Nilima Nigam
Associate Professor of Mathematics
BH 1119
Tel: 514-398-3804
Main Research Publications Teaching

McGill University
Elementary Numerical Analysis - Math 317 Fall 2006
MWF 1:35:2:25 pm


Professor: N. Nigam
Office :   Burnside Hall
 Room No. 1119
Telephone: 398-3804
Email : nigam@math.mcgill.ca
Office Hours :Tuesdays 11:00-12:30, Fr:11:40-1:00
Or by appointment
  • Class stuff: Homework and term project: (30%) Homeworks and/or computer assignments will be collected. The term project will be worth 20% of the final grade, based on discussions, progress reports and a final written report.
    Tests : (25%)  
    FINAL : (45%) There will be a 3-hour cumulative final examination in December '06
  • Course Description: We will discuss numerical root-finding, interpolation and polynomial approximation, numerical differentiation and integration, and an introduction to the iterative solution of linear systems. We shall also study initial  and boundary value problems. We  introduce the finite difference method for linear second order pde, and draw attention to the special characteristics of elliptic, parabolic and hyperbolic solvers. Error analysis and stability will be a recurring theme in the course. This material is covered in the  chapters 1-6, 11 and 12 of the textbook. Where necessary, supplementary notes will be provided.
    In addition, computing assignments will help illustrate concepts learnt in class. You may use any computing language for your assignments, though Maple and Matlab are recommended. Location of computing facilities will be announced in class.
    Finally, term-long group projects shall be used to demonstrate the utility and versatility of numerical analysis. A more detailed outline of the course is given in table 1.
  • Course prerequisites: Calculus 3 (MATH/222), programming (308/202 or equivalent). Taylor's theorem, determinants, eigenvalues and eigenvectors are assumed, and will be briefly reviewed.  Students should be familiar with the mathematical material taught in a first linear algebra and differential equations course.
  • Policies : A full schedule for lecture topics has been provided. You are urged to read the textbook; if possible, read ahead!
    • In general, no make up tests will be given. Exceptions will only be made if a University certified written excuse is provided.
    • No late homework or computing assignments will be accepted under any circumstances barring an absence approved by the instructor
    • On-line communication: Important announcements, due-dates,  course-hand-outs, and discussion forums will be available at the appropriate WebCT location.
    • Email response time: I  attempt to reply to email in a timely fashion, but the average response time is 48 hours. Neither I nor the TAs will reply to email sent
      the day before an exam.
    • Attendence in class: This is not a distance learning course. Should you miss a lecture, you are responsible for making up any material covered in class - use the Tentative Lecture Schedule as a guide.
    • Home works and tests: It is expected that you try sample problems from the textbook at the end of each day. This will help you understand, and use, the concepts explained in class. Homework problems and due dates will be announced, and posted on the web.
      See Table:In TENTATIVE LECTURE SCHEDULE.
      Lecture No. Sections Remarks
      1 Introduction  
      2 1.1, 1.2  
      3 1.2, 1.3  
      4  Review,  2.1  
      5 2.2 Numerical root-finding
      6 2.3  
      7 2.3, 2.4  
      8 2.4  
      9 2.5  
      10  2.6  
      11 Review  
      12 3.1 Polynomial Interpolation
      13 3.1  
      NOTE TEST 1 covers Chapters 1, and 2 NOTE
      14 TEST 1   
      15 3.2  
      16 3.3  
      17 3.4  
      18 3.5  
      19 4.1 Differentiation and quadrature 
      20 4.2
      21 4.3  
      22 4.4  
      23 4.7  
      24 5.1 IVP 
      25 5.2  
      NOTE TEST 2 covers Chapters 3, 4.1-4.4, 4.7, 5.1 NOTE
      26 Test 2  
      27  5.2,5.3 IVP's
      28 5.4  
      29 5.5  
      30 5.11  
      31 6.1 Linear systems 
      32 7.3
      33 11.1 BVP 
      34 11.3 BVP 
      35 11.4  
      36 12.1 PDE 
      37 12.2  
      38 12.2, 12.3  
      39 12.3  

      Homework List
      The section numbers and questions relate to the textbook,
      Numerical Analysis by Burden and Faires,  7th Ed.

  • Academic honesty: The work you hand in should be your own effort.  You must acknowledge  any collaboration, and sources (books, online materials, tutors)  etc. which you have referred to or received help from.  Computer codes will also be  checked for originality. Any evidence of plagiarism/cheating will be taken seriously and dealt with through the established McGill procedures.

    The following statement is included in accordance with McGill Senate regulations:
    McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of
    cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see
    www.mcgill.ca/integrity for more information).

    You may wish to consult the McGill Student guide to avoid plagiarism.
    Plagiarism and academic dishonesty are serious offences, and will be treated as such. 

  • Non-registered students : To get credit for this course, you must be registered for it. No credit will be given otherwise.