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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 Energy Systems Engineering subjects; use theoretical and applied information in these areas to model and solve complex engineering problems. |
5 |
2) |
Ability to identify, formulate, and solve complex Energy Systems Engineering problems; select and apply proper modeling and analysis methods for this purpose.
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3 |
3) |
Ability to design complex Energy systems, processes, devices or products under realistic constraints and conditions, in such a way as to meet the desired result; apply modern design methods for this purpose. |
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4) |
Ability to devise, select, and use modern techniques and tools needed for solving complex problems in Energy Systems Engineering practice; employ information technologies effectively. |
4 |
5) |
Ability to design and conduct numerical or pysical experiments, collect data, analyze and interpret results for investigating the complex problems specific to Energy Systems Engineering. |
3 |
6) |
Ability to cooperate efficiently in intra-disciplinary and multi-disciplinary teams; and show self-reliance when working on Energy Systems-related problems |
2 |
7) |
Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing. Write and understand reports, prepare design and production reports, deliver effective presentations, give and receive clear and understandable instructions. |
2 |
8) |
Recognize the need for life-long learning; show ability to access information, to follow developments in science and technology, and to continuously educate oneself. |
3 |
9) |
Develop an awareness of professional and ethical responsibility, and behave accordingly. Be informed about the standards used in Energy Systems Engineering applications. |
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10) |
Learn about 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) |
Acquire knowledge about the effects of practices of Energys Systems Engineering on health, environment, security in universal and social scope, and the contemporary problems of Energys Systems engineering; is aware of the legal consequences of Energys Systems engineering solutions. |
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