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Week |
Subject |
Related Preparation |
1) |
Introduction to Numerical Analysis: kinds of problems we solve.
Error analysis, round-off and truncation errors.
Taylor Theorem and Taylor series.
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2) |
Loss of Significance
Big O notation
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3) |
Solution of Nonlinear Equations, i.e. f(x)=0.
Bracketing Methods for Locating a Root.
Bisection (Method of Bolzano).
False-position (Regula-Falsi) Method.
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4) |
Newton-Raphson Method (Applications from thermodynamics, fluid mechanics, and electronics) |
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5) |
Solution of Linear Systems of Equations.
Properties of Vectors and Matrices.
Upper-Triangular Linear Systems.
Gaussian Elimination and Pivoting.
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6) |
Triangular Factorization (LU Decomposition) |
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7) |
Iterative Methods for Linear Systems.
Jacobi Method.
Gauss-Sedidel Method.
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8) |
Iterative Methods for Linear Systems
Gauss-Sedidel Method. Diagonally dominant matrix.
Errors is solving linear systems.
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9) |
System of Nonlinear Equations (Newton’s Method) |
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10) |
Interpolation and Polynomial Approximation.
Introduction to Interpolation.
Lagrange Approximation.
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11) |
Newton Interpolation Polynomials.
Piecewise Linear Interpolation, Cubic Spline Functions
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12) |
Curve Fitting (Applications from heat transfer and electrical engineering).
Least-Squares Approximation.
Linearization of Nonlinear Relationships.
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13) |
Eigenvalues and Eigenvectors. The power method |
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14) |
Singular Value decomposition.
Applications from Image Processing
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Course Notes: |
Stephen C. Chapra, Applied Numerical Methods W/MATLAB: for Engineers & Scientists, 3rd Edition, McGrawHill |
References: |
• J. Douglas Faires and Richard L. Burden, Numerical Methods, Brooks/Cole Publishing Co., 4th Edition, 2013.
• Applied Numerical Methods Using MATLAB, Won Young Yang, Wenwu Cao, Tae-Sang Chung, John Morris.
• John H. Mathews and Kurtis D. Fink Numerical Methods Using MATLAB, Pearson, 2004. ISBN 0-13-191178-3
• Mustafa Bayram, Nümerik Analiz, Sürat Üniversite Yayınları, 3. Baskı, 2013.
• İrfan Karagöz, Sayısal Analiz ve Mühendislik Uygulamaları, Nobel Yayın Dağıtım, ISBN: 978-605-395-077-6.
• Ömer Akın, Nümerik Analiz, Ankara Üniversitesi Basımevi, 1998, ISBN: 975-482-448-7
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Program Outcomes |
Level of Contribution |
1) |
Build up a body of knowledge in mathematics, science and industrial engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems. |
5 |
2) |
Identify, formulate, and solve complex engineering problems; select and apply proper analysis and modeling methods for this purpose. |
3 |
3) |
Design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose. The ability to apply modern design methods to meet this objective. |
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4) |
Devise, select, and use modern techniques and tools needed for solving complex problems in industrial engineering practice; employ information technologies effectively. |
3 |
5) |
Design and conduct experiments, collect data, analyze and interpret results for investigating the complex problems specific to industrial engineering. |
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6) |
Cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working independently. |
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7) |
Demonstrate effective communication skills in both oral and written English and Turkish. Writing and understanding reports, preparing design and production reports, making effective presentations, giving and receiving clear and understandable instructions. |
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8) |
Recognize the need for lifelong learning; show ability to access information, to follow developments in science and technology, and to continuously educate him/herself. |
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9) |
Develop an awareness of professional and ethical responsibility, and behaving accordingly. Information about the standards used in engineering applications. |
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10) |
Know business life practices such as project management, risk management, and change management; develop an awareness of entrepreneurship, innovation, and sustainable development. |
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11) |
Know contemporary issues and the global and societal effects of modern age engineering practices on health, environment, and safety; recognize the legal consequences of engineering solutions. |
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12) |
Develop effective and efficient managerial skills. |
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