CS/MTH 364/464 Numerical Analysis (Spring 2021):
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.
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.
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.
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
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:
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
No classes 04/01-04/02
| Notes on Cubic Spline Interpolation
Lab m-file examples:
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)|
|5/10||MTH 464 Presentations ( list of topics )|