MTH/CS 364/464 Numerical Analysis (Fall 2016):
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: Sofya Chepushtanova, office SLC 410, email: firstname.lastname@example.org.
- Class meetings: MWF 2:00-2:50am, room SLC 403.
- Office Hours: SLC 410, MWF 10:00-10:50am and TTh 1:00-1:50pm 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.
|Week||Class Topic||Remarks and Materials|
|8/29||Introduction. Review of Calculus.
Computer Arithmetic (Ch. 5). §4.1 Bisection
|Intro to MATLAB m-file|
|9/5||§4.2 Taylor's Theorem, §4.3 Newton's Method||Monday 9/5 - no class (Labor Day)|
|9/12||§ 4.4 Quasi-Newton methods, § 4.5 Fixed point iteration||Homework 1 due 9/12|
|9/19||§ 4.6 Fractals, § 8.2 Polynomial interpolation||Homework 2 due 9/21|
|9/26|| § 8.2 Polynomial interpolation,
§ 8.3 The Newton form and divided differences
|10/3|| § 8.4 The error in polynomial interpolation
Review and Exam I on Friday, 10/7
|Homework 3 due 10/5|
|10/10||§ 8.5 Interpolation at Chebyshev points,
§ 8.6 Piecewise polynomial interpolation
|No classes 10/13 and 10/14 - Fall Recess|
|10/17||§ 8.6 Piecewise polynomial interpolation (cont.)||Homework 4 due 10/21
Download chebfun (MATLAB)
|10/24||§ 9.1 Numerical Differentiation,
§ 9.2 Richardson Extrapolation
|10/31||§ 10.1 Newton-Cotes Formulas,
§ 10.2 Formulas based on piecewise interpolation
|Homework 5 due 11/7|
|11/7||§ 10.3 Gauss quadrature,
§ 10.4 Clenshaw-Curtis quadrature
|Take-home Exam II|
|11/14||§ 10.5 Romberg Integration,
§ 10.6 The Euler-Maclaurin formula
|11/21||§ 11.1 Existence and Uniqueness of Solutions,
§ 11.2 One-Step Methods
|No classes 11/23-25 - Thanksgiving Recess|
|11/28||§ 11.2 One-Step Methods||Homework 6 due 12/2|
|12/5||Students presentations||List of topics|
|12/12||Students presentations||Take-home final due 12/17/16, 10am|