MATH 221 - CALCULUS II
SPRING 2004
MWF 12:10am - 1:00am, MC 429
R 8:00am - 8:50am , MC 429
Instructor: Dr. Milan Luki´c
Office: MC 521
Office Hours: MF 2:00-3:00, T 12:00-12:50 or by appointment
Phone: (608) 796-3659 (Office); 787-5464 (Home)
e-mail: lmilan@execpc.com
WWW: http://my.execpc.com/˜lmilan
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)
Applications of the integral and techniques of integration. Trigonometric,
logarithmic and exponential functions. Prerequisite: grade of C or
higher in 220.
Text: James Stewart, CALCULUS, Concepts and Contexts, Brooks Cole.
Second edition.
Core (General Education) Skill Objectives:: (1) Thinking Skills:
(a) Students will use reasoned standards in solving problems and
presenting arguments.
(2) 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.
(3) Life Value Skills:
(a) Students will analyze, evaluate and respond to ethical issues from an informed personal value system.
(4) 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.
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(c) . . . participate in activity that broadens their customary way of thinking.
(5) Aesthetic Skills:
(a) Students will develop an aesthetic sensitivity.
Specific Course Goals:: Students will . . .
(1) . . . expand and apply skills and knowledge gained in the first semester of Calculus to the topics of integration and applications of integration.
(2) . . . gain knowledge and skills, and the ability to apply these, to a variety of situations which might be encountered in the world of mathematics, science, or engineering.
(3) . . . further improve their ability to communicate mathematical ideas and solutions to problems.
(4) . . . improve their problem-solving ability.
(5) 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.
General Education Course Objectives:: (1) Thinking Skills: Students will . . .
(a) . . . understand the basic concept of the integral as the limit of a sum.
(b) . . . understand the Fundamental Theorem of Calculus and learn how to use it to evaluate definite integrals.
(c) . . . explore differentiation and integration formulas for a variety of functions, including exponential and logarithmic, trigonometric and inverse trigonometric, hyperbolic and inverse hyperbolic functions.
(d) . . . explore a variety of integration techniques, such as integration by parts, partial fractions, various substitution methods and methods of approximate integration.
(e) . . . investigate a wide variety of applications of integration, including solving simple differential equations, finding areas and arc lengths, and finding volumes and surface areas of solids of rotation.
(f) . . . broaden their ability to work with functions by exploring parametric equations and polar coordinates, including graphing, and differentiation and integration applications.
(g) . . . explore conic sections, including their treatment in polar form.
(h) . . . study convergence of infinite series.
(2) Communication Skills: Students will . . .
(a) . . . collect a portfolio during the course and write a reflection paper.
(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 and Maple V) to solve problems and communicate solutions and explore options.
(d) . . . improve their ability to write logically valid and precise mathematical proofs and solutions.
MATH 221 - CALCULUS II SPRING 2004 3
(3) Life Value Skills: Students will . . .
(a) . . . develop an appreciation for the intellectual honesty of deductive reasoning.
(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.
(4) 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.
(5) Aesthetic Skills: Students will . . .
(a) . . . develop an appreciation for the austere intellectual beauty of deductive reasoning.
(b) . . . develop an appreciation for mathematical elegance.
Content:: We plan to cover Chapters 5 through 8 of the textbook.
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. 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 two-three in-class exams (100 points each), a cumulative final exam (200 points), class participation, take-home problems,
group practice exams (25 points each), . . . .
My grading scale is
A=90%, AB=87%, B=80%, BC=77%, C=70%, CD=67%, D=60%.
I am looking forward to explore this fascinating subject with you, and for all of us to have an interesting and enjoyable semester.
The Learning Center: provides a number of ways to assist you. 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.
Important dates.
Classes begin: January 12.
Humanities Symposium: February 2-4.
Midterm break: February 28 - March 7.
Easter Vacation: April 8-12.
No classes, due to my conferences: Friday, April 16;
Last day of class: Friday, April 30.
Final Exam: May 4, 9:50 - 11:50.
This syllabus is tentative and may be adjusted during the semester.
References
[1] D. Berlinski, A Tour of the Calculus, Pantheon, 1995.
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[2] M. Cohen et.al., Student Research Projects in Calculus, Mathematical Association of America,
1991.
[3] E. Maor, e - The Story of a Number, Princeton University Press, 1994.
[4] J. Stuart, Calculus, Early Transcendentals, Brooks-Cole Publishing, 1995.
[5] E. Wade, Jr., et.al., Maple V Flight Manual, Brooks-Cole, 1992.
Links:
: Viterbo College Home Page
: Mathematics Department Home Page
: My Home Page