Homework

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Reading Assignments and Suggested Problems
Written Assignments
Homework Solutions
Exams
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Reading Assignments and Suggested Problems

The reading assignments given below will generally be a preview of the material you will see in lecture.  My suggestion is to skim the appropriate section prior to lecture to get a sense of the material to be covered.  Then, after each lecture, read the corresponding material more carefully  When doing this careful reading, it is a good idea to test yourself by attempting to prove each Theorem/Lemma/etc. before reading the proof given in the book.  After attempting the proof yourself, then read the proof given in the book to see if you are right, or to see how to do the parts you couldn't figure out on your own.  Once you are confident that you understand all the details, read the section (at least) once more to make sure the "big picture" is clear.

The problems listed below are meant to reinforce material covered in the preceding lecture or reading assigment.  It is suggested that you read and think about these as soon as possible after the corresponding material has been covered in lecture.


For Friday, 4/30: Start reviewing for final.  Try problems 11.6.1 and 11.6.6.

For Wednesday, 4/28: Continue reading section 11.6 up to the statement of Theorem 11.47.

For Monday, 4/26: Read section 11.6 up to the statement of Theorem 11.41.  Try problems 11.4.8, 11.5.9, and 11.5.12(a)-(b).

For Friday, 4/23: Read section 11.5 up to Corollary 11.34, and read the statement of Theorem 11.41 (the proof given in class will be a little different from the one in the book).  Try problems 11.4.1, 11.4.4, and 11.4.11.

For Wednesday, 4/21: Read section 11.4 and section 11.5 up to Corollary 11.34.  Try problems 11.2.5, 11.2.9, and 11.3.5.

For Monday, 4/19: Finish reading section 11.2, and read section 11.3 up to Definition 11.21.  Try problem 11.2.2.

For Friday, 4/16: Read section 11.2 up to Theorem 11.15.  Try problems 11.1.5 and 11.1.6.

For Wednesday, 4/14: Read section 11.2 up to Theorem 11.13  Try problems 11.1.5(a) and 11.1.6(a)-(b).

For Monday, 4/12: (Re)read 11.1 up to Theorem 11.5.  Try problems 11.1.1 and 11.1.2.

For Friday, 4/9: Read section 11.1 up to and including Theorem 11.5.  Try problems 9.4.7 and 9.4.9.

For Wednesday, 4/7: Read section 1.5 and reread section 9.4.   Try problems 9.4.1, 9.4.2, and 9.4.5.

For Monday, 4/5: Finish reading section 9.4 and work through the image/preimage worksheet.

For Friday, 4/2: Read section 9.4 through Example 9.27.  Try problems 9.3.1-9.3.3.

For Wednesday, 3/31: Finish reading section 9.3.  Try problems 9.3.4 and 9.3.8.  Find an example that shows that problem 9.2.2 is wrong as stated in the book.

For Monday, 3/22: Prepare for midterm review.  Try problems 9.2.1, 9.2.2 , and 9.2.4.

For Friday, 3/19 Monday, 3/29: Read 9.3 up through Theorem 9.16.

For Wednesday, 3/17: Read 9.2 and/or 10.4 (my approach in lecture will be closer to that given in 10.4).  Try problems 9.1.4 and 9.1.7.

For Monday, 3/15: Read 9.2 up to the statement of Theorem 9.11.  Try problems 9.1.1, 9.1.2, and 9.1.3.

Have a nice spring break!

For Friday, 3/5: Finish reading section 9.1.  Try problems 8.4.1 and 8.4.2 (this time do the boundary part), 8.4.3, and 8.4.6.

For Wednesday, 3/3: Read the sequences review sheet and section 9.1 through Theorem 9.6.  Try problems 8.4.1, and 8.4.2 (skip the parts about boundaries).

For Monday, 3/1: Read section 8.4.  Try problems 8.3.1, 8.3.3, and 8.3.4.

For Wednesday, 2/24 Friday 2/26: Finish reading section 8.3.

For Monday, 2/22: Continue reading section 8.3 up to Remark 8.29.  Try problems 8.3.1 (ignore the part about connectivity) and 8.3.8.

For Friday, 2/19: Read section 8.2, Definition 8.16 to the end, and read section 8.3 up to Theorem 8.24.

For Wednesday, 2/17: Study for midterm.

For Monday, 2/15: Try problems 8.2.4 and 8.2.5.  Start reviewing for first midterm (2/17).

For Friday, 2/12: Read section 8.2.  Try problems 8.1.1(a)-(d), 8.1.2(a)-(b), and 8.1.9.

For Wednesday, 2/10: Finish reading section 8.1. 

For Monday, 2/8: Read section 8.1 up to the Cauchy-Schwarz inequality.  Try problems 5.4.4 and 5.4.5.  If you are interested in reading a proof of Lebesgue's integrability criterion (discussed but not proved in class) see section 9.6 of the textbook.

For Friday, 2/5: Try problems 5.4.0 and 5.4.2.  Try to construct an example of a function f so that f is not integrable and |f| is integrable.

For Wednesday, 2/3: Try problems 5.3.0(a) and (d), 5.3.1(d), and 5.4.1.

For Monday, 2/1: Read section 5.4.  Try problem 5.3.5.

For Friday, 1/29: Read section 5.3, Remark 5.29 to the end (skip the proof of Theorem 5.34).  Try problems 5.3.0(a), and 5.3.1(a)-(c).

For Wednesday, 1/27: Read section 5.2, Theorem 5.26, and section 5.3, Theorem 5.28 through Theorem 5.31.  Try problems 5.2.0 (b)-(d), and 5.2.6.

For Monday, 1/25: Read section 5.2 from Theorem 5.22 to Theorem 5.26.  Try problems 5.2.0(a) and 5.2.5.

For Friday, 1/22: Read section 5.2 from Theorem 5.20 up to and including Corollary 5.23.  Try problems 5.1.0(c), 5.1.3 (compute the integral this time), and 5.1.6.

For Wednesday, 1/20: Read section 5.2 up to the end of page 142.  Try problems 5.1.0 a, b, d, and 5.1.8.  Try these problems if you want/need to review the concept of uniform continuity.

For Friday, 1/15: Finish reading section 5.1.  Try problems 5.1.1 and 5.1.3 (ignore the part about computing the integrals in both problems).

For Wednesday, 1/13: Read Section 5.1 up to Definition 5.13.


Written Assignments

Before completing your homework assignments, read the Math 421 Homework Guidelines.

HW #0 (due 1/27): Fill out and turn in the info form if you did not already do so in class.
HW #1 (due 1/27)
HW #2 (due 2/3)
HW #3 (due 2/10)
HW #4 (due 2/25)
HW #5 (due 3/3)
HW #6 (due 3/17)
HW #7 (due 3/31)
HW #8 (due 4/7)
HW #9 (due 4/14)
HW #10 (due 4/21)






Homework Solutions

HW #1 Solutions
HW #2 Solutions
HW #3 Solutions
HW #4 Solutions
HW #5 Solutions
HW #6 Solutions (revised 3/31: extra proof added on problems 1 and 4a)
HW #7 Solutions
HW #8 Solutions
HW #9 Solutions
HW #10 Solutions