CS/MTH 364/464 Numerical Analysis (Spring 2023):

  • 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 11:00-11:50 am, room SLC 359.

  • Office Hours: MWR 12:00-12:50 pm and by appointment.

  • 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 Topic Materials and Homework
    1. Introduction. Review of Calculus. Calculus Review Notes
    2. Computer Arithmetic (Ch. 5). Notes on Binary Representation
    Notes on Floating Point Representation

    Due 2/6: Homework 1 ( solutions )
    3. Intro to MATLAB (Ch. 2).

    Computer Arithmetic (Ch. 5) Continued.

    §4.1 Bisection.     		Intro to MATLAB: m-file

    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 Rounding
    4. §4.2 Taylor's Theorem.

    §4.3 Newton's Method.

    §4.4 Quasi-Newton methods.     		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

    Notes on Quasi-Newton Methods

    Due 2/22: Homework 2 ( solutions )
    5. §4.5 Fixed point iteration.

    §4.6 Fractals: Julia set and Mandelbrot set.

    		Notes on Fixed Point Iteration

    Desmos Examples:
    Fixed point "cobweb" plot 1
    Fixed point "cobweb" plot 2

    Fixed point iteration in complex plane: m-file

    Notes on Fractals
    Julia set and Mandelbrot set: slides

    Julia set: m-file
    6. §§8.1,8.2 Lagrange Interpolation Forms.

    §8.3 Newton Interpolation Form.     		Notes on Lagrange Interpolation Forms

    Notes on Newton Interpolation Form

    Due 3/13: Homework 3 ( solutions )
    7. Exam I on 2/27 (Monday)

    §8.3.1 Divided Differences.

    §8.4 Error in Polynomial Interpolation     		Notes on Divided Differences

    Notes on Interpolation Error

    M-files:
    Runge function
    Divided differences
    Vandermonde system

    Exam I outline ( solutions )
    8.Spring Break
    9. §8.5 Interpolation at Chebyshev Points

    §8.6 Piecewise Linear Interpolation     		Notes on Chebyshev Points

    Chebfun package m-file example
    (download chebfun from here)

    Notes on Piecewise Linear Interpolation

    Due 3/27: Homework 4 ( solutions )
    10. §8.6 Piecewise Interpolation Continued
    (Quadratic, Hermite, Cubic Spline)

    §9.1 Numerical Differentiation     		Notes on Hermite Interpolation

    Notes on Cubic Spline Interpolation

    Lab m-file examples:
    Hermite cubic interpolant
    Cubic spline interpolant
    11. §9.1 Numerical Differentiation Continued

    §9.2 Richardson Extrapolation     		Notes on Numerical Differentiation

    Notes on Richardson Extrapolation

    MATLAB Examples from Section 9.1: m-file

    Due 4/12: Homework 5 ( solutions )
    12. §10.1 Numerical Integration

    §10.2 Formulas Based on Piecewise Interpolation

    No class on Friday - Holiday Break    		 Notes on Newton-Cotes Formulas

    Notes on Piecewise Integration
    13. §10.3 Gauss Quadrature

    §10.4 Clenshaw-Curtis Quadrature

    §10.5 Romberg Integration    		 Notes on Gauss (and Clenshaw-Curtis) Quadrature

    Notes on Romberg Integration
    (Romberg integration routine)
    14. §10.7 Singularities

    §11.1 Existence and Uniqueness of Solutions of IVPs     		Take-Home Exam 2 is due 4/21/23

    Notes on Improper Intergals

    Examples of IVPs

    Existence and Uniqueness of Solutions of IVPs

    Due 5/3: Homework 6
    15. §11.2 One-Step Methods
    (Euler's Method, Higher-Order Methods,
    Midpoint Method, Runge-Kutta Methods)     		Notes on Euler's Method

    Notes on Other One-Step Methods

    Notes on Runge-Kutta Methods

    Examples with MATLAB ODE Solver
    16. MTH 464 Presentations Take-home final is due Friday, 5/12, 10 am