### MTH/CS 364/464 Numerical Analysis (Spring 2019):

• 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 410, email: sofya.chepushtanova@wilkes.edu.

• Class meetings: MWF 12:00-2:50am, room SLC 405.

• Office Hours: SLC 410, MWR 10:00-10:50am and 2:00-2:50pm or 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 should be able to use it in labs 409 and 431.
Some MATLAB resources:
• Chapter 2 of our textbook will help you to start.
• Here you can find video lectures "Using MATLAB for the First Time" from MIT OpenCourseWare.
• Numerical Computing with MATLAB is an archive of MATLAB programs of basic numerical algorithms,
it is good both for beginners and advanced MATLAB programmers.
• 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. I will post the LaTeX files for all homework assignments throughout the semester.

• Schedule:

 Week of Class Topic Remarks and Materials 1/13 Introduction. Review of Calculus. Computer Arithmetic (Ch. 5). NOTE: We are meeting in SLC 409 on Friday. Brief intro notes Calculus Review Notes Intro to MATLAB m-file 1/20 §4.1 Bisection, §4.2 Taylor's Theorem, §4.3 Newton's Method Monday 1/21 - no class (MLK Day) Notes on Bisection Method Desmos examples: Newton's method with convergence Newton's method with divergence 1 Newton's method with divergence 2 1/27 §4.3 Newton's Method (cont'd); §4.4 Quasi-Newton methods; §4.5 Fixed point iteration Notes on Newton's Method Notes on Quasi-Newton Methods Homework 1 due 01/28 (Monday) (click here to download a tex file) Homework 1 solutions 2/3 §4.5 Fixed point iteration; §4.6 Fractals: Julia set and Mandelbrot set Notes on Fixed Point Iteration Notes on Fractals Desmos demo: fixed points of x+1/x Demo on Julia set and Mandelbrot set: click here 2/10 §§5.3-5.5 Floating Point Representation Notes on Floating Point Representation Homework 2 due 02/11 (Monday) (click here to download a tex file) Homework 2 solutions 2/17 §§8.1-8.2 Lagrange Interpolation Forms Review for Exam I: study guide Notes on Lagrange Interpolation Forms 2/24 §§8.1-8.2 Lagrange Interpolation Forms §§8.3-8.3.1 The Newton Interpolation Form Exam I on 2/24 (Monday) (see solutions!) Notes on the Newton Form 3/3 No classes - Spring Recess 3/10 §8.4 Error in Polynomial Interpolation Notes on Interpolation Error Homework 3 due 03/11 (Monday) Homework 3 solutions 3/17 §8.4 Interpolation at Chebyshev Points §8.5 Piecewise Interpolation (Hermite, Cubic Spline) Notes on Chebyshev Points Notes on Piecewise Interpolation Notes on Hermite Cubic Interpolation Notes on Cubic Splines 3/24 §9.1 Numerical Differentiation §9.2 Richardson Extrapolation Notes on Numerical Differentiation Notes on Richardson Extrapolation Homework 4 due 03/25 (Monday) Download chebfun (MATLAB) Homework 4 solutions MATLAB Examples from Section 9.1: m-file 3/31 §10.1 Numerical Integration §10.2 Formulas Based on Piecewise Interpolation Notes on Numerical Integration Notes on Formulas Based on Piecewise Interpolation Homework 5 due 4/3 (Wednesday) Homework 5 solutions 4/7 §10.3 Gauss Quadrature §10.4 Clenshaw-Curtis Quadrature §10.5 Romberg Integration Notes on Gauss Quadrature Brief Notes on Clenshaw-Curtis Quadrature Notes on Romberg Integration 4/14 No classes on Thursday and Friday - Holiday Recess §10.7 Singularities §11.1 Existence and Uniqueness of Solutions of IVPs Notes on Existence and Uniqueness of Solutions of IVPs Take-Home Exam due 4/15/19 (see solutions) 4/21 §11.2 One-Step Methods (Euler's Method, Higher-Order Methods, Midpoint Method, Runge-Kutta Methods, etc.) Notes on Euler's Method 4/28 MTH 464 student presentation: Wednesday, 5/1. Final Exams begin on Thursday, 5/2 Homework 6 due 5/1 (Wednesday) Take-Home Final Exam due 5/9/19, at 10 am