MAK502

School of Engineering \ Mechanical Engineering

3

9

Elective

Turkish

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The aim of this course is to develop the problem solving skills of engineering students by using numerical methods, an extremely powerful problem solving tool. This method is capable of solving large systems of equations, nonlinear problems and complex geometries that are common in engineering practice and are often impossible to solve analytically. Today, the intelligent use of computer programs involving numerical methods is usually based on knowledge of the basic theory of these methods. However, some engineering problems cannot be solved using this off-the-shelf software. The successful implementation of numerical methods on a computer and their subsequent application to problems that would otherwise be unsolvable shows how computers can contribute to professional development, while at the same time allowing to understand and control the margins of error of approximate solutions.

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 aim of this course is to develop the problem solving skills of engineering students by using numerical methods, which is an extremely powerful problem solving tool.

1. Development of numerical solution skills for engineering problems. Establishing the necessary foundations for

Week 1 (Lesson 01-04):
Section 1: Roots of Equations and Introduction to MATLAB
Coverage Methods, Open Methods
Week 2 (Lessons 05-08):
Section 2: Optimization
Week 3 (Lessons 09-12):
Section 3: Gaussian Elimination for Solving Linear Algebraic Equations
Section 4: LU Decomposition and Matrix Inversion
Week 4 (Lessons 13-16):
Section 5: Special Matrices and Gauss-Seidel Method
Section 6: Case Studies: Linear Algebraic Equations
Week 5 (Lesson 17-20):
Section 7: Curve Fitting with Least Squares Regression
Section 8: Curve Fitting Using Interpolation
Week 6:
Midterm Exam
Week 7 (Lessons 21-24):
Chapter 9: Numerical Integration - Newton-Cotes, Trapezoidal, Simpson's Rules
Week 8 (Lessons 25-28):
Chapter 10: Numerical Integration of Equations - Romberg Integration
Chapter 11: Numerical Derivative
Week 9 (Lesson 29-32):
Chapter 12: Ordinary Differential Equations - Runge-Kutta Methods
Week 10 (Lesson 33-36):
Chapter 12: Ordinary Differential Equations - Runge-Kutta Methods
Week 11 (Lessons 37-40):
Chapter 14: Partial Differential Equations - Finite Difference Method
Week 12 (Lesson 41-42):
Chapter 14: Partial Differential Equations - Finite Element Method