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

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Introduction

Lecture NotesDr. Rakhmad Arief SiregarUniversiti Malaysia Perlis

0124430010

Applied Numerical Method for Engineers and Scientists

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Text bookApplied Numerical Methods with MATLAB

McGraw-Hill, 2005 Steven C. Chapra

Hardcover Paperback RM55

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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

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Computer software

Spreadsheet software (Calc or Excel) MATLAB LS-DYNA

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Learning Approach

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

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Evaluation contribution

Final Examination: 50% Course Works: 50%

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Course work (50%)

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

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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

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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)

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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

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Course Objective

No. Hasil

Pembelajaran, CO

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PO

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1 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 3 2 1 3 1 0 2 0

Lecture, Tutorial, Lab

QuizExam,Report

2. Student capable of utilizing proper technique of solving engineering problem using numerical analysis

2 3 2 2 2 0 2 2 0 2 0

Lecture, Tutorial, Lab

AssignmentQuizExam,Report

3. Student able to analyze and identify application of mechanical engineering using FEM

3 3 2 3 2 0 2 2 0 2 0

Lecture, Tutorial, Lab

AssignmentQuizExam,Report

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Course Objective

1. Students can understand basic concepts of heat transfer i.e fundamental theory of numerical analysis for engineering

2. 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

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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

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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

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Errors

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

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Summary of part of topics

Roots equations

Linear of algebraic equation

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Summary of part of topics

Curve Fitting

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Summary of part of topics

Integration

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Summary of part of topics

Integration

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Summary of part of topics

Finite Element Method

Advance topic (will not be covered)

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Summary of part of topics

Finite Element Method

Bar element only for Numerical Analysis topic

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