MATH 221 - CALCULUS II
SYLLABUS - SPRING 2005
MWF 9:00 - 9:50, MRC 414
R 8:00 - 8:50 , MRC 4414
Instructor: Dr. Milan Luki´c
Office: MC 521
Office Hours: MF 10:00-10:50, TW 2:00-3:00 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) 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.
Supplements: Weaknesses in basic algebra and trigonometry often present a major obstacle for a progress in calculus. Even though we tried to address those in Calculus I, it is quite possible (likely?) that we will run into some of those difficulties again. It will be your responsibility to bring yourself to the level necessary. Two main tools that we used in Calculus I:
• A book: “Advanced Trigonometry” by C.V. Durell and A. Robson - Dover Publications;
• A computer software: ALEKS. It can be obtained through the Mc- Graw Hill publisher. We will talk some more about this software during the first week of class. might still be needed. However, I will not be monitoring use of those in this course.
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
2 MATH 221 - CALCULUS II SYLLABUS - SPRING 2005
main emphasis throughout the course will be on problem solving and developing thinking skills.
General Education courses at Viterbo are expected to make a positive effect on your Thinking Skills, Communication Skills, Life Value Skills, Cultural Skills, and Aesthetic Skills. Here are some ideas how this calculus course might influence those skills. Thinking Skills: We will do a lot of problem solving, trying to understand new (sometimes rather abstract) ideas, constantly question and try to justify our assertions, try to connect things we know in order to apply them in new situations. In addition to that, we will see examples of applying abstract mathematical concepts in the areas of science, economics, and some practical problems in general.
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: Students will analyze, evaluate and respond to ethical issues from an informed personal value system.
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
Ten Principles1 for a short list of those principles/lessons. 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.
(c) . . . participate in activity that broadens their customary way of thinking.
(d) In the context of Calculus, I expect that you will develop an appreciation of the history of Calculus and the role it has played in mathematics and in other disciplines.
Aesthetic Skills: Students will develop an aesthetic sensitivity. In the calculus context, we emphasize an appreciation for the austere intellectual beauty of deductive reasoning, and an appreciation for mathematical elegance.
Course-level Outcomes. Here we spell out some calculus specific outcomes related to the application of the general goals, listed above.
Content: Areas, distances, volumes; antiderivatives, definite integral; the
Fundamental Theorem of Calculus. Various techniques of integration, i.e., various applications of substitution rule and integration by parts. Integration of rational, algebraic, trigonometric, exponential and logarithmic functions. Numerical integration. Applications of calculus, including some differential equations. Infinite series, including power series, Taylor and
Maclaurin series, Binomial series.
MATH 221 - CALCULUS II SYLLABUS - SPRING 2005 3
In other words, we are talking about chapters 5 − 8 from the book.
Mathematical Reasoning: The emphasis will be on precise language and correct use of mathematical notation. We will constantly ask the “Why” question. As we learn “How” to do certain procedures, we will also try to understand why the things work in a particular way. We will constantly strive to justify our statements by reference to appropriate definitions, principles, rules, and theorems.
Problem Solving: We will solve a variety of problems both pure and applied, easy and difficult. As much as the time permits, we will explore different ways to solve a given problem. We will see how various abstract concepts arise naturally as a result of solving a major problem.
Communication: Learning how to communicate mathematics is very much a part of the process of learning mathematics itself. The standard expected from you in the written communication (HW, exams) is
Show your work! State your reasoning!
The oral communication:
• You are expected to participate in in-class discussion;
• One of the written assignments will have an oral component;
• Depending on the class size, and the availability of time, there might be an “in-class presentation” assignment.
Technology: You will probably use the calculator on a daily basis. I expect you to be comfortable in using calculator for computation and graph analysis. No class time instruction is planned for those tasks.
Regardless of the capabilities your calculator has, I don’t want you to use the calculator on HW/exams for anything other than basic graphing and numerical calculations!!
By now, all of you should have some familiarity with a CAS (Computer
Algebra System), such as DERIVE, for example. I encourage you to use a
CAS as a tool to check your calculations. However, we are going to raise your proficiency in using CAS to another level; see about the semester project below.
It is becoming customary these days to communicate your work via some form of electronic media. To type up your mathematics HW, assuming you want all your symbols and formulas look good . . . , is considerably more complicated than with an English paper, say. All of you are expected to take some more serious math/science courses after this one. The tool for typesetting mathematical, chemical, . . . formulas is (at least in my opinion)
LATEX. We will try to get some rudimentary “hands on” experience of dealing with LATEX as well.
