Math 5152, Introduction to Real Analysis 2
Spring 2000
MW 6:00 - 7:15 p.m.
102 Arnold Hall

Instructor:   Dr. Tim Howard
Office:         215 Faculty Office Building
Phone:         568-2172
Email:          thoward@colstate.edu
Web site:     http://math.colstate.edu/thoward/
Office Hours:  Please find my office hours listed on my web site at http://math.colstate.edu/thoward/schedule.html .  If those times aren't suitable, I'll be happy to arrange an alternative time.

The policies in this syllabus may be subject to change. Check the above www address weekly for the latest version.
Most recent update:  January 10, 1999.

Text.  An Introduction to Analysis, Second Edition, by James R. Kirkwood.

Prerequisites.  Math 5151, Introduction to Real Analysis 1.

Desired Course Outcomes.  Exposure to real analysis is important for those who enter graduate school in mathematics or mathematics education, as well as those who plan to teach mathematics at the secondary level or higher.  For the purposes of this course, you might think of "real analysis" as "advanced calculus".  That is, we're going to revisit many of the topics from calculus, but in a more rigorous fashion.  We'll also delve into some new topics which illustrate the power and applicability of real analysis.  As a result of your successful completion of this course, you should gain the following:


Grading.

   Your course grades will be based on homework, a mid term exam, and a final exam.  Each of these will be weighted as follows:
 

Component
Weight
Homework exercises
34 %
Mid term exam
33 %
Final exam
33 %

Your letter grade for the course will be computed according to how many of the total points you receive as follows:

        A: 90 - 100% of the total points     B: 80 - 89%     C: 70 - 79%     D: 60 - 69%

Homework.  Homework problems will be assigned from the text and collected on designated days.  You will be expected to present some homework solutions orally.  You also will be asked to present material to the class from the text and/or your own independent research.  Your homework grade will be based both upon the written work you submit and upon your oral presentations.

Tests. No makeup tests will be given; please refer to the absentee policy below for more information.  Each student is responsible for frequently checking the announcements listed on the course web page for updates.

Noteworthy Dates:

  • Mon., Jan. 17 -- No classes, Martin Luther King, Jr. holiday
  • Wed., Feb. 23 -- mid term exam
  • March 6-10 -- Spring Break
  • Wed., May 3 -- Final exam, 6:15-8:15 p.m.
    • Course web page.  Any modifications to the course policies and/or course syllabus will be announced on the course web page.  You are expected to check the web page at least once per week.  If you miss a class day, you should take special care to check the course page as soon as possible after that class period.

    Absentee Policy.  You are expected to attend every course meeting. According to the attendance policy published on page 6 of the Student Handbook, if you accumulate 10 or more course hours of absences during the semester, I am authorized to assign the grade of "WF".

    No makeup tests will be given. If a student misses a test with instructor approval, the weight of the final will be increased to replace the missing test score (likewise for additional missed tests).  If the absence has not been approved by the instructor, then a zero will be recorded for that test score.

    Academic Withdrawal. The student handbook states the following:

    To leave the university with a clear record at times other than at the end of a semester students must complete a "withdrawal form."  This form, which includes instructions, is available in the Office of the Registrar, Richards Hall.
    Any course dropped after January 11 becomes a part of your academic record.  From that date until mid-term (March 1) a grade of "W" will be assigned for withdrawal forms submitted to the Registrar.  A grade of "WF" will be assigned for withdrawal forms received after mid-term.  The student is responsible for completing the paperwork and submitting it to the Registrar’s Office.

    Students with Disabilities: If you have a documented disability, as described by the Americans with Disabilities Act (ADA), it is recommended that you contact the Office of Disability Services at (706)568-2330.  The office will assist you in arranging appropriate accommodations with the instructor.
     

    Tentative List of Topics

    Chapter 4:  Continuous Functions

    4.1  Limits and continuity
    4.2  Monotone and inverse functions

    Chapter 5:  Differentiation

    5.1  The derivative of a function
    5.2  Some mean value theorems

    Chapter 6:  Integration

    6.1  The Riemann integral
    6.2  Properties and applications of the Riemann integral

    Chapter 7:  Series of Real Numbers

    7.1  Tests for convergence of series
    7.2  Operations involving series

    Chapter 8:  Sequences and Series of Functions

    8.1  Sequences of functions
    8.2  Series of functions
    8.3  Taylor series

    Chapter 9:  Fourier Series (time permitting)

    9.1  Fourier coefficients
    9.2  Representation by Fourier series

     
    Real Analysis Course Page
    Tim Howard's Home Page
    CSU Math Dept.
    CSU Home Page