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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) |
Adequate knowledge in mathematics, science and computer engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems.
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2) |
Ability to identify, formulate, and solve complex engineering problems; ability to select and apply appropriate analysis and modeling methods for this purpose.
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3) |
Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose.
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4) |
Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in computer engineering applications; ability to use information technologies effectively.
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5) |
Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or computer engineering research topics.
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6) |
Ability to work effectively within and multi-disciplinary teams; individual study skills.
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7) |
Ability to communicate effectively in verbal and written Turkish; knowledge of at least one foreign language; ability to write active reports and understand written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions.
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8) |
Awareness of the necessity of lifelong learning; ability to access information, to follow developments in science and technology and to renew continuously.
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9) |
To act in accordance with ethical principles, professional and ethical responsibility; information on the standards used in engineering applications.
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10) |
Information on business practices such as project management, risk management and change management; awareness of entrepreneurship and innovation; information about sustainable development.
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11) |
Knowledge of the effects of engineering practices on health, environment and safety in the universal and social scale and the problems of the era reflected in engineering; awareness of the legal consequences of engineering solutions.
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