Homework Assignment

Week 1 (Jan. 7 - 11) (due by Wednesday of Week 2)

  • Read Sections 1.1-1.4. Do the following problems:
  • Section 1.2: 1, 3, 6, 7, 10, 12.
  • Section 1.3: 2, 3, 5a, 6abc, 9abc.
  • Section 1.4: 1, 4, 5.
  • Monday: intrioduction, sets and functions.
  • Tuesday: logic and proof. Least upper bound
  • Wednesday: Axiom of choices, least upper bound, density of Q.
  • Friday: Existencec of square root of 2. Countability.

    Week 2 (Jan. 14 - 18) (due by Wednesday of Week 3)

  • Read Sections 1.4, 2.1,2.2. Do the following problems:
  • Section 1.3: 4, 5b.
  • Section 1.4: 6.
  • Section 2.2: 1a, b, 2, 3, 4, 6.
  • Monday: Cardinality. Sequences.
  • Tuesday: Convergence of a sequence, epsilon-N definition.
  • Wednesday: epsilon-N definition, convergence sequence is bounded.
  • Friday: 1st Quiz. Algebraic limit theorem.

    Week 3 (Jan. 21 - 25, MLK holiday) (due by Wednesday of Week 4)

  • Read Section 2.2 - 2.3. Do the following problems:
  • Section 1.2: 5.
  • Section 1.3: 8.
  • Section 2.2: 7, 8.
  • Section 2.3: 1, 4, 6, 8.
  • Monday: MLK holiday
  • Tuesday: Algebraic theorem of limits.
  • Wednesday: Algebraic and order limit theorem.
  • Friday: Monotone convergence theorem and infinite series.

    Week 4 (Jan. 28 - Feb. 1) (due by Wednesday of Week 5)

  • Read Section 2.4 - 2.6. Do the following problems:
  • Section 2.3: 3, 5, 7, 9, 10.
  • Section 2.4: 2.
  • Section 2.5: 1, 2, 3.
  • Section 2.6: 2.
  • Monday: Infinite series, Cauchy Test.
  • Tuesday: Subsequence, Bolzano-Weierstrass theorem.
  • Wednesday: Cauchy sequence.
  • Friday: 1st Midterm.

    Week 5 (Feb. 4 - Feb. 8) (due by Wednesday of Week 6)

  • Read Sections 2.6, 2.7, 3.2. Do the following problems:
  • Section 2.4: 3.
  • Section 2.6: 1, 5, 6b.
  • Section 2.7: 1 (do either (b) or (c)), 2b, 3.
  • Section 3.2: 1, 3, 4.
  • Monday: Cauchy criterion.
  • Tuesday: Properties of infinite series.
  • Wednesday: Absolutely vs conditionally convergence, rearrangement.
  • Friday: End of chapter 2. Open set and limit points.

    Week 6 (Feb. 11 - 15) (due by Wednesday of Week 7)

  • Read Sections 3.2 - 3.3. Do the following problems:
  • Section 3.2: 6, 7, 9, 11, 12a,b,c.
  • Section 3.3: 1, 4, 5b,d,e,f.
  • Monday: Limit points and closed sets.
  • Tuesday: Closed sets.
  • Wednesday: Compact sets.
  • Friday: 2nd Quize, open cover.

    Week 7 (Feb. 18 - 22) (due by Wednesday of Week 8)

  • Read Sections 4.1 - 4.3. Do the following problems:
  • Section 3.3: 2, 7a,b,d.
  • Section 4.2: 1, 2, 3, 5a,b,c (in 5c, do only the proof using sequences), 9.
  • Section 4.3: 1a, 2a, 5.
  • Monday: Symmary of Chapter 3. Limit of functions.
  • Tuesday: Limit of functions.
  • Wednesday: Limit and continuout function.
  • Friday: Continuous functions.

    Week 8 (Feb. 24 - March 1) (due Wednesday of Week 9)

  • Read Sections 4.4, 5.1 - 3. Do the following problems:
  • Section 4.3: 8.
  • Section 4.4: 4.
  • Section 5.2: 1, 2ab, 4, 6.
  • Section 5.3: 1, 3.
  • Monday: Conuitnuous function on compact set. End of Chapter 4.
  • Tuesday: Derivatives.
  • Wednesday: The mean value theorem.
  • Friday: 2nd Midterm.

    Week 9 (March 4 - Mar. 8

  • Read Sections 5.3. Do the following problems:
  • Section 5.3: 4a, 7, 8.
  • Section 7.2: 1, 2, 3, 6.
  • Section 7.4: 1, 4 ac.
  • Section 7.5: 1, 2, 4.
  • Monday: Mean value theorem, L'Hospital rules.
  • Tuesday: Chapt 7.Upper and lower sum, definition of Riemann integral.
  • Wednesday: Riemann Integral. Uniform continuity.
  • Friday: Uniform continuity. Continuous functions are integrable.

    Week 10 (Mar. 11 - 15) Deadweek

  • Monday: Integrability. Properties of integrals.
  • Tuesday: Fundamental theorem of calculus.
  • Wednesday: Finishing Chapter 7. Reivew.
  • Friday: Review.