Introduction

1. Introduction Lecture Notes Dr. Rakhmad Arief Siregar Universiti Malaysia Perlis 0164396522 Applied Numerical Method for Engineers and Scientists

2. 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 15% • 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. 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 13-14  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

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