## MATH 685-001/CSI 700-001/OR 682-001 Spring 2012 Numerical Analysis

##### | About the Course | Instructor | Prerequisites | Learning Outcomes | About Matlab | Course Evaluation | Course Outline | Lecture Notes | Homework | Project | Academic Integrity | Disability Accomodation |

It is well-known that the use of numerical methods for the analysis, simulation, and design of engineering processes and industrial systems has been increasing at a rapid rate. Therefore, this course is intended to better prepare future engineers and computational scientists (as well as to assist practicing engineers and computational scientists), in understanding the fundamentals of numerical methods, especially their application, limitations, and potentials. This course is designed as an introductory course in computational techniques for solving problems from science and engineering with emphasis on applications. The course will cover the classical fundamental topics in numerical methods such as, approximation, numerical integration, numerical linear algebra, solution of nonlinear algebraic systems and solution of ordinary and partial differential equations. The viewpoint will be modern, with connections made between each topic and a variety of applications. By the end of the course, the student should not only be familiar, but more confident, in effectively using numerical tools to solve problems in their own field of interest.
• Lectures: M (4:30 pm - 7:10 pm)
• Venue: Robinson Hall B208

### INSTRUCTOR

• Office:MATH 222B
• Office Hours: M W (2:00 pm - 3:30 pm) and by appointment
• E-mail: pseshaiy@gmu.edu

### PREREQUISITES

Sufficient recall of undergraduate linear algebra, differential equations and computer literacy including familiarity with MATLAB.

### EXPECTED LEARNING OUTCOMES

In this course, the emphasis will be to apply well-know numerical techniques to solve engineering problems and evaluate the results. The objective will be to train students to understand why the methods work, what type of errors to expect, and when an application might lead to difficulties. In particular, the students will become proficient in:
1. Understanding the theoretical and practical aspects of the use of numerical methods

2. Implementing numerical methods for a variety of multidisciplinary applications

The expected learning outcomes for the course will be assessed through: Exams, homeworks, in-class activities and class discussions. Problem-based learning will be an integral part of the course.

The software package MATLAB will be used for scientific computation, analysis and presentation of data. MATLAB is an interactive programming language for general scientific and technical computation with powerful graphics and library functions.

### COURSE EVALUATION

Evaluation for the course will be based on the following criteria:

 Homework 30% Computer Projects 30% Midterm Exam 15% Final Exam 25% TOTAL 100%

• There will be five homework assignments during the semester each worth 6%. There will also be computer projects which is worth 30%. These items should be written up and handed in on time to receive full credit as they add towards 60 % of the total grade.
• There will be one midsemester exam and one comprehensive final exam in this course.
• The Final Exam will be on Monday, May 14, 2012 from 4:30 PM - 7:15 PM and will be comprehensive.
• Make-up exams may be possible only in the case of documented emergencies.

### COURSE OUTLINE

Problem-based learning (both in and out of class) will be an integral part of the course. The primary reference will be "Classical and Modern Numerical Analysis", by A. Ackleh, E. Allen, R. Kearfott and P. Seshaiyer. Lecture notes will also be provided by the instructor that will be posted on the course website on a regular basis.