Course Syllabus MATH 4310/5310
Numerical Analysis
Spring Semester 2009

Meeting times:

Tuesday and Thursday 1:00 - 2:25.


Kirksey Od Main, Room 202


Jan Zijlstra, Ph.D.

Office :

Kirksey Old Main 257    (615) 898-2691/5422

Web Materials:


Office Hours:

  • Monday : 8:30 - 11:00 and 12:30 - 2:30

  • Tuesday: 8:30 - 9:30

  • Wednesday: 8:30 - 11:00 and 12:30 - 2:30

  • Thursday: 8:30 - 9:30 and 11:00 - 12:30

  • Friday: 8:30 - 11:00 and 12:30 - 2:30
     Other times by appointment, please.

Prerequisite: Math 3180 (Intro to Num. Anly.) must have been completed successfully.
Prior experience with a higher order programming language such as Fortran or C is expected.
Note: Contact your instructor immediately if this requirement has not been met.
Course Materials: Textbook: Burden, Richard L and J Douglas Faires: Numerical Analysis. 8th ed. Brooks/Cole Publishers, 2005.
                   ISBN 0-534-39200-8.
Calculator: Texas Instruments 83/84(plus) graphing calculator.
Miscellaneous: Engineering pad, straight-edge and compasses.
Main Topics:
  • Review of some key results from Real Analysis: Rolle's Theorem, Intermediate Value Theorem, Mean Value Theorem, Extreme Value Theorem and Taylor's Theorem.
  • Machine computation and Error:
    • Chopping vs Rounding Arithmetic,
    • Absolute and Relative error and error propagation
  • Solution of Equations in one variable
    • Bisection*
    • Fixed point iteration*
    • the Newton-Raphson algorithm*
    • Roots of Polynomials: Horners and Muellers Methods*
  • Interpolation Techniques
    • Lagrange Polynomials*
    • Divided Differences*
    • Hermite interpolation
    • Cubic Spline Interpolation*
    • Bezier Curves*
  • Numerical Differentiation
    • (n+1)-point formulas
    • Richardson Extrapolation
  • Numerical Integration
    • Trapezoid and Simpson's Rules
    • Romberg Integration*
    • Adaptive Quadrature
    • Gaussian Quadrature*
  • Numerical Treatment of Initial Value Problems
    • Euler's method
    • Higher Order Taylor Methods
    • Runge-Kutta Methods*
  • The solution of Systems of Linear Equations
    • Gaussian Elimination with Back-substitution
    • Pivoting Strategies*

Scale :

Approx. 8  laboratory with programming assignments from the starred topics:  50 points each
                                               1 in-class mid term exam   : 100 points
(5310 only) Presentation:                                         : 50 points.
                        Comprehensive in-class Final Exam       : 200 points

A: 100-90, B+: 89-87, B:86-83, B-: 82-80, C+: 79-77, C:76-73, C-: 72-70, D+: 69-67, D:66-63, D-: 62-60, F: < 60 points.

Absences: Tests can be made up only with a Valid University Excuse, see Student Handbook for details.
  • Throughout the course, we will use the computer algebra system MAPLE to support computational and graphing tasks. Prior experience with a higher order programming language such as Fortran or C is expected.  Introductory MAPLE and MATLAB sessions will be held as soon as lab space is secured.
  • The 8 laboratories are take-home sets of assignments which will address both theoretical and practical (modeling) questions.
  • Students enrolled in 5310 will be given additional exercises including proofs of relavant theorems and are to give a short presentation on an assigned topic towards the end of the semester. 
  • If you have a disability that may require assistance or accomodation, or you have questions related to accomodations for  testing, note-takers, readers, etc., please contact me as soon as possible. You may also contact the Office of Disabled Student Services (898-2783) with questions about such services.
  • To retain Tennessee Education Lottery Scholarship (TELS) eligibility, you must earn a cumulative TELS GPA of 2.75 after 24 attempted hours and a cumulative TELS GPA of 3.0 thereafter. A grade of C, D, F, or I in this class may negatively impact TELS eligibility. Dropping a class after 14 days may also impact eligibility. If you withdraw from this class and it results in an enrollment status of less than full time, you may lose eligibility for your lottery scholarship. For additional lottery scholarship rules please refer to your Lottery Statement of Understanding form, review lottery scholarship requirements on the web at, or contact the MTSU financial aid office at 898-2830.
Important Dates: January 15: First Day of Classes
January 19: MLK Day - no Classes
January 28: Last day to drop without a grade.
March 9 - 14: Spring Break, no classes.
March 4: Last day to drop with a 'W'. No 'W' will be granted after this date.
April 22: Deadline to withdraw from the University i.e. from all classes
April 29: Last Day of Classes.
Final Exam: Tuesday May 5, 1:00 - 3:00