M345 Real Analysis Semester 001 (Fall 2000)
Course Syllabus

Instructor: Karen E. Donnelly
Office: 257 Core Building
Office Phone: 6297 Home Phone: 866-8997
email: karend@saintjoe.edu
Office Hours:

Monday       1:00 -- 3:00 p.m.
Tuesday       2:00 -- 3:00 p.m.
Wednesday    10:00 -- 10:50 a.m.
Thursday      2:00 -- 4:00 p.m.
Friday       12:00 -- 1:00 p.m.
If you need an appointment other than during these hourse, please call or send e-mail to arrange.
Instructor's web page URL: www.saintjoe.edu/~karend
Real Analysis web page URL: www.saintjoe.edu/~karend/m345

Text: Real Analysis, Fitzpatrick, Patrick M. PWS Publishing Company 1995

Course Objectives:

1. To investigate the fundamental concepts of analysis for real functions of a single variable, including

    1. properties of real numbers
    2. sequences and series
    3. continuity and limits
    4. differentiation
    5. integration
2. To develop the student's appreciation of methods of proof and ability to develop and present rigorous mathematical arguments.

Course Outline:

  1. Preliminaries: (Chapter 1)
    1. Basics of set theory, mathematical induction, and the real number system
  2. Sequences of Real Numbers (Chapter 2)
    1. Convergent sequences
    2. Monotone sequences, subsequences
  3. Continuity and Limits (Chapter 3)
    1. Properties of continuous functions
    2. Extreme Value Theorem and Intermediate Value Theorem
    3. Uniform continuity concepts
    4. Limits
  4. Differentiation (Chapter 4, parts of Chapter 5)
    1. Properties of derivatives
    2. Mean-value theorems
    3. Elementary functions as solutions of differential equations
  5. Integration (Chapter 6 and parts of Chapter 7)
    1. Definition of the integral and integrability
    2. First Fundamental Theorem of Calculus
    3. Darboux Sums and Rieman Sums
    4. Second Fundamental Theorem of Calculus
  6. Infinite Series (Parts of Chapters 8 and 9)
    1. Approximation by Taylor polynomials

      2. Convergence of sequences and series of functions
Grade Distribution:
Assignments, Quizzes: 35%
Three Exams: 35%
Final Exam: 20%
Attendance and Participation: 10%
Grading Scale:
 
93%-100% A
90%-92% A- 
  
87%-89% B+
83%-86% B
80%-82% B- 
77%-79% C+
73%-76% C
70%-72% C-
67%-69% D+
60%-66% D 
  
59% or lower F 
    

Expectations and Requirements:

Special Note: If you are a student with a disability, please meet with me immediately to discuss the accommodations you will need during class activity, examinations, and out of class assignments in order to participate fully and demonstrate your abilities.

1. Academic Honesty: Plagiarism or other forms of academic dishonesty on any assignments, tests, or quizzes will not be tolerated. If the instructor finds that a student has engaged in dishonesty, the student may be referred to the Dean of Academic Affairs for appropriate action.

2. Quizzes and Exams: Students are expected to be present for all exams. No exams or quizzes may be made up unless the student has contacted the instructor and received permission prior to the date of the original exam or quiz. This includes students participating in athletics who must arrange to take the quiz or exam on or before the scheduled date.

3. Assignments: Assignments, unless otherwise specified by the instructor, are to be completed individually. While students are encouraged to consult each other for ideas for assignments, the solutions should be completed individually. Any help one student gives another should be instructional help only. If the instructor feels that a student has not completed an assignment individually, the instructor may question the student on that assignment. The student should be able to explain how he/she worked the problem and should be able to work similar problems. Late assignments will not be accepted without permission.  For problem assignments, write out complete answers NEATLY and CLEARLY. You must show your work! Partial credit is given when work is shown even if the answer is incorrect. However, correct answers without any work shown will in general be given no credit. Start homework early and see me for help with problems you don't know how to work! It is inappropriate to ask how to do a problem in class the day it is due!!!!  Staple your pages together before submitting.

4. Class Preparation and Participation:

a) Keep up with reading assignments. To receive the maximum grade on attendance and participation the student must read assignments prior to class, be prepared to ask and respond to questions, and be an actively engaged participant in class.
b) Take good notes and review notes on a regular basis as well as promptly begin and continue work on assignments as they are assigned.
c) Attendance is required. If you must miss class due to illness or other valid excuse (e.g. athletic event) please send me email or telephone with an explanation.

5. Getting Help:

Students who do not understand a concept should do the following:
a) Ask questions in class. (More than likely other students do not understand as well.)
b) Seek individual help from the instructor. I am more than willing to give you the extra help you may need. Come in during office hours or make an appointment. Tutoring (free) can also be arranged either through me or through counseling services.
c) Share with me any concerns you may have or any suggestions you have for the class structure that will help you learn more effectively.

The above content and requirements are tentative and subject to change according to time constraints and other factors as determined by the instructor.