Applied Numerical Method for Engineers and Scientists Introduction Lecture Notes Dr. Rakhmad Arief Siregar Universiti Malaysia Perlis 0124430010 Applied Numerical Method for Engineers and Scientists

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

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

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

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

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

Course work (50%) Lab 25% (4 MATLAB report + 1 FEM report) Mid test 15% 4 Assignments / 2 tests 10%

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

(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)

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

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

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

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

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

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

Summary of part of topics Roots equations Linear of algebraic equation

Summary of part of topics Curve Fitting

Summary of part of topics Integration

Summary of part of topics Integration

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

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

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