Introductory Numerical Analysis

Course number: MA-UY 4423
Semester: Spring 2016
Time & Location: Tues & Thurs, 2:00pm - 3:30pm in JABS 673
Instructor: Mike O'Neil (
Office hours: Tues & Thurs, 3:30pm - 5:00pm in RH 321F
Course description

This course will serve as an introduction to the topic of numerial analysis for those students interested in gaining some knowledge of the computational aspects of mathematics on modern day computers. This course is intended for students that have completed Calculus II, Ordinary Differential Equations, and (maybe) have some programming experience. Topics covered in this class will include: floating-point arithmetic, numerical integration and differentiation, interpolation, numerical linear algebra, orthogonal polynomials, and solution of ODEs. Time permitting, algorithms used in Monte Carlo methods and optimization will be covered. Programming assignments will be in Matlab.


The course text will be Greenbaum and Chartier, Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms. Notes covering additional topics in numerical linear algebra will be provided. Course homework will partially be drawn from the textbook.

Other textbooks that might serve as useful supplements are:

  • Burden and Faires, Numerical Analysis
  • Suli and Mayers, An Introduction to Numerical Analysis
  • Stoer and Bulirsch, Introduction to Numerical Analysis (more advanced)


The grades in the course will be determined based on homework, a midterm exam, and a final exam. Details to follow.


Important information, and homework assignments, for the course will appear below as necessary.


Below is an updated list of lecture topics along with any documents that were distributed, or relevant code.

Date Topics Materials
Tues. Jan 26 Introduction & overview
Thurs. Jan 28 Newton, secant method, fixed point
Tues. Feb 2 Multivariate Newton, optimization newton.pdf
Thurs. Feb 4 Floating point arithmetic
Tues. Feb 9 Conditioning and stability
Thurs. Feb 11 LU factorization
Tues. Feb 16 Matrix conditioning
Thurs. Feb 18 Least squares, SVD
Tues. Feb 23 Lagrange interpolation
Thurs. Feb 25 Interpolation error, Chebyshev polynomials
Tues. Mar 1 Splines, numerical differentiation
Thurs. Mar 3 Numerical differentiation, finite differences
Tues. Mar 8 Review for midterm
Thurs. Mar 10 Midterm exam
Tues. Mar 15 No class - spring break
Thurs. Mar 17 No class - spring break
Tues. Mar 22 Richardson extrapolation, trapezoidal rule
Thurs. Mar 24 Gaussian quadrature integration.pdf
Tues. Mar 29 ODE: Euler's method
Thurs. Mar 31 ODE: Trapezoidal method, Heun's method
Tues. Apr 5 ODE: Runge-Kutta methods
Thurs. Apr 7 ODE: Linear difference equations
Tues. Apr 12 ODE: Stability
Thurs. Apr 14 Intro to eigenvalue computation
Tues. Apr 19 Power methods
Thurs. Apr 21 Iterative solvers iterative.pdf
Tues. Apr 26 The FFT fft.pdf
Thurs. Apr 28 The FFT
Tues. May 3 Methods for PDEs
Thurs. May 5 Review for final exam
Tues. May 17 Final exam