SYLLABUS, MATH 1520 Spring, 1996-1997

INSTRUCTOR: Alice Iverson

TEXT: Calculus in Context by James Callahan, David Cox, Kenneth Hoffman, Donald O'Shea, Harriet Pollatsek, Lester Senechal published by W. H. Freeman and Company.

EQUIPMENT: Every student must have available a scientific calculator for use in class and homework assignments. Bring it to class every day.

TIME and PLACE: 9:15 a.m.-10:20 a.m., MWF and 11:00 a.m.-12:50 p.m., TH. All classes are held in C21.

FINAL EXAM: Friday, May , a.m. - a.m.

PREREQUISITES: MATH 1510 or the equivalent.

OFFICE HOURS: 2:15 p.m.-3:15 p.m. MWF., 1:00 p.m.-2:00 p.m. Th. My office is located on the sixth floor of Carlson at the west end of the hall. If it is impossible for you to see me during my office hours, please make an appointment to see me at another time.

I am eager to help if you experience any difficulty understanding the concepts or doing the problems of calculus Also, it would be my pleasure to get to know you personally.

INTRODUCTION: Calculus is one of the greatest achievements of the human intellect. Inspired by problems in astronomy, Newton and Liebniz developed the basic ideas of calculus 300 years ago. Since then, each century has demonstrated the power of calculus to illuminate questions in mathematics, the physical, social and biological sciences and engineering. In the sequence of two courses, Math 1510 and Math 1520, you will learn the traditional concepts of calculus in the context of these questions, which are still vital in the late twentieth century. There will be less emphasis on the techniques of calculus and more on the overall view of these underlying questions that calculus is designed to clarify.

In this course, as in MATH 1510, we will think of mathematics as an experimental science. You learn mathematics by doing mathematics. Calculus is somewhat like a participatory sport. The more you do it the more you will learn. There are not as many routine problems in this course as you may be accustomed to in you previous mathematics courses. But you will be expected to think more about what you are doing.

COMPUTERS: We will continue using computers, where appropriate, as a tool for learning calculus and its applications. In addition, the computers will radically enlarge the range and complexity of questions we will be able to explore and the ways we can address them. They will provide the computational power to solve some very complex real world problems that we will be studying.

You will be expected to use a calculator or computer to solve a particular problem in the textbook without specific instructions to do so. However, for some kinds of problems you will be told explicitly not to use a calculator or computer because for those problems it is important that you develop pencil and paper skills.

Although the Class Schedule designates Monday, Wednesday and Friday as lecture days and Thursday as a lab day, we will make no such distinction. Sometimes we will be using the computers on MWF and sometimes we will have lecture/discussion on a Thursday.

OBJECTIVES: By the end of the semester you should

¥ Have a firm intuitive grasp of the concepts of Calculus II: the integral, the fundamental theorem of calculus, periodicity, dynamical systems, functions of several variables, series and approximations, and techniques of integration.

¥ Have developed a stronger intuitive grasp of the fundamental concepts of calculus I: functions, limits, local linearity, the derivative, continuity, differential equations, partial derivatives, optimization and Riemann sums. You should be able to give informal definitions of them and apply them in a variety of contexts.

· Have increased your skill in learning mathematics independently through reading the text and working through the explanations and examples. The ability to learn independently is perhaps the most important goal of education.

¥ Be able to use successive approximations as a key tool of calculus.

¥ Know how to apply calculus to such areas as oscillating springs, the pendulum, predator- prey ecology, the SIR model, etc.

¥ Know how to read, use and modify programs which have been prewritten in Mathematica.. Programming skills are not required or developed in this course.

¥ Have developed skill in applying the computer programs Mathematica and x-Function to the problems of calculus where appropriate.

¥ Have become proficient in expressing your understanding of mathematical concepts in good English.

¥ Have developed skill in working together with another student to learn mathematics

GROUND RULES: ¥ More than two absences will result in your grade being lowered by one letter.

¥ Students whose chairs are facing away from the front of the room should turn their chairs around and face the front when I am lecturing or leading a class discussion.

¥ When I am lecturing or leading a class discussion you are asked not to talk to one another, even if you are discussing the lesson being presented. If you do so I will ask you to leave the room and consider you to be absent that day. It is also not acceptable to be working individually on homework for calculus or any her course during lecture/discussion periods.

¥ If I am lecturing or leading a discussion the computers should be turned off. If you have your computer on when I am lecturing or leading a discussion, I will ask you to turn it off and consider you to be absent that day.

HOMEWORK ¥ Plan on spending time on your calculus homework on the average of two hours outside of class for every hour in class. You will find that if you do not keep up with the homework day by day you will not understand the lecture/discussions. Reading the text before the lecture/discussion is absolutely essential. Because mathematics is a cumulative subject, cramming for examinations is not a very successful way to learn it.

¥ All homework should be clearly labeled with the Chapter and Section of the Text that is the source of the problems and the problems should be clearly numbered.

¥ Computer homework should be saved so that your three initials appear in the title. Usually computer homework will be done with two students working together on the same computer. If the work has been done by two of you working together, both sets of initials should appear in the title. When two people have worked together on a homework assignment, both should sign it as a pledge that both have contributed a fair amount of the required work.

¥ Homework will be assigned each class period and will usually be due the next class period by 4:30 p.m. Late homework will be checked in, but not graded.

¥ We will usually spend one class period on each section of the text.

¥ Due to the nature of this course, many homework exercises require you to describe the results of hand computation or computer processes and then explain them Such exercises should be answered in complete coherent sentences and paragraphs. Good English and neatness count in the grading of your homework and examinations.

PROJECTS Information about these will be forthcoming.

GRADES: ¥ There will be three examination given during semester. Some components of these will be Òtake-homeÓ examinations. Quizzes will also be given during the semester. Some quizzes will be given without being announced in advance in order to encourage you to keep up with the assignments day by day. All examinations will be announced at least one week in advance of the time they are given.

¥ Illness is the only excuse for missing an examination.

¥ Missed quizzes cannot be made up, but your lowest quiz grade will be dropped.

¥ Grades will be computed on the following basis:

Three class examinations 3/8 Final Examination 2/ 8 Quizzes 1/ 8 Homework 1/ 8 Projects 1/8

Here is a Mathematica demonstration