1. Applied Numerical Method for Engineers and Scientists
Introduction
Lecture Notes
Dr. Rakhmad Arief Siregar
Universiti Malaysia Perlis
Applied Numerical Method for
Engineers and Scientists

2. Applied Numerical Methods with MATLAB
Text book
Applied Numerical Methods with MATLAB
McGraw-Hill, 2005
Steven C. Chapra
Hardcover
Paperback RM55

3. Exercise book Each student should have one exercise book
This book is needed in to exercise answering questions
It will be checked in any time without notice

4. Computer software
Spreadsheet software (Calc or Excel)
MATLAB
LS-DYNA

5. Learning Approach Lecture : 28 hours (33%) Practical : 42 hours (50%)
Tutorials : 14 hours (17%)

6. Evaluation contribution
Final Examination: 50%
Course Works: 50%

7. Course work (50%) Lab 25% (4 MATLAB report + 1 FEM report)
Mid test %
4 Assignments / 2 tests 10%

8. HEA requirement Round-off and truncation errors Roots of equations
Systems of simultaneous linear algebraic equations
Curve fitting
Numerical integration
Ordinary differential equations
Basic concept of Finite Element Method
Stiffness Matrices, Spring and Bar Elements
Interpolation function for general element formulation
Application in Engineering

9. (Mid test will be done before or after mid semester break)
Plan of Lecture
Week 1  Chapter 1 (Mathematical Modeling and Engineering Problem Solving)
Week 2  Chapter 3 (Approximations and round-off errors)
 Chapter 4 (Truncation errors and the Taylor Series)
Week 3  Chapter 5-6 (Bracketing Methods & Open Methods)
Week 4  Chapter 9-11 (Gauss Elimination and Gauss Seidel)
Week 5  Mid semester break
(Mid test will be done before or after mid semester break)
Week 6  Chapter 17 (Least-squares regression)
Week 7  Chapter 18 (Interpolation)
Week 8  Chapter 21 (Newton-Cotes Integration Formulas)

10. Plan of Lecture Week 9  Chapter 22 (Integration of Equations)
Week 10  Chapter 25 & 26 (Runge-Kutta Methods & Stiffness method)
Week 11  Chapter 29 (Elliptic Equation)
Week 12  Chapter 30 (Finite difference: parabolic equation)
Week  Chapter 13 (Finite Element Method)
Final Semester Examination
Note: Some topics that are not stated in HEA may be eliminated to due time constrains

11. Course Objective No. Hasil Pembelajaran, CO PO 1 PO 2 PO 3 PO 4 PO 5
Delivery Mode
Assess-ment 1.
Students can understand basic concepts of heat transfer i.e fundamental theory of numerical analysis for engineering 3 2 1
Lecture, Tutorial,
Lab
Quiz
Exam,
Report 2.
Student capable of utilizing proper technique of solving engineering problem using numerical analysis
Assignment 3.
Student able to analyze and identify application of mechanical engineering using FEM

12. Course Objective
Students can understand basic concepts of heat transfer i.e fundamental theory of numerical analysis for engineering
Student capable of utilizing proper technique of solving engineering problem using numerical analysis
3. Student able to analyze and identify application of mechanical engineering using FEM

13. Introduction Importance of Numerical Methods in Engineering
Most engineering analysis problems involve
The development of a mathematical model to represent all the important characteristics of the physical system;
The derivation of the governing equations of the the model by applying a physical laws, such as equilibrium equation, Newton’s laws of motion, conservation of mass and conservation of energy
Solution of the governing equations
Interpretation of the solution

14. Computer Programming Languages
Some high-level languages: FORTRAN, BASIC, C, C++, PASCAL, etc
Programming structure:
For typical high-level language uses the following types of statements to process the data:
Assignment
Input/Output
Control of decision
Specification
Subprogram

15. Errors Error and relative error Propagation error Truncation error
Round-off Error
Computational Error

16. Summary of part of topics
Roots equations
Linear of algebraic equation

17. Summary of part of topics
Curve Fitting

18. Summary of part of topics
Integration

19. Summary of part of topics
Integration

20. Summary of part of topics
Finite Element Method
Advance topic (will not be covered)

21. Summary of part of topics
Finite Element Method
Bar element only for Numerical Analysis topic

22. END