Math 31B, Winter 2008

Integration and Infinite Series

  • Final exam: Wednesday, March 19, 2008, 11:30am- 2:30pm.
  • All sections are covered for the final.
    Lectures: MWF 9:00am - 9:50am, Franz 1260

    Instructor: Virginia B. Pasour
    Office: MS 6617B
    Office hours: Wednesday 1-2pm, Thursday 2-3pm, or by appointment.
    E-mail: pasour@math.ucla.edu

    Discussion Sections:
    2a BOELTER 5273 T 9:00A-9:50A SMITH, LAURA
    2b BUNCHE 3170 R 9:00A-9:50A SMITH, LAURA
    2c ROYCE 154 T 9:00A-9:50A VANVALKENBURGH, MICHAEL JAMES
    2d MS 5128 R 9:00A-9:50A VANVALKENBURGH, MICHAEL JAMES

    Teaching Assistants: Laura Smith (MS 3905), Michael Vanvalkenburgh (MS 3949)
    Office hours:
    Michael's office hours: Thursdays from 5:15-6:15pm in MS 3949 (or by appointment), Mondays from 2-3, SMC
    E-mail: lsmith@math.ucla.edu, mvanvalk@math.ucla.edu

    Textbook:J. Rogawski, Single Variable Calculus, (1st Edition) , W.H. Freeman & CO.
    Transcendental functions; methods and applications of integration; sequences and series.
    Requisites: courses 31A with a grade of C- or better.

    Class Web Page: http://www.math.ucla.edu/~pasour/31b.2.08w/index.html

    Homework Assignments:
    There will be weekly homework assignments, which will be collected and returned on Friday (lecture). No late homework will be accepted. Please check the Class Web Page for the current homework. It is part of your duty to work additional problems from the textbook, and not only those assigned in the homeworks. You are allowed and encouraged to work together on homework assignments. However, you are expected to write up the homework solutions on your own. When solving problems for homework or exams, you must provide complete solutions with key steps described in detail.

    Examinations: Two midterm exams and one final exam.
    Midterms: Monday, January 28th, February 25th (in lecture).
    Final: Wednesday, March 19, 2008, 11:30am- 2:30pm.
    The examinations are closed-book and closed-note. No calculators will be permitted in any exams.
    No exams at a time other than the designated ones will be allowed (exceptions for illness with document proof, or emergency).

    Grading Policy: Homework assignments: 10%. Midterms: 25% each. Final: 40%.
    Your lowest homework score will not be counted towards your final homework grade.

    LECTURES/HOMEWORK ASSIGNMENTS
    January 7:Section 7.1 Derivative of exponential functions
    HW: 1, 5, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 59, 61, 65, 71, 74.

    January 9: Section 7.2 Inverse functions
    HW: 2, 4, 5, 8, 9, 18, 21, 24, 25, 27, 37.

    January 11: Section 7.3 Logarithms and their derivatives
    HW: 3, 7, 15, 19, 22, 25, 27, 33, 35, 43, 49, 57, 63, 69, 87, 91, 101.
    January 14: Section 7.4 Exponential growth and decay
    HW: 3, 7, 9, 13, 17, 19, 23.

    January 16: Sections 7.5-7.6 Compound interest, Models involving y'=k(y-b)
    HW: 7.5 - 1, 3, 5, 7, 9, 15.
    7.6 - 1, 3, 5, 11, 15.

    January 18: Section 7.7 L'Hopital's Rule
    HW: 1, 5, 9, 11, 13, 21, 25, 29, 43, 55, 59.
    January 21: Martin Luther King, Jr, holiday

    January 23: Section 8.1 Numerical integration. Error bounds for numerical integration
    HW: 1, 5, 9, 15, 19, 21, 23, 29, 39, 41, 47, 55.

    January 25: Section 8.2 Integration by parts
    HW: 3, 5, 9, 11, 13, 21, 23, 33, 35, 39, 43, 47, 51, 63, 67.
    January 28: Exam 1

    January 30: Section 8.3 Trigonometric integrals
    HW: 1, 3, 13, 15, 19, 21, 23, 33, 39, 51, 57.

    February 1: Section 8.4 Trigonometric substitution
    HW: 8.4 - 13, 17, 21, 23, 25, 27, 33, 53.
    February 4: Section 8.5 Method of partial fractions
    HW: 3, 5, 9, 13, 17, 23, 27, 33, 43, 47, 51, 53, 61.

    February 6: Section 8.6 Inproper integrals
    HW: 5, 7, 11, 25, 39, 43, 51, 65, 67, 69, 71, 77.

    February 8: Section 9.1 Arc length
    HW: 3, 5, 9, 11, 19, 21, 25, 33, 37.
    February 11: Section 9.2 Fluid pressure and force
    HW: 1, 3, 5, 9, 11, 19. (warning: answers in back are not necessarily correct)

    February 13: Section 9.4 Taylor polynomials
    HW: 3, 9, 11, 15, 19, 23, 43, 45, 47. (Look at 25 - solution will be provided)

    February 15: Section 9.4 (continued) Taylor's Theorem, Error bounds
    HW: 27 (computer problem - not to turn in), 29, 31, 33, 35, 37, 39.
    February 18: Presidents' Day holiday

    February 20: Section 11.1 Sequences and infinite series
    HW: 3, 7, 11, 15, 21, 27, 33, 37, 39, 41, 42, 49, 51, 59, 65, 71, 75.

    February 22: Section 11.2 Infinite series
    HW: 1, 3, 5, 9, 11, 13, 15, 17.
    February 25: Exam 2

    February 27: Section 11.2 (continued)
    HW: 19, 21, 23, 27, 29, 33, 35, 37, 39.

    February 29: Section 11.3 Convergence of series with positive terms
    HW: 3, 5, 11, 15, 17, 19, 23, 27, 29, 35, 37, 45, 49, 53, 59, 65, 69, 73.
    March 3: Section 11.4 Conditional convergence
    HW: 1, 3, 7, 11, 13, 17, 19, 21, 25, 28, 29.

    March 5: Section 11.5 Ratio and root tests
    HW: 1, 5, 9, 13, 17, 21, 23, 25, 27, 29, 33, 35, 39, 41, 45, 49.

    March 7: Section 11.6 Power series
    HW: 1, 3, 5, 9, 11, 15, 19, 23, 27, 31, 35, 41, 45.
    March 10: Section 11.6 (continued) More on power series
    HW: 46, 47, 51, 53.

    March 12: Section 11.7 Taylor series
    HW: 1, 5, 9, 13, 21, 26, 27, 31, 35, 39, 53, 55, 59, 63, 75.

    March 14: Section 11.7 Taylor series (continued)
    HW: 41, 42, 72.