PSU
Mark
Eberly College of Science Mathematics Department

Math 312 Section 3 and 4 - Spring 2013

Concepts of Real Analysis


Schedule of classes:

Section 3, M W F 11:15 AM - 12:05 PM in 203 WILLARD
Section 4, M W F 10:10 AM - 11:05 AM in 106 SACKETT


FINAL EXAM: MAY 2, 12:20 - 2:10 PM, 022 DEIKE (comprehensive).
REVIEW SESSION FRIDAY APRIL 26 in class. FINAL QUIZ WEDNESDAY APRIL 24.


Finals Week Office Hours: SUNDAY 4:00-5:30 PM, WEDNESDAY 11:00 AM- 12:30 PM.


Topics for the final exam.
Review Problems for the final exam.
Practice tests with solutions available on ANGEL.


MIDTERM 2: MONDAY MARCH 25 in class.
REVIEW SESSION FRIDAY MARCH 22 in class.
Office hours for the exam: 12:15 - 1:45 PM, Friday March 22. NO Office hours, Monday March 25.


Topics for the exam.
Review Problems for the exam.
Practice Test (SKIP Problem 1, solutions available on ANGEL).


MIDTERM 1: FRIDAY FEB 8 in class.
REVIEW SESSION WEDNESDAY FEB 6 in class.

Topics for the exam.
Review Problems for the exam.
Practice Test (solutions available on ANGEL).


Make-up Classes: MONDAY JANUARY 21 at the usual time and place for each section
SUNDAY JANUARY 27, 4:00 - 5:30 PM in 101 OSMOND (both sections).

NO classes MONDAY FEB 4, MONDAY FEB 18, FRIDAY FEB 22.



Syllabus.


Topics:
  1. Chapter 1, Real Numbers: Review of properties of real numbers (Sections 1.1.1,1.1.2,1.2.1,1.2.2,1.5), irrational numbers (1.1.3), modulus and distance (1.2.3), triangle inequality, Bernoulli and Cauchy-Schwartz inequalities (1.3), sumpremum and infimum, completeness (1.4), Archimedean and density properties (1.1.4).
  2. Chapter 2, Sequences: monotonic sequences (2.1), null sequences (2.2), convergent and divergent sequences (2.3, 2.4), the Monotone Convergence Theorem (2.5).
  3. Chapter 3, Series: definition and examples, geometric series, telescoping series, non-null test (3.1), series of positive terms, comparison, root and ratio, Cauchy tests (3.2), alternating series, rearrangements, products (3.3), the exponential function (3.4).


Homework Problems (from the textbook): every problem is worth 5 points. Complete solutions available on ANGEL under "Lessons" tab.
  1. Section 1.1: 5, Section 1.3: 1, 7. Section 1.4: 4, 5 a), 6 (note |a+b| should be |a-b| in the second formula of this problem), pages 35-36. DUE WEDNESDAY JANUARY 23.
  2. Section 2.1: 2,3. Section 2.2: 1, 2, 3, 7 (Hint: it is equivalent to show that (a_n) is null if (a_n^2) is null), pages 79-80. DUE WEDNESDAY JANUARY 30.
  3. Section 2.2: 4, 5, 6. Section 2.3: 1, page 80. DUE WEDNESDAY FEBRUARY 6.
  4. Section 2.3: 2, 3 (you MUST use the definition of converegent sequences for this problem), page 80-81. DUE WEDNESDAY FEBRUARY 13.
  5. Section 2.4: 1, 4 a), b), c), d), e), page 81 (note: a divergent sequence is a sequence does not converge, an unbounded sequence is a sequence that is not bounded.) DUE WEDNESDAY FEBRUARY 20.
  6. Section 2.4: 2, 3, 5 (Hint: consider first the case of eventually monotonic sequences) page 81. DUE WEDNESDAY FEBRUARY 27.
  7. Section 2.5: 1, 2, 3, 6 page 81-82. DUE WEDNESDAY MARCH 13.
  8. Section 2.5: 5 page 82. Section 3.1: 1, 2 page 127. DUE WEDNESDAY MARCH 20.
  9. Section 3.1: 3, 4, page 128 (you MUST use the techniques of Section 3.1). Section 3.2: 1 a), b), page 128. DUE WEDNESDAY MARCH 27.
  10. Section 3.2: 1 c), d), e), f), 2, 3, page 128. DUE WEDNESDAY APRIL 3.
  11. Section 3.2: 4. Section 3.3: 1, page 128. DUE WEDNESDAY APRIL 10.
  12. Section 3.3: 2, 3 (Hint: use Theorem 3 on page 112), pages 128-129. DUE WEDENSDAY APRIL 17.
  13. Work out the problems found here. DUE WEDENSDAY APRIL 24.



The feedback form is temporarily disabled due to server issues.



© Anna Mazzucato
Last modified: Wed Apr 24 15:23:29 EDT 2013