Math 151A, Lecture 2, Winter 2007

Applied Numerical Methods

  • Final exam: Thursday, March 22, 2007, 11:30am-2:30pm, in MS 5127.
  • Office Hours before the final exam: Wednesday, 1.30pm - 3.30pm, MS 7620-D.
  • All sections are covered for the final. However, slightly more questions will be given from the material covered after the midterm (sections 1.2, 2.1-2.4, 3.1, 3.2, 4.1, 4.3, 4.4, 4.7, 6.1, 6.2, 6.5, 6.6).
  • Old final exams are posted below (without solutions)
  • Midterm solutions are posted below.
    Lectures: MWF 11:00am - 11:50am, MS 5127

    Instructor: Luminita A. Vese
    Office: MS 7620-D
    Office hours: Mon 3-4pm, Wed 2-4pm, or by appointment.
    E-mail: lvese@math.ucla.edu

    Discussion Section: Thursday, 11.00am - 11.50am, MS 5127

    Teaching Assistant: Aleka McAdams.
    Office: MS 3973.
    Office hours: Tuesday 12:30-1:30, Thursday 1:30-2:30 or by appointment.
    E-mail: amcadams@math.ucla.edu

    Textbook: R.L. Burden and J.D. Faires, Numerical Analysis, 8th ed. , Brooks/ Cole.
    Introduction to numerical methods with emphasis on algorithms, analysis of algorithms, and computer implementation issues. Solution of nonlinear equations. Numerical differentiation, integration, and interpolation. Direct methods for solving linear systems.

    Errata for the textbook

    A copy of the textbook has been placed on reserve at the SEL Library.

    Requisites: courses 32B, 33B, 115A, Program in Computing 10A.

    Useful Links:
  • Course Info on Math 151ab
  • General Course Outline & Catalog Description for Math 151a
  • Virtual Office Hours
  • PIC Lab: Boelter Hall 2817
    http://www.pic.ucla.edu/piclab/
  • MATLAB documentation
  • More about matlab
  • Another MATLAB Documentation, thanks to Prof. C. Anderson, UCLA
  • Numerical Recipes in C

    Class Web Page: http://www.math.ucla.edu/~lvese/151a.2.07w/index.html

    Homework Assignments:
    Homework assignments consist of both theoretical ("pencil-and-paper" type) and computational work (at calculator level, but we will also do some programming).
    The homework assignments will be assigned and graded every week.
    The homework assignments will be collected every week 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.

    Computing:
    Enrolled students will have accounts in the computer labs in Boelter Hall 2817.
    The students can use any software and any language for the computational assignments.
    Matlab is a very good choice. C++ is also a good choice.
    The algorithms from the textbook will be provided to you in Matlab and C++ (available on the Class Web Page, with the homework assignments).

    Examinations: One midterm exam and one final exam.
    Midterm: Wednesday, February 21st, 11pm-11.50pm (lecture).
    Final: Examination Code: 04 - Thursday, March 22, 2007, 11:30am-2:30pm, in MS 5127.
    The examinations are closed-book and closed-note.
    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: 25%. Midterm: 25%. Final: 50%.
    Your lowest homework score will not be counted towards your final homework grade.

    Sample Matlab code for fixed-point iteration, to solve Example 3, pages 57-58

  • Solutions to selected exercises
  • Old midterm exam I (without solutions)
  • Old midterm exam II (without solutions)
  • Old midterm exam III (without solutions)

    Sample old final exams (without solutions)
  • Old final exam I
  • Old final exam II
  • Old final exam III
  • Old final exam IV

  • Midterm Solutions

    HOMEWORK ASSIGNMENTS
    HW # 1: Due on Friday, January 12. HW1.pdf
  • Reading: sections 1.1, 1.3, 1.4 and the matlab code given below (compare with algorithm 2.1. from the textbook, page 47).
  • Problems from section 2.1: #1 (with a hand calculator), #2(a) (with a hand calculator), #7(ab), #12, #15.
    For the longer calculations, you can use one of the codes below or online:
    Matlab code for the bisection method
    In matlab, when the code prompts you to enter the function (for example cos(x)), you must enter: 'cos(x)'
    C++ code for the Bisection method
    Mathematica code for the Bisection method
    You can also run the codes in Java, online, from here
    HW # 2: Due on Friday, January 19. HW2.pdf
  • Reading: sections 2.1 and 2.2
  • Problems from section 2.2: #1(a,b), #2 (for #1ab only), #7, #9, #19(a).
    No explicit code is provided this time. You may want to write your own fixed-point iteration code in the language of your choice for the longer calculations. Please include your code with the solutions.
    HW # 3: Due on Friday, January 26. HW3.pdf
    C Newton's algorithm
    C Secant algorithm
    Matlab Newton's algorithm
    Matlab Secant algorithm
    Mathematica Newton's algorithm
    Mathematica Secant algorithm
    HW # 4: Due on Friday, February 2. HW4.pdf
    HW # 5: Due on Friday, February 9.
  • Reading: sections 1.2 and 3.1
  • Problems:
    Section 1.2: # 13(a), 21.
    Section 3.1: # 2(a), 4 (for 2(a) only), 8 (for 6(a) only), 19a, 22
    HW # 6: Due on Friday, February 16.
  • Reading: 3.1, 3.2, 4.1.
  • Problems:
    Section 3.2, # 2(a), 16.
    Section 4.1, # Problems # 6(a), 8(a), 20, 22.
    HW # 7: Due on Friday, March 2.
  • Reading: Sections 4.3, 4.4, 4.7.
  • Problems: Section 4.3, numbers 2(a), 4(a), 6(a), 8(a), 10(a), 12(a), 14, 16, 18, 20.
    HW # 8: Due on Friday, March 9.
  • Reading: Sections 4.4, 4.7.
  • Problems:
    Section 4.4: # 8, 14(a,c), 21
    Section 4.7: # 1(a), 2(a), 6, 8.
    HW # 9: Due on Friday, March 16.
  • Reading: Sections 6.1, 6.2, 6.5, 6.6
  • Problems:
    Section 6.1, problems # 6(a,c), 9
    Section 6.2, problems # 10(a), 14(a), 18(a)
    Section 6.5, problems # 6(a), 8(c)