MAT 317, Spring 2018

Homework Assignments

Week 1 (Apr 2-6) (due by Wednesday of Week 2)

Reading: Section 3.1, 3.3, 4.4. Also reread 4.2 and 4.3 with an eye towards functions defined on arbitrary subsets of R. Then do exercises:
Section 3.3: 1, 2, 5, 7, 8, 11
Section 4.3: 5
Section 4.4: 1, 4

Week 2 (Apr 9-13) (due by Wednesday of Week 3)

Reading: Section 4.4, 5.2, we may have time for 5.1. Then do exercises:
Section 4.4: 3, 6, 7, 9, 10
Section 5.2: 2, 3ab, 5, 6

  • I really like the exercises in these chapters of the book. I want to assign them all!

    Extra credit assignment (hand in (separately, i.e. to me, not the grader) any time before the midterm):

  • Read about Thomae's function t(x) in chapter 4.1.
  • Prove that t(x) is continuous at all irrational points, and not continuous at any rational point.
  • Is t(x) differentiable at the square root of 2? Is it differentiable at any point? Prove it.

    Week 3 (Apr 16-20) (due by Friday of Week 4)

    Reading: Section 5.1, 5.4, 5.5 (good motivation and background), page 203, and some of 5.3. Then do exercises:
    Section 5.2: 9, 12 (assume the bit on continuity)
    Section 5.3: 1a, 2, 3, 6
    Section 5.4: 6a, 7a
    Section 6.6: 6.

  • For 5.3.6c, the conjecture is enough, I don't need a proof.
  • For 6.6.6b, the general description can be something like: a polynomial of degree 5 (don't know the coefficients) divided by a polynomial of degree 17 times...

    Week 4 (Apr 23-27) (due by Friday of Week 5)

    Reading: Section 5.3, 6.2, starting 6.3. Then do exercises:
    Section 5.3: 4, 10
    Section 6.2: 1, 2, 3, 5, 6, 8, 12.

    Week 5 (Apr 30-May 4) (due by Friday of Week 6)

    Reading: Section 6.3, 6.4. Then do exercises:
    Section 6.3: 1, 2, 5, 6
    Section 6.4: 2, 3.

    Week 6 (May 7-May 11) (due by Friday of Week 7)

    Reading: Section 6.5. Then do exercises:
    Section 6.4: 4, 5, 7, 9
    Section 6.5: 4, 5, 6, 8, 11.

  • For 6.4.7b, the question is not asking you to prove definitively one way or another whether it is twice-differentiable or not, but just asking whether the techniques you know can be applied.

    Week 7 (May 14-May 18) (due by Friday of Week 8)

    Reading: Section 6.5, Section 6.6 without the two pages on Lagrange Remainder Theorem, Section 2.8 and 2.9. Then do exercises:
    Section 6.5: 7ab, 9
    Section 6.6: 1, 2
    And the three problems from this pdf.

    Week 8 (May 21-May 25) (due by Friday of Week 9)

    Reading: Lagrange Remainder theorem from 6.6, 7.1, 7.2, 7.3. Then do exercises:
    Section 6.6: 5a, 7, 10a (see below)
    Section 7.2: 2, 3b, 4, 7
    Section 7.3: 1, 3.

  • Please do 6.6.10a but only on the interval [0,1/2), not including the point 1/2.
  • For 6.6.5a, you don't need to do the parts you've done before, just show that the power series does converge to e^x.
  • You can do 7.3.7 for extra credit, hand it in to me on a separate sheet.

    Week 9 (May 28-June 1) (due by Friday of Week 10)

    Reading (including the reading for week 10): 7.3, 7.4, 7.5. Then do exercises:
    Section 7.3: 5, 6
    Section 7.4: 3, 6
    Section 7.5: 1, 2, 4, 6a, 8ab

    Ben Elias
    Department of Mathematics
    Fenton Hall, Room 210
    University of Oregon
    Eugene, OR 97403
    Phone: (541) 346-5629
    Fax: (541) 346-0987
    e-mail: bezzzzlizzzzas@uorezzzzgon.edu