CS/MTH 364/464 Numerical Analysis (Spring 2021):

  • Overview:
    This course is an introduction to numerical algorithms as tools to providing solutions to common problems formulated in mathematics, science, and engineering. Focus is given to developing the basic understanding of the construction of numerical algorithms, their applicability, and their limitations. Topics include numerical techniques for solving equations, polynomial interpolation, numerical integration and differentiation, numerical solution of ordinary differential equations, error analysis and applications. Here is the course syllabus.

  • Instructor: Dr. Sofya Chepushtanova, office SLC 408, email: sofya.chepushtanova@wilkes.edu.

  • Class meetings: MWF 12:00-2:50 am, room SLC 424.

  • Office Hours: MWR 10:00-11:00 am and 2:00-03:00 pm or by appointment.
    Note that most office hours will be held virtually via Google Meet. The following link will allow you to sign up for a 20-minute slot (within office hour times listed above): sign-up calendar.

  • Textbook: Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms by Anne Greebaum and Timothy Chartier, Princeton University Press, 2012.

  • Our programming language is MATLAB. You will be able to use it in our lab as well as remotely.
    Some MATLAB resources:
  • LaTeX: a markup language to typeset documents. It excels at making math and the overall layout beautiful. You may want to use it to type your homework solutions, and I encourage you to do so. Read the tutorial here. You may find the following LaTeX cheat-sheet useful.


  • Schedule (updated as the semester progresses):

    Week Class Topic Remarks and Materials

    2/1 Introduction. Review of Calculus. Introduction

    Calculus Review Notes

    2/8 Intro to MATLAB (Ch. 2).
    Computer Arithmetic (Ch. 5).
    Intro to MATLAB: m-file

    Notes on Computer Arithmetic

    2/15 (Ch.4) §4.1 Bisection.

    §4.2 Taylor's Theorem, §4.3 Newton's Method.
    Notes on Bisection Method

    Bisection routine: m-file
    You can call "bisection" from here: m-file
    (and choose your own function and interval)

    Notes on Newton's Method

    Desmos examples:
    Newton's method with convergence
    Newton's method with divergence 1
    Newton's method with divergence 2

    Newton's method routine: m-file

    Homework 1 due 02/17 ( solutions )

    2/22 §4.4 Quasi-Newton methods.

    §4.5 Fixed point iteration.
    Notes on Quasi-Newton Methods

    Notes on Fixed Point Iteration

    "Cobweb plotting" routine: m-file
    "Defining a function" routine: m-file

    3/1 §4.6 Fractals: Julia set and Mandelbrot set.

    §8.2 Lagrange Interpolation Forms.
    Notes on Fractals

    Julia set: m-file

    Demo on Julia set and Mandelbrot set: click here

    Notes on Lagrange Interpolation Forms

    Homework 2 due 03/03 ( solutions )

    3/8 §8.3 Newton Interpolation Form.

    §8.3.1 Divided Differences.
    Notes on Newton Interpolation Form

    Notes on Divided Differences

    3/15 Exam I on 3/19 (Friday)

    §8.4 Error in Polynomial Interpolation
    Notes on Interpolation Error

    Lab m-file examples:
    Runge function
    Divided differences
    Vandermonde system

    Exam I study guide and solutions

    Homework 3 due 03/17 ( solutions )

    3/22 §8.5 Interpolation at Chebyshev Points

    §8.6 Piecewise Interpolation
    (Linear, Quadratic, Hermite, Cubic Spline)
    Notes on Chebyshev Points

    Chebfun package m-file example
    (download chebfun here )

    Notes on Piecewise Linear Interpolation

    Notes on Hermite Cubic Interpolation

    3/29 §8.6 Continued

    No classes 04/01-04/02
    Notes on Cubic Spline Interpolation

    Lab m-file examples:
    Chebfun polynomial
    Barycentric formula with Chebyshev points
    Hermite cubic interpolant
    Cubic spline interpolant


    4/5 §9.1 Numerical Differentiation

    §9.2 Richardson Extrapolation
    Notes on Numerical Differentiation

    Notes on Richardson Extrapolation

    MATLAB Examples from Section 9.1: m-file

    Homework 4 due 4/5 ( solutions )

    4/12 §10.1 Numerical Integration

    §10.2 Formulas Based on Piecewise Interpolation
    Notes on Newton-Cotes Formulas

    Notes on Piecewise Integration

    4/19 Homework 5 due 4/19 (Monday)

    4/26 No class on 4/28 (Wednesday)

    5/3

    5/10 MTH 464 Presentations ( list of topics )