Advanced Calculus I

Instructor: Prof. Josh Barnard Office: 426 Instructional Laboratory Building [ILB] Phone: 460-6264, ext. 2617 Email: jbarnardATjaguar1 usouthal edu Course Webpage: www.usouthalabama.edu/mathstat/personal_pages/jbarnard/F07-334/ Office Hours: MT 1:30-2:25, W 3:30-4:25, R 2-3 or by appointment Prerequisites: MA 227 & MA 237. Textbook: Fundamental Ideas of Analysis, by Michael Reed (Wiley & Sons 1998). Course Description: This is the first of a two course sequence designed to provide students with the theoretical context of concepts encountered in MA 125 through MA 227. Topics covered include the completeness axiom, sequences of real numbers, suprema and infima, Cauchy sequences, open sets and accumulation points in Euclidean space, completeness of Euclidean space, series of real numbers and vectors, compactness, Heine-Borel theorem, connectedness, continuity, extremum theorem, intermediate value theorem, and differentiation of functions of one variable. Objectives: The goal of this course is to study more closely the ideas and concepts involved in the calculus of one real variable. Students will gain a rigorous understanding and working knowledge of the main concepts, theorems, and techniques. Mathematical exposition will be emphasized, and students will be expected to understand and produce proofs. Standards of written work: Solutions must be neatly and clearly written and logically structured. Any theorems proven in class may be used as long as they are clearly cited. You may discuss homework problems with other students and with me, but the final write-up must be your own. Announcements and Handouts: The main course page has an announcement section and a handout section. Both of these should be checked regularly, and you are responsible for any information found there. In particular, the requirements and policies for this course may be modified as circumstances dictate. Such changes will be provided to students in class and on these course webpages. Schedule of Topics: On the main course page, there will be links to three Schedule of Topics pages, broken up by test dates. Each of these pages is a list, arranged by class date, of important terms, theorems, textbook examples, and textbook exercises that pertain to what is covered in class that day. This is meant to be a guide for your study outside of class. Grading: Grades will be determined according to the following: Homework -- 30% Two Midterms -- 20% each Final Exam -- 30% Homework: Homework problems will be posted on the schedule of topics page for the appropriate test. The homework assignments are there to provide you with a minimum level of exposure to the materials outside of class time. You will need to do many more problems before you feel comfortable with the concepts involved. The way to succeed in a math course is to work (and understand) a large number of problems. Tests: There will be two in-class tests. Tentative dates for these tests are as follows: Midterm 1: Wednesday, September 26 Midterm 2: Wednesday, November 7 Final Exam: There will be a two-hour cumulative final exam. It is currently scheduled for Friday, December 7, 6:00-8:00. Attendance: Routine attendance in class is essential and expected. As in any course, you should read the relevant sections of the textbook before attending lectures. The schedule of topics page lists relevant sections and examples to go over. Routine participation in class is also expected. Attendance and participation will be considered in determining borderline grades. Calculators: Calculators will be neither allowed nor necessary in this course. Office Hours: If you have any questions or problems, you are encouraged to come by my office during office hours, or make an appointment to come by some other time. Email is the best way to contact me. If you plan on coming during office hours, you need not notify me ahead of time. Office hours are public hours, so you should expect that there may be other students there also. Student Disabilities: If you have a specific disability that qualifies you for academic accommodations, please notify me and provide certification from the Office of Special Student Services. This office is directed by Ms. Bernita Pulmas and is located in the Student Center, Room 270, Phone 460-7212. Academic Misconduct: Students are assumed to be familiar with the current Academic Misconduct Code (.pdf file).

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Last Modified 10th Sep 07