## MATH 315 - Advanced Numerical Analysis

Advanced Numerical Analysis - MATH 315

Lecture Meeting: Tuesday 0800 - 1000

Catalog Description

Numerical Methods for boundary value problems: shooting, parallel shooting and finite difference methods for linear and nonlinear problems. Finite difference methods for partial differential equations, derivation and error analysis, consistency, stability and convergence. Numerical methods for the matrix eigenvalue problems: power method and its variants, Householder method, the QR algorithm. Iterative methods for solving linear systems: Jacobi, Gauss-Seidel and SOR methods, derivation and error analysis. Numerical Methods for initial value problems: Euler, Taylor, Runge-Kutta, multistep, predictor-corrector methods.

Course Objectives

The course aims to provide students with the specialist knowledge in advanced Numerical Analysis. With this overall aim, the course strives to enable students to: Understand analytical, developmental and technical principles that relate to Numerical Linear Algebra, Numerical Methods for solving Differential Equations, and Numerical Optimization, develop the academic abilities required to solve problems and applications in Numerical Analysis and/or Numerical Optimization and critically assess relevant aspects of the industry, and demonstrate an ability to initiate and sustain in-depth research in Numerical Analysis or Numerical Optimization.

Course Outcomes

1) Knowledge and Understanding: During the lecture the student understands the nature and operations of Numerical Analysis, demonstrates familiarity with theories and concepts used in Numerical Analysis, and identifies the steps required to carry out a piece of research on a topic in Numerical Analysis.

3) Intellectual Skills: By the end of the course the student is expected to recognize and apply appropriate theories, principles and concepts relevant to Numerical Analysis, critically assess and evaluate the literature within the field of Numerical Analysis, analyze and interpret information from a variety of sources relevant to Numerical Analysis.

4) Practical Skills: By the end of the course student will have the ability to compare the computational methods for advantages and drawbacks, choose the suitable computational method among several existing methods, implement the computational methods using any of existing programming languages, testing such methods and compare between them, identify the suitable computational technique for a specific type of problems, and develop the computational method that is suitable for the underlying problem. 3) Transferable Skills: Within the lectures the student is able to transfer ideas and experience, work effectively as a part of a group and independently.

Student Outcomes

K1-Knowledge of basic theorems and concepts in the different areas of mathematics.

K2-Knowledgeof the implementation of theories in problem solving.

K3-Knowledge of different areas of research in mathematics.

I1-Ability to understand the different math concepts and be able to implement them in our everyday problems.

P1-Efficient use of computers, laboratories and soft wares to handle problems that are difficult to be solved
manually.

P2-Understanding of professional and ethical responsibilities

P3-Effecient use of the techniques, skills, and tools of modern mathematics