The purpose of this course is to introduce the key
concepts and principles of scientific and numerical computation.
Two attentive students of Scientific Computing
Calendar entry
Elementary techniques for the numerical solution of mathematical problems on a computer,
including methods for solving linear and non-linear equations,
numerical integration, and interpolation.
Course Hours: H(3-2T)
Prerequisite(s): One of Computer Science 319 or 331,
one of Mathematics 211 or 213,
and one of Mathematics 249, 251, 265, 275, 281, or Applied Mathematics 217.
Antirequisite(s): Not open to students with credit in Applied Mathematics 491 or 493.
CPSC 491 OUTLINE
The students will be presented with an introduction to scientific computing
methodologies. They will acquire basic knowledge of errors in numerical
computations. They will gain a basic understanding of computer arithmetic.
The students will acquire a basic understanding of linear equations in n
dimensions and be able to assess the existence and uniqueness of solutions.
They will become familiar with the standard direct elimination methods for
linear equations.
The students will understand what is meant by stability and conditioning of
linear equations and how these concepts affect how linear equations are
solved.
The students will know how to solve linear least squares problems in one and
more dimensions. They will know how to assess existence and uniqueness of
linear least squares problems.
The students will become familiar with eigenvalue and eigenvector problems
for linear equations. They will be able to compute eigenvalues and
eigenvectors of systems of equations using standard tools.
For the linear algebra portion of the course the book: Linear Algebra and its Applications (David Lay, Pearson/Addison Wesley 2004)
provides an excellent reference to a variety of interesting applications
in engineering, science and social science.
The sections on SVD and PCA are of particular interest.