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Numerical Analysis (CS 450) Fall 2021

What	Where
Time/place	Tue/Thu 11:00am--12:15pm 0027/1025 Campus Instructional Facility / Catalog
Class URL	https://bit.ly/cs450-f21
Class recordings	Illinois Mediaspace
Live Lecture	Meeting Link
Online Office Hours	Meeting Link (on Zoom)
Web forum	Discuss » · Help Desk
Instant Message	Send »
Calendar	View »

Quizzes

Take quiz for next lecture »

Older quizzes

You can also find past quizzes under their corresponding lecture in the class calendar.

Homework

Homework Set 1 (due: Sep 1, 2021, 10pm)
Homework Set 2 (due: Sep 8, 2021, 10pm)
Homework Set 3 (due: Sep 22, 2021, 10pm)
Homework Set 4 (due: Sep 29, 2021, 10pm)
Homework Set 5 (due: Oct 15, 2021, 10pm)
Homework Set 6 (due: Oct 20, 2021, 10pm)
Homework Set 7 (due: Nov 3, 2021, 10pm)
Homework Set 8 (due: Nov 12, 2021, 10pm)
Homework Set 9 (due: Dec 1, 2021, 10pm)
Homework Set 10 (due: Dec 8, 2021, 10pm. May be turned in without penalty until Dec 10, 2021 10pm.)

4-Credit Hour Assignment

Assignment 1 (4-credit hour) (due: Nov 9, 2021, 10pm)
Assignment 2 (4-credit hour) (due: Dec 8, 2021, 10pm. May be turned in without penalty until Dec 10, 2021 10pm.)

Exams

Please find information on our upcoming exams in the corresponding section of the class calendar. Reserve your time slots in the testing facility as soon as possible--otherwise your preferred times may no longer be available.

Course Outline

Introduction to Scientific Computing
Systems of Linear Equations
Linear Least Squares
Eigenvalue Problems
Nonlinear Equations
Optimization
- Introduction
- Methods for unconstrained opt. in one dimension
- In-Class Activity: Optimization Theory
- Methods for unconstrained opt. in $n$ dimensions
- In-Class Activity: Optimization Methods
- Nonlinear Least Squares
- Constrained Optimization
- Demo: Conjugate Gradient Method
- Demo: Gauss-Newton
- Demo: Golden Section Proportions
- Demo: Nelder-Mead Method
- Demo: Newton's Method in 1D
- Demo: Newton's Method in n dimensions
- Demo: Sequential Quadratic Programming
- Demo: Steepest Descent
Interpolation
Numerical Integration and Differentiation
- Numerical Integration
- Quadrature Methods
- Accuracy and Stability
- Gaussian Quadrature
- Composite Quadrature
- Numerical Differentiation
- Richardson Extrapolation
- In-Class Activity: Differentiation and Quadrature
- Demo: Accuracy of Newton-Cotes
- Demo: Finite Differences vs Noise
- Demo: Floating point vs Finite Differences
- Demo: Gaussian quadrature weight finder
- Demo: Newton-Cotes weight finder
- Demo: Richardson with Finite Differences
- Demo: Taking Derivatives with Vandermonde Matrices
Initial Value Problems for ODEs
- Existence, Uniqueness, Conditioning
- Numerical Methods (I)
- Accuracy and Stability
- Stiffness
- Numerical Methods (II)
- In-Class Activity: Initial Value Problems
- Demo: Backward Euler stability
- Demo: Dissipation in Runge-Kutta Methods
- Demo: Forward Euler stability
- Demo: Predator-Prey System
- Demo: Stability regions
- Demo: Stiffness
Boundary Value Problems for ODEs
- Existence, Uniqueness, Conditioning
- Numerical Methods
- Demo: Finite differences
- Demo: Shooting method
- Demo: Sparse matrices
Partial Differential Equations and Sparse Linear Algebra
Fast Fourier Transform
Additional Topics
- Demo: An Introduction to Sympy

Class scribbles (click to view)

CAUTION!

These scribbled PDFs are an unedited reflection of what I wrote during class. They need to be viewed in the context of the class discussion that led to them. See the lecture videos for that.

If you would like actual, self-contained class notes, look in the outline above.

These scribbles are provided here to provide a record of our class discussion, to be used in perhaps the following ways:

as a way to cross-check your own notes
to look up a formula that you know was shown in a certain class
to remind yourself of what exactly was covered on a given day

By continuing to read them, you acknowledge that these files are provided as supplementary material on an as-is basis.

Team

Andreas Kloeckner

(Instructor)

Email: andreask@illinois.edu

Office: 4318 Siebel

Xiaoyu Wei

(Instructor)

Email: xywei@illinois.edu

Office: 4215 Siebel

Nathanael Assefa

(TA)

Email: nassefa2@illinois.edu

Office: 0207 Siebel

Navjot Singh

(TA)

Email: navjot2@illinois.edu

Office: 0207 Siebel

Lukas Spies

(TA)

Email: lspies@illinois.edu

Office: 0207 Siebel

Mina Sun

(TA)

Email: ms65@illinois.edu

Office: 0207 Siebel

Textbook

Scientific Computing: An Introductory Survey / E-Book (accessible free of charge from campus network/VPN)

Michael T. Heath, Revised Second Edition, Society for Industrial and Applied Mathematics

Resource site

Also see our class Piazza forum for a discount code for purchasing the book from SIAM.

Computing

We will be using Python with the libraries numpy, scipy and matplotlib for in-class work and assignments. No other languages are permitted. Python has a very gentle learning curve, so you should feel at home even if you've never done any work in Python.

Running Code on your Own Computer

While running code in this online system should technically suffice to do your work for this class, you may find it useful to also install Python on your own computer.

The recommended and perhaps one of the easier ways of doing so involves downloading the Anaconda Python distribution. Note that this is a commercial product (even if it is free of charge), and this is not intended as an endorsement of the company or the product. Note that we cannot promise to provide technical support for this installation.

Download Anaconda Python »

Another way to obtain a Python installation is through a virtual machine image:

Download Virtual Machine »