MAK502

Mühendislik Fakültesi \ Makine Mühendisliği

3

9

Seçmeli

Türkçe

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The purpose of this course is to enhance the problem-solving skills of engineering students using an extremely powerful problem-solving tool, namely numerical methods. This tool is capable of handling large systems of equations, non‐linearities, and complicated geometries that are not uncommon in engineering practice and that are often impossible to solve analytically. Nowadays, the intelligent use of computer programs that involve numerical methods is often predicated on the knowledge of the basic theory underlying these methods. However, some engineering problems cannot be approached using these pre‐packaged software’s. Successful implementation of numerical methods on a computer and then their application to solve otherwise intractable problems, provides a demonstration of how computers can serve one’s professional development, and helps acknowledge and control the errors of approximation.

1. A. Gilat & V. Subramaniam. Numerical Methods for Engineers and Scientists, 3rd edition, Wiley ,2013 2. Ramin S. Esfandiari. Numerical Methods for Engineers and Scientists Using MATLAB. CRC Press Taylor & Francis Group, 2017

The purpose of this course is to enhance the problem-solving skills of engineering students using an extremely powerful problem-solving tool, namely numerical methods. This tool is capable of handling large systems of equations, non‐linearities, and complicated geometries that are not uncommon in engineering practice and that are often impossible to solve analytically. Nowadays, the intelligent use of computer programs that involve numerical methods is often predicated on the knowledge of the basic theory underlying these methods. However, some engineering problems cannot be approached using these pre‐packaged software’s. Successful implementation of numerical methods on a computer and then their application to solve otherwise intractable problems, provides a demonstration of how computers can serve one’s professional development, and helps acknowledge and control the errors of approximation.

1. Mühendislik problemlerinin sayısal çözüm yeteneklerinin geliştirilmesi için gereken temellerin oluşturulması.

1. Hafta: (Lecture 01-04):
- Chapter 1: Roots of Equations and Introduction to MATLAB
Bracketing Methods, Open Methods
2. Hafta: (Lecture 05-08):
- Chapter 2: Optimization
3. Hafta: (Lecture 09-12):
- Chapter 3: Gauss elimination to solve linear algebraic equations
-Chapter 4: LU Decomposition and Matrix Inversion
4. Hafta: (Lecture 13-16):
-Chapter 5: Special Matrices and Gauss Siedel
-Chapter 6: Case Studies: Linear Algebraic Equations
5. Hafta: (Lecture 17-20):
-Chapter 7: Curve Fitting using Least-Squares Regression
-Chapter 8: Curve Fitting using Interpolation
6. Hafta:
-Midterm
7. Hafta: (Lecture 21-24):
-Chapter 9: Numerical Integration – Newton-Cotes, Trapezoidal, Simpon’s Rules
8. Hafta: (Lecture 25-28)
-Chapter 10: Numerical Integration of Equations – Romberg Integration
-Chapter 11: Numerical Differentiation
9. Hafta: (Lecture 29-32)
-Chapter 12: Ordinary differential equations – Runge-Kutta Methods
10.. Hafta: (Lecture 33-36)
-Chapter 12: Ordinary differential equations – Runge-Kutta Methods
11. Hafta: (Lecture 37-40):
Chapter 14: Partial Differential Equations – Finite Difference
12. Hafta: (Lecture 41-42):
Chapter 14: Partial Differential Equations – Finite Element Method