Calculus II Honors, Fall 2007

Math 231 : MWF 1:00-1:50, 148 Henry

Math 249 : Th 3:00-3:50, 154 Henry


Class cancelled Thursday, Nov. 15


Instructor

Kevin Ford (Altgeld 361, phone 265-6255, e-mail: ford@math.uiuc.edu )
Office hours: MWF 2:00-2:45 or by appointment

Textbook and Syllabus

Calculus (Early Transcendentals) , by Smith and Minton, 3rd ed. We will cover the standard syllabus, Ch. 6, 8 and 9 plus 7.1. About half the course will be spent on Chapter 8 on infinite series, the main topic of the course. The standard material will be supplemented and we will treat each topic in a more thorough way than is done in the standard 231 sections. Additional enrichment topics will also be covered, such as complex numbers.

Pre-requisites

Math 220/221 with a grade of A, or a score of 5 on the Calculus AB Advanced Placement Exam.

Homework and Quizzes

There will be two types of homework assignments: (1) Assignments of standard material, which are performed electronically using MathZone ; (2) Honors assignments covering more advanced material and harder problems, which are hand written and turned in (specific due dates below).

Exams

Three "midterm" exams will be given during the semester Make up exams will not be given. (except if an absence is approved by the Emergency Dean).

Grades

Math 231: homework (10%), exams (20% each), final exam (30%). All grades will be numerical (e.g., 0-100). For the final course grades, 90% guarantees an A-, 80% guarantees a B-, 65% guarantees a C-, 50% guarantees a D-. The standards for this grade are identical to those in a regular 231 section.
Math 249: This grade will be the average of your Math 231 grade and your grade on the Honors assignments.

Homework assignments (MathZone)

  1. Due Monday, Aug. 27, 1 PM. Sums and Integrals. This is for practicing using MathZone and will not count toward your homework grade.
  2. Due Monday, Sep. 3, 1 PM. Mean Value Theorem, Integration by Parts.
  3. Due Monday, Sep. 10, 1 PM. Trigonometric methods; partial fractions.
  4. Due Wednesday, Sep. 19, 1 PM. Improper integrals; exponential growth and decay.
  5. Due Thursday, Sep. 27, 1 PM. Definition of limits.
  6. Due Thursday, Oct. 4, 1 PM. Sequences.
  7. Due Friday, Oct. 12, 1 PM. Series, integral test.
  8. Due Friday, Oct. 19, 1 PM. Comparison tests; alternating series.
  9. Due Thursday, Oct. 25, 1 PM. Absolute convergence, ratio and root tests.
  10. Due Friday, Nov. 2, 1 PM. Power series.
  11. Due Friday, Nov. 9, 1 PM. Taylor series and applications.
  12. Due Friday, Nov. 16, 1 PM. Polar coordinates.
  13. Due Thursday, Nov. 29, 3 PM. Parametric curves.

Homework assignments (honors - write by hand)