Additional comments: 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. A basic goal of this course is to establish a solid foundation for that three-semester, and beyond, journey.
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, for this class, is at least 10 hours. Working every day on calculus problems is a must. Also, an active class
4 MATH 221 - CALCULUS II SYLLABUS - SPRING 2005 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.
Mathematics is not a spectator sport. It is learned by doing. Viterbo University is striving to be a Learner-centered institution. That entails an expectation of maturity and taking responsibility for their learning on the part of students. I see my job as one helping you succeed in this learning process.
In spite of my best efforts, I may not always manage to say things the way which best leads to your full comprehension. You can also help me by providing as much of a feedback as you can. I will try to do a formal evaluation survey around the middle of the semester. Other than that, I find the questions in class, and especially when someone comes to my office for assistance, very helpful.
As a further assistance to you:
• About a week prior to any exam, you will receive a practice exam which will be, in terms of format and type of problems, very much like the actual exam.
• I am asking you to keep a The Learner’s Journal. This is to be a separate notebook that should contain a record of your study/practice on daily basis. I would also like you to keep a time log - date, hour from-to - for each study session. I would prefer that you use a pen for writing in that journal. If you are going to use pencil, then please do not use erasers, and in any case, do not tear pages out. For a learning to take place, you have to try to do something. In trying, you are likely to make mistakes. The real learning will start taking place once you start understanding and correcting your mistakes.
You turn that journal in together with your exam, and then you will be graded for the portion of that journal that covers the period preceding that current exam. Up to 30% of the exam score is possible to earn this way.
The elements that will play the key role in grading the journal are
– Organization - readability: In order to evaluate, I have to able to read it first. I should not have a difficult time navigating through those notes.
– Mathematical correctness.
– The quality of the work and the amount of time spent on studying.
• Take-home problems: These assignments should test/help a better integration of material. Some will include more difficult problems. One of those assignments will be a group HW. In general, I encourage you to find some time to study together, but unless stated otherwise, the HW is to be written up on your own.
I will try to space those assignments so that you could have some time to catch up. This should leave significant room for exploring the book on your own, and I encourage you to find your own balance between solving some problems in full, and just sketching solutions to some. You should try to read, meaning to the point where you really understand the question, most of the book problems. The work in class, your book, HW, and practice exams should give you a pretty clear idea what is that you are expected to learn. It is your job to, perhaps through
MATH 221 - CALCULUS II SYLLABUS - SPRING 2005 5 trial and error, find learning strategies that work best for you. Remember, learning is something you do, rather than something I do to you.
Grading will be based on two in-class exams (100 points each), a cumulative final exam (200 points), a group project (150 points), class participation (5%), take-home problems, and the Learner’s Journal (30% of the corresponding exam).
There might be an in-class presentation (worth 50 points), if the time permits. The project will involve some use of technology (CAS and LATEX). The details will be given later. You will be required to work hard, and will have every opportunity to show what you have learned.
One of the writing 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.
One, or more, 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:
Viterbo Policies2 and 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.
 D. Berlinski, A Tour of the Calculus, Pantheon, 1995.
 M. Cohen et.al., Student Research Projects in Calculus, Mathematical Association of America,
 C.V. Durell and A. Robson, Advanced Trigonometry, Dover.
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 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
Antiderivatives Jan 17 Chapter 4
Definite R, FTC Jan 24, Chapter 5
Integration techniques Jan 31 Chapter 5
More R, Exam 1 Feb 7 Chapter 5
Numerical integration Feb 14 Chapter 5
Sequences Feb 21 Chapter 8
Power Series Feb 28
Spring Break March 7
Taylor Series March 14
Series - applications, Exam 2 March 21 Easter break
Applications of R March 29 Chapter 6
April 4 Chapter 6
Differential Equations April 11 Chapter 7
Project presentations April 25
Review May 2
Classes begin: January 17, 2005.
Midterm break: March 5-13.
Easter Break: March 24 − 28.
Last day of class: Friday, May 6.
No class: -
• Friday, April 15;
due to my absence - attending a conference.
Semester Exams: • Exam 1: at the end of Chapter 5
• Exam 2 - Chapter 8.
Final Exam: Monday May 9, 12:50-2:50
This syllabus is tentative and may be adjusted during the semester.
I am looking forward to explore this fascinating subject with you, and for all of
us to have an interesting and enjoyable semester.