MATH 220 - CALCULUS I
MWF 12:10 - 1:00, MC 406
T 11:00am - 11:50am , MC 406
Instructor: Dr. Milan Luki´c
Office: MC 521
Office Hours: MWF 10:00-10:50, Tuesday 2:00-2:50, or by appointment
Phone: (608) 796-3659 (Office); 787-5464 (Home)
Course essentials. I am one of those who believe that Calculus is among our species’ deepest, richest, farthest-reaching and most beautiful intellectual achievements.
This course provides an opportunity for you to discover and appreciate some of the jewels of Calculus. It is my privilege to be in a position to assist you in making those discoveries.
Course Description: (from the catalog) Limits and continuity. Derivatives and applications. Differentiation of polynomial, rational, trigonometric, logarithmic and exponential functions.
Prerequisite: Acceptable placement score (or ACT math score of at least 28), or at least 3 years of high school algebra and trigonometry with at least a B average, or a grade C or better in MATH 180.
This course is recommended as a general education liberal studies elective course.
Text: James Stewart, CALCULUS, Concepts and Contexts, Brooks Cole.
You will find two versions of the textbook in the bookstore. The “bigger” book covers a 3-4 semester volume of material and is intended for those who plan on taking Calculus II and III (math majors, chemistry majors, . . . )
The smaller book is for those who plan to take Calculus I only. We plan to cover Chapters 1 through 4 of the textbook.
The General Education aspects of this course. The content and the methods of this course are designed in accordance with general education objectives and the work in this course should help you in developing a number of skills included in the NCTM (National Council of Teachers of Mathematics) standards for mathematics education, and also being among the general education objectives at Viterbo. The main emphasis throughout the course will be on problem solving and developing thinking skills.
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Thinking Skills: For some of you this course might serve to satisfy the math competency requirement, for others this will be just one of the mathematics courses required by your major/minor program. In any case, the main goal of this course is to help you develop and strengthen the foundations of your analytical thinking.
Every day, we are faced with numerous questions, such us: Should I run through this yellow light? What should I eat today? Which courses to enroll next semester? . . . We often have to resolve those questions, make appropriate decisions, and then act according to those decisions. The thinking process required for resolving all kinds of questions, puzzles, problems, is known by the name of analytical thinking. We can use mathematics as a convenient tool for working on the analytical thinking skills. In order to achieve this goal of developing and strengthening your analytical thinking skills, via mathematics, our focus will be on the following questions:
• What does it mean to do mathematics?
• What does it mean to think mathematically?
• What does it mean to understand a piece of mathematics?
In other words, I expect you to:
• Do some mathematics;
• Use mathematical reasoning, i.e., ask questions such as:
– What does (something) mean?
– How did we get from A to B?
– Is this (a statement, claim, formula, . . . ) correct?
– How do I know that it is correct?
• Strive to understand every idea, concept, problem, solution that we
encounter in this course.
The mathematical content (calculus) which we will use to achieve these objectives will expose you to a variety of problems and ideas. You will probably use everything you have learned in mathematics so far, and will also learn some more, quite a bit more, about basic algebra and trigonometry.
The basic principles (strategies) of thinking that we will use over and over go beyond calculus, beyond mathematics. I believe that those principles have a value of lessons for life. Please check
http://my.execpc.com/~lmilan/ten-principles.htmlfor a short list of those principles/lessons.
Communication Skills: Students will . . .
(a) . . . read with comprehension and the ability to analyze and evaluate.
(b) . . . listen with an open mind and respond with respect.
(c) . . . access information and communicate using current technology.
Life Value Skills: (a) Students will analyze, evaluate and respond to ethical
issues from an informed personal value system.
Cultural Skills: Students will . . .
(a) . . . understand culture as an evolving set of world views with diverse
historical roots that provides a framework for guiding, expressing, and
interpreting human behavior.
(b) . . . demonstrate knowledge of the signs and symbols of another culture.
MATH 220 - CALCULUS I SPRING 2003 3
(c) . . . participate in activity that broadens their customary way of thinking.
Aesthetic Skills: (a) Students will develop an aesthetic sensitivity.
Core (General Education) Skill Objectives. Here we spell out some specific
objectives related to the application of the general goals, listed above, to calclulus.
Thinking Skills: Students will . . .
(1) . . . gain a better understanding of the concept of a function;
(2) . . . use graphs to estimate related values, relative rates, extreme values,
(3) . . . learn how to do those things algebraically;
(4) . . . develop a concept of limit;
(5) . . . understand the derivative;
(6) . . . use calculators and computers efficiently as tools;
(7) . . . also learn how to estimate functions by polynomials, so that the
numbers such as p3 30, ln 5, log3 5, sin 1, arctan 2, etc. can be estimated
using simple addition and multiplication only;
(8) . . .model problems from geometry and other disciplines using calculus;
(9) . . . further improve their ability to communicate mathematical ideas
and solutions to problems.
(10) . . . improve their problem-solving ability.
(11) From a most general perspective, the student should see growth in his/her mathematical maturity. The three-semester sequence of calculus courses form the foundation of any serious study of mathematics or other mathematically-oriented disciplines.
Communication Skills: (1) Written: Students will:
(a) . . . state their reasoning when presenting solutions of problems
on exams and assignments.
