Introduction to Numerical Analysis

Math 5610/6860


Name: Michael Medvinsky
Lectures: MTWH 10:45-11:35 , SW 137
Office Hours: MTWH 11:50am - 12:30pm, or by appointment
Office: JWB 125

Note: Office hours are tentative, i.e. it may be some changes, but you always welcome to knock on my door if you around.


Multivariate calculus (e.g. Math 2210 Calculus III), basic linear algebra (e.g. Math 2250 or Math 2270) and basic programming.


Atkinson, K, An Introduction to Numerical Analysis, 2nd ed, New York. Wiley, 1989. ISBN-13: 9780471624899

The course

The purpose of this course is the understanding of numerical methods utilized in the sciences. Specifically, the goals are that each student will gain a working understanding of the following topics: error analysis, numerical solutions of non linear equations, interpolation and extrapolation methods, numerical differentiation and integration, numerical linear algebra and approximation of functions. Another goal of the course is that the student will be able to program one or more of the numerical methods discussed in the course. Emphasis will be placed on understanding the basic concepts behind the various numerical methods studied, implementing basic numerical methods using the MATLAB structured programming environment.

Tentative Plan of Lectures

The topics may be changed, reordered, added or omitted, depending on time constraints.

  1. Calculus review, Taylor's theorem(Chap 1), Assymptotic Order Notations, Matlab primer
  2. Computer Representation of Numbers, Error Analysis, Stability (Chap 1)
  3. Root finding of nonlinear equations, Fixed Point Iteration (Chap 2)
  4. Interpolation and polynomial approximation, Splines (Chap 3), Chebyshev Interpolation Points (Chap 4)
  5. Numerical differentiation and integration (Chapters 3 & 5)
  6. Approximation of functions (Chap 4)
  7. Direct and Iterative numerical solution of systems of linear equations (Chap 7 & 8)
  8. (if time permits) Numerical Solution to differential equations (Chap 6)
  9. (if time permits) Approximating eigenvalues (Chap 9)

Computer Lab

The Math Department's Computer lab is located between LCB and JWB in the T. Benny Rushing Mathematics Center, room 155C. Hours are 8am-8pm Monday-Thursday and 8am-6pm on Friday.


There will be a homework assignment every one or two weeks, due on Mondays by the end of class.
Download your first assignment here.

Term Project

To be announced later in class.


Grades are computed as a weighted average comprising 40\% homework scores, 30\% for term project score and 30\% the final exam score.

Math 6860 Option

For graduate students, you can take this class as Math 6860. If you take this class as Math 6860 you are required to do some extra work and will be evaluated differently. For example (the precise details will be discussed with the instructor during first week or so):
  • In your homework and/or final exam you may get extra problems or questions, that require a deeper understanding of the material. They will be clearly indicated and may substitute questions for Math 5610 students. Some of the questions intended for graduate students may be counted as extra credit for the rest of the class.
  • More rigorous solutions are expected.
  • The project you choose should be sufficiently challenging (to be discussed with the instructor).
  • You may be asked to give a presentation or lecture in the class.

Lectures notes

The material that I handed out in class can be found here (be careful, it may have mistakes).


The final exam will be in our regular classroom on

Monday, Dec. 15, 2014 10:30 am - 12:30 pm

The Date is fixed. Please plan your schedule around these dates now.

ADA Statement

The Americans with Disabilities Act requires that reasonable accommodations be provided for students with physical, sensory, cognitive, systemic, learning and psychiatric disabilities. Please contact me at the beginning of the semester to discuss any such accommodations for the course.

Copyright notice

All printed and electronic materials provided to you in this course are protected by copyright laws.

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