From biological modeling, to physical simulation, to graphics and image processing, to
data mining and analysis, the need for accurate and fast numerical algorithms is expanding.
With problems of very large size and under the limitations of
finite precision arithmetic, the design of practical algorithms becomes
a challenging task. Scientific computation is the broad field concerned
with the design and analysis of efficient numerical algorithms.
In this introductory course, we will use MATLAB as a problem-solving
environment (PSE) to learn basic ideas and fundamental techniques
in scientific computation. You can ``play'' with the mathematics
that stands behind each and every new method that you learn, use
graphics to appreciate convergence and error, use matrix-vector programming
language to solidify the understanding of
linear algebra and to prepare for advanced array-level computing.
Topics to be covered:
Tools of trade, including Matlab tutorial
Linear system of equations: theory and algorithms
Data interpolation and extrapolation
Zeros and roots
Data (curve) fitting and linear least squares problem
Quadrature
Matrix eigenvalue and singular value decompositions
