(ENGR 391, Winter 2004)



Section X

Dr. Ali Akgunduz 



Department: MIE

Office Hours: Tuesdays 2 PM-5 PM

Office: H549-28

Tel: 848-2424 ext. 3179



Days: W, F

Time: 11:45 – 13:00 

Room: H-407

See announcements for updates


April 7

Crib Sheet for Final

April 7, 2004

Sample Final Exams




 Text Book:

-         Numerical Methods for Engineers, Chapra and Canale, 4th edition, McGraw-Hill, 2002.


Grading Scheme:  

·        Assignments                                                    20%

·        Midterm exam                                                 20%

·        Final exam (closed book and notes)                60%


You must fill out and sign the appropriate originality form with your assignments before you submit them

Originality Forms:      Software, Assignment, Lab report, Report


 However you must pass the final examination with a 50% grade to pass the course.



Assignments and General notes:


Assignments include problems to be solved with a hand calculator as well as problems to be solved on the computer. Computer accounts are available on the PC Network and can be obtained from the Computer Center at H 925. Marked assignments will be returned approximately 1 week after the due date, they will be placed in a box in the Mechanical Engineering Department located at H 549.


Prerequisites:      EMA T 232; COMP 212 or COMP 293






Engineers depend on mathematical equations to describe behavior of many systems. In practice these equations cannot be solved analytically, therefore, numerical methods are often used.  This course introduces engineering students to these 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, Electromagnetic, etc.




  1. Introduction and Taylor Series Expansion (Section PT1 and Section 4.1)


  1. Numerical Differentiation (Section 4.1.3)
    • Backward, Forward, and Centered Differencing


  1. Roots of Equations

·        Interval Bisection Method (Section 5.2)


·        Method of False Position (Section 5.3)

·        Incremental Search Method (Section 5.4)

·        Newton Method (Section 6.2)  


·        Secant Method (Section 6.3)


·     Multiple Roots (Section 6.4)


  1. Linear and Non-Linear Algebraic Equations

·        Gauss-Jordan Elimination and Pivoting strategies ((Sections PT3.2,  9.1, 9.2 and 9.3)

1.      Pivoting strategies (Additional Notes)


Code for HW question


·        Newton’s Method (Section 9.6)


·        LU-Decomposition (Section 10.1)

·        Gauss-Siedel Methods (Section 11.2)


            Homework #3: 9.11, 9.16, 10.2, 10.5, 11.9, and 11.14 from the text book

          Due is on February 6th, Friday. No late HW will be accepted.


5.      Curve Fitting

·        Least Square Regression

a)      Linear (Section 17.1)

b)      Polynomial (Section 17.2)

c)      General Linear (Section 17.4)

d)      Non-Linear (Section 17.5)

·     Interpolation

a)      Lagrange Polynomials (Section 18.2)

b)      Splines (Section 18.6)


Homework #4: 17.5, 17.13, 18.4 (a), and 18.11 from the text book

          Due is on March 12th, Friday. No late HW will be accepted.


1.      Numerical Integration and Differentiation

·        Trapezoidal Rule (Section 21.1)

·        Simpson’s Rule (Section 21.2)

·        Romberg Integration (Section 22.2)

·        Gauss Quadrature (Section 22.3)

·        High Accuracy Differentiation Formulas (Section 23.1)


Homework #5: 21.8, 21.12, 21.26, 22.3, 22.12, 23.1 from the text book

          Due is on March 24th, Wednesday. No late HW will be accepted.


2.      Ordinary Differential Equations

·        Euler’s Methods (Section 25.1)

·        Runge-Kutta Methods (Section 25.3)

·        Finite Differences and Boundary Value Problems (Section 27.1)



3.      Partial Differential Equations

·        Classification [Elliptic, Parabolic and Hyperbolic]

·        Finite Difference Method (Section 29.1 and 30.1)

·        Finite Element Method (Section 31.1)