Math 151A, Lecture 1, Spring 2014

Applied Numerical Methods


Lectures: MWF 4:00pm - 4:50pm, MS 4000A

Instructor: Luminita A. Vese
Office: MS 7620-D
Office hours: Usually after the class in MS 4000A.
E-mail: lvese@math.ucla.edu

Discussion Section: Tuesday, 4.00pm - 4.50pm, MS 5128

Teaching Assistant: Stephanie Lewkiewicz.
Office: MS 6146.
Office hours: Tues 5-7 PM / SMC Hour: Tues 1 - 2 PM.
E-mail: slewkiewicz@math.ucla.edu


Textbook: R.L. Burden and J.D. Faires, Numerical Analysis, 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.

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 151A: Description, Textbook, Schedule of Lectures
  • PIC Lab: Boelter Hall 2817
    http://www.pic.ucla.edu/piclab/
  • MATLAB documentation
  • More about matlab
  • Another MATLAB Documentation, thanks to Professor Chris Anderson (UCLA)
  • Numerical Recipes

    Class Web Page: http://www.math.ucla.edu/~lvese/151a.1.14s/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, May 7, 4pm-4.50pm (during lecture).
    Final: Monday, June 9, 2014, 11:30am-2:30pm.
    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: 30%. Midterm: 30%. Final: 40%.
    Your lowest homework score will not be counted towards your final homework grade.
    Late homework may be turned in, but it will only get credit if it is turned in and received before the reader has started grading the assignments.

    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 Wednesday, April 9.
    HW1.pdf
  • Reading: sections 1.1, 1.3, 1.4 and the matlab code given below (compare with algorithm 2.1. from the textbook).
    You can use a hand calculator. 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 from here
    HW # 2: Due on Wednesday, April 16.
    HW2.pdf
    Matlab code for Newton's Method
    In matlab, when the code prompts you to enter the function (for example cos(x)), you must enter: 'cos(x)'
    C++ code for Newton's Method
    You can also run the codes from here
    HW # 3: Due on Wednesday, April 23.
    HW3.pdf
    HW # 4: Due on Wednesday, April 30.
    HW4.pdf
    HW # 5: Due on Wednesday, May 7.
    HW5.pdf
    HW # 6: Due on Wednesday, May 14.
    HW6.pdf
    HW # 7: Due on Wednesday, May 21, or on Friday, May 23.
  • Reading: Sections 4.2 and 4.3.
  • Problems:
    Section 4.2: Exercises #8 and #9.
    Section 4.3: Exercises #2(a), #4(a), #6(a), #8(a), and #20.
    HW # 8: Due on Friday, May 30.
  • Problems:
    Section 4.4: #1(e), #3(e), #5(e), #11.
    Section 4.7: # 1(a), # 2(a), #6.
    HW # 9: Due on Friday, June 6.
  • 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)
    Section 6.6, problems #1(a)(b)(c)