REAL ANALYSIS 2-MA 207 (4 credits)-Spring 2009

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Continuous but nowhere differentiable

INSTRUCTOR: Dr. Botsko

TEXT: An Invitation to Real Analysis (3rd edition) by Michael W. Botsko

PREREQUISITE: MA 206

COURSE CONTENT:

We will cover the concepts found in chapters 6, 7, 9, 10, and 11 of the above text. A list of topics that we will study includes:

  1. Vector calculus
  2. The Mean Value Theorem for vector-valued functions
  3. Functions of bounded variation
  4. Rectifiable curves and arc length
  5. Some topology in En
  6. The Full Cover Theorem in En
  7. Limits and continuity of functions of several variables
  8. Partial derivatives
  9. Differentiability of functions of several variables and of vector fields
  10. Differentials, directional derivatives and the Chain Rule
  11. The Mean Value Theorem and Taylor's Theorem for functions of several variables
  12. Optimization for functions of several variables
  13. Line integrals
  14. The Inversion Theorem
  15. The Implicit Function Theorem
  16. Infinite series of numbers and functions
  17. Uniform convergence
  18. Consequences of uniform convergence
  19. A continuous nowhere differentiable functions

OBJECTIVES:

To know the basic definitions and fundamental theorems of Real Analysis, to be able to prove simple propositions and to develop proficiency in applying the problem-solving techniques treated in the course, to be able to connect Real Analysis with other branches of mathematics. Class discussions and exams will be used to assess the level to which these objectives are being attained.

EXAMS:

There will be three exams and a final and you will be given a week's notice for each exam.

GRADING POLICY:

The final will count as 1/4 of your grade as will each of the three in class exams. The grading system will be according to the current SVC bulletin.

ACADEMIC HONESTY:
“Saint Vincent College assumes that all students come for a serious purpose and expects them to be responsible individuals who demand of themselves high standards of honesty and personal conduct. Therefore, it is college policy to have as few rules and regulations as are consistent with efficient administration and general welfare.

Fundamental to the principle of independent learning and professional growth is the requirement of honesty and integrity in the performance of academic assignments, both in the classroom and outside, and in the conduct of personal life. Accordingly, Saint Vincent College holds its students to the highest standards of intellectual integrity and thus the attempt of any student to present as his or her own any work which he or she has not performed or to pass any examinations by improper means is regarded by the faculty as a most serious offense.”
Saint Vincent College 2003-2005 Bulletin, page 32.

CLASS ATTENDANCE:

Attendance is very important in an upper division mathematics class. Please make a sincere effort to be present at every class. If for some reason class is cancelled, an announcement will be posted on the Blackboard site for this course.

OFFICE HOURS:

I will be in my office (4th floor of Alfred Hall) at the following times during the week. When coming for help be sure to bring along your textbook, notes, and your efforts at solving the problems.

Monday: 9:30 to 10:30 and 3 to 4

Tuesday: 10:30 to 11:30

Wednesday: 9:30 to 10:30 and 3 to 4

Friday: 9:30 to 10:30

Note: The function at the top of this page is an example of a function that is continuous everywhere yet differentiable nowhere. To see the animation again, simply click the "refresh" or "reload" icon at the top of the screen. If you would like to see this function constructed frame by frame, click here .

Click here for a nice interactive page in Real Analysis.

Blackboard (If this link doesn't work, try here.)