Faculty : Institute of Basic and Applied Sciences

School :

Course Description :

This course covers selected topics in inner product spaces, matrix norms, orthogonality, the Gram-Schmidt process, least squares approx-imation, sparse matrices, positive definite, symmetric matrices and Cholesky's algorithm, quadratic forms, eigenvalues and eigenvectors. The course will also present the spectral theorem, optimization princi-ples for eigenvalues and eigenvectors, singular value decomposition, the Schur decomposition and methods for computing eigenvalues, non-negative matrices, graphs, networks, random walks, the Perron-Frobenius theorem.

Faculty : Institute of Basic and Applied Sciences

School :

Course Description :

Dynamical systems play a central role in modeling complex phenomena in science and engineering. We begin the course with existence and uniqueness for solutions of ordinary differential equations, linear sys-tems, nonlinear systems, stability, Limit cycle, bifurcation theory and Chaos. Theory and theoretical examples are complemented by compu-tational, model driven examples from biological, physical and engineer-ing sciences will also be included and discussed.

Faculty : Institute of Basic and Applied Sciences

School :

Course Description :

This is an introductory course in fractional differential equations. Dif-ferent types of fractional derivatives and fractional integrals, ordinary fractional differential equations are considered. The course will also examine the existence and the uniqueness of solutions. Numerical and analytical methods for solving fractional differential equations are provided.

Faculty : Institute of Basic and Applied Sciences

School :

Course Description :

This course covers fundamental material necessary for using high performance computing in science and engineering (Introduction to C++ programming language and/ or introduction to Matlab, Mathematica, and Maple). There is a special emphasis on algorithm de-velopment, computer implementation, Numerical solutions of linear and nonlinear systems, approximation of functions, integration, differential equations and the application of these methods to specific problems in science and engineering.

Faculty : Institute of Basic and Applied Sciences

School :

Course Description :

The aim of this course is to provide students with both a deep under-standing of the fundamentals of the elements of functional analysis such as Normed spaces, Banach space, Escolli theory, Weierstrass theory, Banach theory, Ritz theory, Hilbert’s space and Sobolev space. Also, applications to DEs are concluded.