The document outlines a course on Applied Numerical Methods at Universiti Teknologi Malaysia, detailing the syllabus, learning outcomes, and assessment requirements. Students must attend at least 80% of lectures and can utilize various programming tools such as Fortran, C, and MATLAB for numerical problem-solving. The course aims to equip students with skills to model complex physical systems and solve governing equations using numerical methods.

1. 1
Muhammad Faruq Foong, Dr.
Department of Aeronautics, Automotive, & Ocean Engineering
School of Mechanical Engineering, Faculty of Engineering,
Universiti Teknologi Malaysia
Email: faruqfoong@mail.fkm.utm.my No. HP: 0137119720
Introduction to Engineering Analysis
March 2020
APPLIED NUMERICAL METHODS
SEMM/SKMM3023

2. 2
Timetable

3. 3
Course Synopsis

4. 4
Course Timeline

5. 5
Course Assesments

6. 6
Attendance
■ Student must attend not less than 80% of lecture hours as
required for the subject
■ The student will be prohibited from attending any lecture and
assessment activities upon failure to comply the above
requirement.
■ Zero mark will be given to the subject.

7. Learning Outcomes
■ Construct mathematical models or the governing equations for the
complex physical systems under investigation.
■ Solve the governing equations using appropriate numerical methods.
■ Develop a well-structured and reliable computer program for the chosen
numerical method.
■ Analyze the validity and accuracy of the numerical solutions.
7

8. 8
1. Introduction
2. Scientific Methods
3. Bibliography
Contents for today

9. 9
Scientific Methods
What’s the
difference?
Analytical
Method
Experimental
Method
Numerical
Method
Which is more
accurate?

10. 10
Example on Scientific Methods
• From the model, we can obtain the exact
solution for the optimum load resistance
through differentiation:
• The optimum value can also be found using
finite difference approximation
Experiment: 3.60 Ω
Analytical: 4.00 Ω
Numerical: 3.98 Ω
Finding optimum load resistance

11. 11
Errors
■ Absolute error
■ Percentage error
Percentage errors are most commonly use to compare experiment with
analytical

12. 12
Examples of Numerical Problems
e−x
− x = 0
When do we use
numerical
methods?

13. 13
Tools for Numerical Problems
What do you need
to solve numerical
problems?

14. 14
Tools for Numerical Problems
■ Fortran program
■ C program
■ MATLAB
■ MATHCAD
■ Octave (free software)
■ Finite Element Software (Abaqus, Ansys)

15. 15
Numerical Methods to Solve:
■ Solution of nonlinear equations
■ Simultaneous linear algebraic equations
■ Solution of Matrix Eigenvalue problem
■ Curve fitting and interpolation
■ Numerical differentiation
■ Numerical integration
■ Solution of ODE
■ Solution of PDE

16. 16
Activity
How do you solve this?
■ Differentiate
with respect to t

17. 17
Downloads
• MATLAB software (Please use your
student account to install)
• Octave free version

18. 18
1. STEVEN C. CHAPRA & RAYMOND P. CANALE (2009): Numerical methods
for Engineers, 6ed,ISBN 0-39-095080-7, McGraw-Hill
2. SINGIRESU S. RAO (2002): Applied Numerical Methods for Engineers and
Scientists, ISBN 0-13-089480-X, Prentice Hall
3. DAVID KINCAID & WARD CHENEY (1991): Numerical Analysis: Mathematics
of Scientific Computing, ISBN 0-534-13014-3, Brooks/Cole Publishing Co.
4. STEVEN C. CHAPRA (2012): Applied Numerical Methods with MATLAB for
Engineers and Scientists, 3ed, ISBN 978-0-07-340110-2, McGraw-Hill
5. JOHN H. MATHEWS & KURTIS D. FINK (2004): Numerical Methods Using
Matlab, 4ed, ISBN 0-13-065248-2, Prentice Hall
Bibliography