CONCORDIA UNIVERSITY
FACULTY OF ENGINEERING AND COMPUTER SCIENCE
Numerical methods in engineering (engr 391)
Winter 2011
Instructor: Dr. Lyes Kadem, Room EV 004.207
Tel: (514) 848-2424 ext 3143
E-mail:
Office Hours: Tuesdays (3:00 – 4:00 pm) and Wednesdays (4:00 – 5:00 pm)
Website: http://users.encs.concordia.ca/~kadem/
Lectures: Wednesdays and Fridays 8:45 – 10:00 am (H-507)
Tutorials: Section XA Friday 13:15-14:05 in H-439
Section XB Friday 15:15-16:05 in H-603
Section XC Friday 13:15-14:05 in H-623
Prerequisites: ENGR 213, 233; COMP 248 or COEN 243 or MECH 215 or BCEE 232
Course Objective:
Engineers depend on mathematical equations to describe behavior of many physical systems. In practice these equations cannot be solved analytically, therefore, numerical methods are often used. This course introduces engineering students to a variety of numerical methods and algorithms. It is an introductory course, and can be complemented by a variety of other courses geared at different approaches to numerical simulation of the many phenomena occurring in different engineering disciplines, e.g. Fluid mechanics, solid mechanics, electromagnetics, etc. The numerical techniques learned in this course enable students to work with mathematical models of technology and systems.
General Topics:
1. Introduction and error analysis
2. Roots of equations
3. Linear algebraic equations
4. Regression and interpolation
5. Numerical integration and differentiation
6. Ordinary differential equations
Text Book:
Numerical Methods for Engineers and Scientists: An Introduction with Applications Using Matlab. A. Gilat and V. Subramaniam, John Wiley & Sons, Inc.
Additional References:
Numerical Methods for Engineers, S.C. Chapra and R.P. Canale, 5th edition, McGraw-Hill.
Numerical Analysis, T. Bauer, Pearson Education, 2006.
Numerical Analysis, R.L. Burden and J.D. Faires, 7th ed. Brook/Cole Publishing Company.
Numerical Methods Using Matlab, J.H. Mathews and K.D. Fink, Pearson Education, 2004.
Elementary Numerical Analysis, Atkinson and Han, 3th edition, Wiley, 2004.
Graduate Attributes:
This course covers the following graduate attributes:
Problem analysis
An ability to use appropriate knowledge and skills to identify, formulate, analyze, and solve complex engineering problems in order to reach substantiated conclusions.
Use of engineering tools
An ability to create, select, apply, adapt, and extend appropriate techniques, resources, and modern engineering tools to a range of engineering activities, from simple to complex, with an understanding of the associated limitations
Grading Scheme:
· Assignments 20%
· Midterm exam 30% (tentatively scheduled for March 4, 2011)
· Final exam 50%
Assignments:
Assignments will be given and due dates will be written on the question sheet or on the course website. Assignments will be due in class at the beginning of the lecture. Late assignments will NOT be accepted under any circumstance. While general discussions of assignments among students are permitted, all solution write-ups and submissions must be done independently. Students should be aware of the University's Code of Conduct (academic) concerning cheating, plagiarism and the possible consequences of violating this code.
Midterm and Final Exam:
Closed book; Closed notes. ENCS Faculty approved calculator only. Electronic communication devices (including cell phones) will not be allowed in examination rooms. A single-sided letter-sized sheet of paper as a crib sheet will be allowed in the final exam only.
Students with Disabilities:
Student with disabilities are encouraged to contact the instructor as early as possible in order to efficiently accommodate their needs.
Other Remarks:
There is no fixed relationship between marks and letter grades.
You need to repeat the course if you did not write the final exam and get less than 20 out of 50% for the semester work (assignments and midterm).
All exams are mandatory and all exams will be counted.
You need to obtain a passing mark (50%) for the final exam in order to pass the course.
Events beyond the control of the instructor may require changes to this outline.
COURSE OUTLINE
Topics
1. Introduction, errors and Taylor Series Expansion
2. Roots of Equations
· Bisection Method
· Method of False Position
· Fixed-Point Iteration
· Newton-Raphson’s Method
· Secant Method
3. System of Linear Algebraic Equations
· Gauss Elimination with
Pivoting strategies
· LU-Decomposition with
Pivoting strategies
· Inverse of a Matrix
· Gauss-Seidel Methods
4. Curve Fitting and Interpolation
· Least Square Regression
a) Linear
b) Polynomial
c) General Linear
d) Non-Linear
· Interpolation
a) Newton’s Polynomials
b) Lagrange Polynomials
c) Cubic Splines
5. Numerical Integration and Differentiation
· Finite Difference Approximation of the Derivative
· Trapezoidal Rule and Simpson’s Rule
· Method of Undetermined Coefficients
· Gauss Quadrature
6. Ordinary Differential Equations
· Euler’s Methods
· Runge-Kutta Methods
· System of First-Order ODEs and Higher-Order Initial Value Problems
· Finite Differences and Boundary Value Problems