It is necessary you have MATLAB handy, and
highly recommended that you get the
Student Edition
Course Objectives:
From biological modeling, to physical simulation, to graphics and image
(data) processing, to data mining and social network 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.
5/4, 14, 16, 18: Eigenvalues and singular values (Chepter 10)
Eigenvalues and eigenvectors
Eigenvalue decomposition (Matlab's function eig)
The power method and inverse iteration
The QR algorithm
Singular values and singular vectors
Relationship between eigenpairs and singular triplets
Singular value decomposition (SVD) (Matlab's function svd)
Application of SVD for data/image compression
Homework 5 assignment, Due: 4:00pm,
May 30
5/21, 23 25
Quadrature -- numerical integration (Chapter 6)
Ordinary differential equations (Chapter 7)
Homework and project assignments (Homework Box 2131 Kemper)
Homework 0 Exercises 1.1, 1.2, 1.5, 1.6, 1.8, 1.20, 1.38
(do not need to turn, solutions will be discussed in the class)
Homework 1 (Linear systems):
2.1, 2.2, 2.8, 2.10, 2.11, 2.7, 2.5
(note: there are two typos in the previous posting: 1.11 and 2.9.
the correct ones should 2.11 and 2.10)