(b) . . . do group work (labs and practice exams) throughout the
course, which will involve both written and oral communication.
(c) . . . use current technology (graphing calculators, Derive and/or
Maple V) to solve problems and communicate solutions and explore
(d) . . . improve their ability to write logically valid and precise mathematical
proofs and solutions.
(2) Oral: Students will communicate mathematics orally via in-class discussions,
in-class presentations, and via some assignments that will
have an oral part.
Life Value Skills: Students will . . .
(a) . . . develop an appreciation for the intellectual honesty of deductive
(b) . . . listen with an open mind and respond with respect.
(c) . . . understand the need to do one’s own work, to honestly challenge
oneself to master the material.
Cultural Skills: Students will . . .
(a) . . . develop an appreciation of the history of Calculus and the role it
has played in mathematics and in other disciplines.
(b) . . . learn to use symbolical notation correctly and appropriately.
Aesthetic Skills: Students will . . .
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(a) . . . develop an appreciation for the austere intellectual beauty of deductive
(b) . . . develop an appreciation for mathematical elegance.
Course Philosophy and Procedure. Two key components of a success in the course are regular attendance and a fair amount of constant, everyday study. You should try to make sure that your total study time per week at least triples the time spent in class. Working every day on calculus problems is a must. Also, an active class participation, working in small groups, not hesitating to ask me for help both in class and in my office can greatly enhance the success and quality of your learning. You should also use the Learning Center facilities (MC 320) as much as possible.
Grading will be based on three in-class exams (100 points each), a cumulative final exam (200 points), class participation, take-home problems, group practice exams (25 points each), and two in-class presentations (50 points total). You will be required to work hard, and will have every opportunity to show what you have learned.
Some of the homework assignments will be graded in two parts - the second part will require you to come to my office and explain your reasoning, answer some questions. Some of those assignments will be “group assignments”.
In all your work, written and oral, it is essential to provide explanations, justify your reasoning. My grading scale is
A=90%, AB=87%, B=80%, BC=77%, C=70%, CD=67%, D=60%.
The following exceptions to that scale are possible:
• An A on the final exam (more than 180/200 points) will raise your grade up, one letter, i.e., a B will turn into an A, a BC will become AB, . . . .
• An outstanding presentation can raise your grade up a half letter, i.e., a C will turn into a BC, . . . .
• If one is failing the course by the end of the semester, but has over 40% average on exams, and earns at least 55% points on the final, he/she can get a D for the final grade.
• If one is passing the course by the time of the final exam, but earns less than 30% points (a score less than 60/200), that will result in an F for the final grade.
1. The University facilities and policies
The Learning Center: provides a number of ways to assist you. In particular, there are drop in hours MTWRF 11:00-11:50 and 3:10-4:00.
Important University Policies: Please follow the links at:
http://my.execpc.com/~lmilan/viterbo-policies.htmland read the corresponding statements on attendance, plagiarism, and sexual harassment.
Americans with Disability Act: If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me and Wayne Wojciechowski in Murphy Center Room 320 (796-
3085) within ten days to discuss your accommodation needs.
MATH 220 - CALCULUS I SPRING 2003 5
 D. Berlinski, A Tour of the Calculus, Pantheon, 1995.
 M. Cohen et.al., Student Research Projects in Calculus, Mathematical Association of America, 1991.
 Leonhard Euler, Introductio in Analysin Infinitorum, 1748. Translated as Introduction to
Analysis of the Infinite, in two books. Viterbo library has Book II. I would say better, or at least more interesting one is Book I, which you can find in the UWL library.
 Leonhard Euler, Institutiones Calculi Differentialis, 1755. Euler published this book in two volumes. The first volume was translated to English and published as Foundations of Differential
Calculus, Springer, 2000.
 E. Maor, e - The Story of a Number, Princeton University Press, 1994.
 Carl Boyer, The History of the Calculus and its Conceptual Development, Dover, New York,
Topic Week Book - Section
Precalculus Jan. 13 Chapter 1, Appendix A-C
History – Jan. 20, Jan. 27 Other books, Internet important problems
Functions Jan. 27, Feb. 3 Chapter 1
Limits Feb. 10, Feb. 17 Chapter 2
Continuity Feb. 24 Chapter 2 and 4
Derivative - by definition Mar. 3, Mar. 10 Chapter 3
Derivative - rules Mar. 17, Mar. 24 Chapter 3
Presentations Mar. 31; Apr. 28
Basic Theorems Apr. 7 Chapter 4
Linear approximation Apr. 7 Chapter 4
Optimization Apr. 14 Chapter 4
Science, Economics Apr. 21 Chapter 4
Graphing functions Apr. 21 Chapter 4
Classes begin: January 13.
Midterm break: March 10-14.
Easter vacation: April 17-21.
Easter: April 20.
Last day of class: Friday, May 2.
No class: -
• Friday, March 28;
• Friday, April 25;
due to my absence - attending some conferences.
Semester Exams: • Exam 1: Friday, February 14.
• Exam 2: Tuesday April 1.
• Exam 3: Wednesday, April 30.
Final Exam: Friday, May 9, 7:40-9:40 a.m.
This syllabus is tentative and may be adjusted during the semester.
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I am looking forward to explore this fascinating subject with you, and for all of
us to have an interesting and enjoyable semester.