  1. Due Friday, Sep. 7 at the beginning of class.
    2.9#40 (10 points): Show that |cos u - cos v| &le |u-v| for all u,v. Hint:use the Mean Value Theorem.
    3.4#52 (10 points): Suppose that a function f is increasing and f has an inverse. Show that the inverse of f is also an increasing function. There is a way to solve this without using the mean value theorem.
    4.5#74 (10 points): identify each sum as a Riemann sum and evaluate the limit.
    (a) limn&rarr&infin (1/n) (e4/n + e8/n + &hellip + e4). (b) limn&rarr&infin (4/n) (2/n1/2 + 2&sdot 21/2 /n1/2 + 2&sdot 31/2/n1/2 + &hellip + 2).
    6.3 Exploratory exercise #2 (20 points). (a) Let In = &int0&pi/2 sinn x dx. Show that In = (n-1)/n In-2 (the formula given in the book is wrong).
    (b) Show that I2n+1/I2n = (22 42 &hellip (2n)2 &sdot 2)/(32 52 &hellip (2n-1)2 (2n+1) &pi).
    (c) Use the Squeeze Theorem to show that limn&rarr &infin I2n+1/I2n = 1, and conclude from (b) a limit formula for &pi called Wallis' formula.
  2. Due Friday, Sept. 17.
    Section 6.4, Exploratory Exercise 1 (10 points).
    Section 6.4, Exploratory exercise 2 (20 points). Assume that p and q are rational numbers (quotients of integers) for the last part.
    Section 6.6 # 46, 54 (explain WHY it is true or it is false), 69 (10 points each).
  3. Due Friday, Oct. 5.
    Section 1.6 # 40, 52, 58 (10 points each)
    Section 8.1 # 26, 32, 58 (10 points each)
    BONUS (30 points) The coffee problem: You have a cup of very hot coffee, and you have a small amount of cold water you want to add to it to make it cooler. It will also cool on its own by Newton's Law of Cooling, at a rate proportional to the difference between the liquid temperature and room temperature. Determine which will result in cooler coffee: (a) add the cold water immediately and then wait 5 minutes; (b) wait 5 minutes and then add the cold water. Let R be room temperature, T the initial coffee temperature, W the temperature of the cold water, and x the ratio of the volume of cold water to volume of coffee. Hint: the answer to the above question depends on whether R>W or W>R.
  4. Due Wednesday, Oct. 17
    Section 8.2 # 47, 48, 51 (10 points each)
    Section 8.3 # 36, 65 (10 points each)
    Section 8.4 # 39 (10 points)
    BONUS (30 points) Section 8.3 Exploratory exercise #2.
  5. Due Thursday, Nov. 1. First five problems are 10 points each.
    Section 8.5 # 40
    Section 8.6 # 38, 40
    Section 8.7 # 43, 44
    BONUS (30 points) . Determine, with proof, whether the series &Sigman=1&infin (-1) n(n+1)/2 (1/n) converges or diverges.
  6. Due Monday, November 12.
    Section 8.9 # 11, 21, 29, 30, 31, 32, 34, 40 (10 points each).
  7. Due Wednesday, Dec.5.
    Complex numbers handout, #47, 48
    Section 9.2 # 42.
    Section 9.5 # 49, 50.

Reading assignments.

  1. For Thursday, Aug. 23. Read sec. 4.2, 4.3, 4.4.
  2. For Friday, Aug. 24. Read sec. 4.5.
  3. For Monday, Aug. 27. Read sec. 2.9.
  4. For Wednesday, Aug. 29. Read sec. 6.1, 6.2.
  5. For Friday, Aug. 31. Read sec. 6.3.
  6. For Wednesday, Sep. 5. Read sec. 6.4.
  7. For Wednesday, Sep. 10. Read sec. 6.6.
  8. For Friday, Sep. 14. Read sec. 7.1.
  9. For Thursday, Sep. 20. Read sec. 1.6
  10. For Wednesday, Sep. 26. Read sec. 8.1
  11. For Monday, Oct. 1. Read sec. 8.2
  12. For Thursday, Oct. 4. Read sec. 8.3
  13. For Thursday, Oct. 11. Read Sec. 8.4
  14. For Monday, Oct. 15. Read sec. 8.5
  15. For Monday, Oct. 22. Read sec. 8.6
  16. For Monday, Oct. 29. Read sec. 8.7, 8.8.
  17. For Wednesday, Nov. 7. Read handout on complex numbers.
  18. For Monday, Nov. 12. Read sec. 9.4.
  19. For Wednesday, Nov. 14. Read sec. 9.1.
  20. For Friday, Nov. 16. Read sec. 9.2
  21. For Wednesday, Nov. 26. Read sec. 9.3

Exam #1. Wednesday, September 19. Covers Chapter 6 and Section 7.1

Exam #2. Friday, October 26. Covers sections 8.1-8.5
Practice Exam

Exam #3. Friday, November 30. Covers sections 8.6-8.8, 9.1, 9.2 and 9.5.
Practice Exam

Final Exam. Thursday, Dec. 13, 1:30-4:30.