate general results involving definite integrals on the basis
of examples.