1:00 MTWThF in C106 CNS
Professor Stout
Office hours: 3-4 MWTh, 2-3 TTh
Office C209C Center for Natural Sciences, 556-3038
e-mail: lstout@iwu.edu Web Page:http://www.iwu.edu/~lstout
Return to L.N. Stout's home page.
Text: Small and Hosack Calculus, an Integrated Approach, McGraw Hill
The Analysis 1 and 2 sequence provides a unified approach to calculus in one and several variables. The first course deals with differentiation and the second with integration. The sequence differs from the calculus you saw in high school both in its organization and in its depth. This course concentrates much more on rigorous concept development than it does on mechanical technique.
At the start you will see little that looks like the calculus you studied in high school. We will concentrate on successive approximation as the way we gain information about real numbers. Since the least upper bound property is what distinguishes the real numbers from the rationals, we will spend some time exploring boundedness and its consequences for sets of real numbers and sets in R^n . Many of the exercises will ask you to come up with examples of sets or functions with particular properties or say why no such example exists.
Limits of sequences as a way of approximating real numbers form the basis for our analysis of limits of functions and continuity. We will also look at the more standard delta-epsilon definition, since some theorems are easier to prove using that definition. The sequence definition is nice because it carries over without modification to higher dimensions.
Two chapters on differentiation finish the course. We will stress the derivative as a rate of change, as the slope of a tangent line, and as a best linear approximation to a function near a point. The Mean Value Theorem and its consequences form the base for much of our further theory and almost all of the applications of the derivative. The course ends with a study of maxima and minima in one and several variables.
We will cover one or two sections of the book each week. Class will have lecture, small group problem solving and theory development, and some discussion on Monday through Thursday. Friday will be a problem session. You should have the homework worked through in rough form by Friday, so that questions relate to material you have worked on rather than new ideas. I will expect you to write up your homework neatly over the weekend, so that what I see on Monday is a polished version rather than a first draft. This is particularly important for examples and proofs, since how you find a proof or an example often differs from how you write it up once you have found it.
There will be four exams (each counting 100 points) and a comprehensive final (counting 150). See the calendar for tentative dates. I will assign homework daily. In this course few homework problems will be routine exercises you need to practice on to develop technique, many problems ask for examples or counterexamples of your own construction, some ask for proofs of important results, and some will be projects aimed at deeper understanding or more realistic applications. The homework portion of the grade will be determined by grades on projects or selected problems or quizzes. It will provide 100 points which can be used to replace the lowest exam score if that helps you.
My exams always include definitions, examples of how those definitions apply, proofs of theorems, and problems of varying difficulty. Competence in the mechanics of the subject will earn you a C; mastery of the technique and the definitions and reasonable facility with the applications is B work; I expect facility with the theory, mastery of the technique and applications, and clear expression of mathematical ideas for an A.
I use a straight scale for determining grades. To allow flexibility at boundaries, I reserve the right to change the boundaries, but I will draw them no higher than
Classes and office hours are what you pay tuition for, so take advantage of them. If you don't come to class you will not learn the material with the same emphasis that I put on it. That will hurt your exam scores and detract from what you learn. I do not deduct points for classes missed.
Work handed in for a grade is expected to be your own work. On Take Home exams and individual projects there should be no collaboration: this will be made explicit on the assignment sheet. On daily homework there is something to be gained by talking and working with your fellow students: we will be discussing homework before you write it up to hand in. I do want to see your own write up, not just a copy of your notes from the problem sessions. If you use outside sources, cite them. If you get help from an individual, give credit. It is not wise for you to neglect learning how to do the work on your own, since exams will all require all work to be done individually.
Any cheating on exams or collaboration on assignments where it has been explicitly prohibited will be treated as a violation of the policy on academic dishonesty in the student handbook and will be reported to the Associate Provost.
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