MAT 3751
Real Analysis II
Winter 2010
 

Current Assignments

• Due Friday, March 12:
  Turn in the following exercises: 29.2, 29.7, 29.11, 30.1, 30.2, 30.4, 30.7, 31.1, 31.3, 31.5, 31.13
  (Note: for 31.5, you may use the result of 31.4 as needed)
   

• The take-home final is due by 10:30 on Wednesday, March 17.  The in-class final is 10:30-12:30 on Wednesday March 17.
   

Tentative Future Assignments

Past Assignments and Solutions

• Due Monday, January 11:

  • Turn in Lab 7.  Complete all of the computations in section 7.2 and answer all of the questions in section 7.3.  Answer questions 2 and 3 from section 7.4.  You can skip the rest of 7.4.  You can complete this lab in groups of two or three and turn in a single copy for the group.

  • Turn in exercises 17.3 (give detailed explanations like example 17.2), 17.4, 17.5 (no formal proofs are needed, but provide some brief justification for how you determined each limit -- for example, which theorems from the section are you using?), 17.6, 17.13  Solutions (17.4 still needs to be added)
     

• Wednesday, January 13:

  • There will be a quiz on definitions and terminology.  You should be able to state definitions of convergent, bounded, increasing, decreasing, monotone, and Cauchy sequences.  You should also be able to state the monotone convergence theorem and the Cauchy convergence criterion.

  • In class on Wednesday, you will work in groups of 2-3 students on Lab 8: Understanding the Limit Superior and Limit Inferior.  No technology is required.
     

• Due Friday, January 15:

  • Turn in exercises 18.3bd, 18.4, 18.7, 18.11, and 18.13.  Solutions

  • In class on Friday, you will work in groups of 2-3 students on Lab 9: Continuity and Sequences.  You will need to use Maple for this lab.  The required Maplet can be found on Facshare.
     

• Due Friday, January 22:

  • Turn in Lab #8.  Complete all parts of sections 8.2, 8.3, and 8.4.  In addition, answer questions 1, 2, 4, and 7 from the Questions for Reflection (Section 8.5).  You may turn in a single copy of the lab write-up for your group.

  • Quiz: Know the definitions of a compact set, open cover, subcover, and subsequence.  Be able to state the Heine-Borel Theorem, the Bolzano-Weierstrass Theorem for Sets, the Nested Interval Property, and the Bolzano-Weierstrass Theorem for Sequences
     

• Due Monday, January 25:

  • Turn in Lab #9.  Complete all parts of sections 9.2, 9.3, and 9.4.  In addition, answer questions 1, 2, 3, 4, and 5 from the Questions for Reflection (Section 9.5).  You may turn in a single copy of the lab write-up for your group.

  • Turn in exercises 14.1, 14.2, 14.3, 14.8b, 19.1, 19.2, and 19.4. Solutions
     

• Due Friday, January 29:
  Turn in Exercises 19.6, 19.7, 19.9, 19.16, and 19.18
  (Note that exercise 19.16 shows that the definition of limit superior given in the lab is equivalent to the definition given in the textbook when the sequences are bounded.  It is easy to show that when a sequence is unbounded, the two definitions both give infinity, so the definitions are equivalent.)
   

• Due Friday, February 5:
  Turn in Exercises 20.1, 20.2, 20.3abdh (for each computation, clearly explain how your computations are justified based on limit theorems we have discussed), 20.6a, 20.7bc, 20.9bc, 20.12 (just prove the theorem for products, no the other parts), 20.13, and 20.18.  Partial Solutions
   

• Due Wednesday, February 10:
  Turn in Exercises 21.1, 21.3, 21.4, 21.6, 21.12, 21.13, and 21.15. Solutions
   

• The in-class midterm will be Friday, March 12.  The take-home midterm is due at the start of class on Friday.
   

• Due Monday, February 22:
  Turn in exercises 22.1, 22.2, 22.3, 22.4, 22.8, 22.9, and 22.16.  Solutions
   

• Due Friday, February 26:
  Exercises 23.1, 23.2, 23.3, 23.4ab, 23.6, 23.11, and 23.14. Solutions
   

• Due Wednesday, March 3:
  Exercises 25.1, 25.2, 25.3, 25.4bc, 25.5, 25.7ab, 25.8, 25.10, and 25.15 (there is a typo: it should say use exercise 25.4(c), not 25.3(c)).  Solutions
   

• Exercises 29.3 and 29.4 Solutions
   

• Due Monday, March 5:
  26.1, 26.2, 26.6, 26.8, 26.13, 26.14, 26.16, 26.21, 27.1, 27.3, 27.5, and 27.12.