Revised March 17, 2014
CS 370: Numerical Computation
Watch a video introduction to the course on YouTube.
General description
This course introduces students to the basic algorithms, software environments, and applications of scientific
computing. Simple but realistic examples
are used to motivate the study of
numerical methods.
Logistics
Audience
- CS major students and students pursuing a CS minor
- Students interested in a career in
computational support of engineering or scientific
applications, such as CAD/CAM, graphics, or finance
Normally available
Related courses
- Predecessors: (One of MATH 118, 119, 128, 138, 148), (One of MATH 114, 115, 106/125, 136, 146), (One of CS 234, 241, 246); Not open to General Mathematics students
- Successors: CS 475, 476
- Anti-requisites: AMATH 242/341/CM 271/CS 371, CS 335, 337, ECE 204, 304
For official details, see the UW calendar.
Software/hardware used
Typical reference(s)
- Numerical Computing with MATLAB, Cleve Moler, SIAM, 2004
- Course notes
Required preparation
At the start of the course, students should be able to
- Program in a high-procedural programming language and use control instructions, such as loops and conditional statements,
basic datatypes, and simple data structures, such as arrays
- Perform basic mathematical computations and have knowledge of
- limits and derivatives, Taylor series, curves, and other basic
concepts encountered in calculus
- matrix operations, inverse, products,
Gaussian elimination
- complex arithmetic and trigonometric functions
Learning objectives
At the end of the course, students should be able to
- Explain the principles of floating point number systems and the concepts
of chopping, rounding, machine precision, and error of floating point
arithmetic
- Analyze stability and conditioning of simple numerical problems
- Use MATLAB built-in functions and graphing capabilities of
1D and 2D data
- Implement efficient code using vectorization
- Compute polynomial and spline interpolants
and apply splines to curve drawing in two and three
dimensions
- Use numerical algorithms to solve ordinary differential
equations and understand and apply methods
to analyze the stability and efficiency of these methods
- Design simple procedures using FFT based algorithms for applications,
such as signal and image processing and data compression
- Solve linear equations in a floating point environment
taking into consideration error propagation and measures of
conditioning
- Give examples of the issues involved in a large scale linear algebra
computation (e.g., Google Page Rank)
Typical syllabus
Floating point numbers (3) hours
- Floating point numbers, propagation of round off,
stability of recursions
Interpolation (6) hours
- Interpolation: Vandermonde matrix, Lagrange
interpolation, cubic splines, B splines
- Example application: scalable fonts
Ordinary differential equations (9) hours
- Forward, backward,
modified Euler, local truncation error, stability,
global error
- Example application: pursuit problems, SIR disease propagation model
Discrete Fourier analysis (9) hours
- Fourier series, FFT
algorithm (butterfly)
- Example application: JPEG, image and signal
processing, MP-3
Numerical linear algebra (9) hours
- LU decomposition, pivoting, condition
number, QR decomposition
- Example application: Google Page Rank
Last modified: Tuesday, 09-Jul-2019 15:55:36 EDT