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Week
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Topics
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Study Metarials
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1
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Preliminaries, absolute error, relative error, rounding error and truncation error, convergence order
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R1: Section 1.1-1.3
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2
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Numerical solution of nonlinear equations: bisection and Regula-Falsi methods, Newton`s method, convergence and error analysis
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R1: Section 2.1-2.3
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3
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Secant method, convergence and error analysis, fixed point iteration methods, convergence order, Aitken`s method
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R1: Section 2.3-2.5
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4
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Solution of nonlinear systems, Newton`s, Jacobi and Gauss-Seidel methods, convergence
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R1: Section 10.1-10.2
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5
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Solution of systems of linear equations, direct methods: Gauss elimination method and pivoting, LU and Cholesky factorizations
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R1: Section 6.1-6.3, 6.5
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6
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Iterative methods: Jacobi, Gauss-Seidel and SOR methods
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R1: Section 7.3-7.4
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7
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Norms, convergence and error analysis for iterative methods
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R1: Section 7.1, 7.5
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8
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Matrix eigenvalue problem, power and inverse power methods
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R1: Section 9.1, 9.3
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9
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Interpolation: interpolation theory, polynomial interpolation, Lagrange interpolation, divided differences, finite differences and Newton interpolation methods
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R1: Section 3.1-3.3
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10
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Hermite interpolation
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R1: Section 3.4
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11
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Spline interpolation
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R1: Section 3.5
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12
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Curve-fitting, least squares method
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R1: Section 8.1-8.2
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13
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Numerical differentiation, finite difference formulas, Richardson extrapolation
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R1: Section 4.1-4.2
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14
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Numerical integration: trapezoidal rule, Simpson`s rule, Newton-Cotes formulation, Romberg method
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R1: Section 4.3-4.5
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Prerequisites
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-
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Language of Instruction
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English
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Responsible
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Prof. Dr. Ahmet Yaşar ÖZBAN
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Instructors
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-
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Assistants
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-
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Resources
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R1. Burden, R.L., Faires, J.D., Numerical Analysis, Nihth Edition, Brooks&Cole, 2011.
R2. Mathews, J.H., Fink, K.D., Numerical Methods Using MATLAB, Fourth Edition, Pearson, 2009.
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Supplementary Book
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SR1. Atkinson, K., Han, W., Elementary Numerical Analysis, John Wiley&Sons, 2004.
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Goals
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To teach the methods used in the numerical solution of mathematical problems and the ways of derivation of the methods, the characteristics of numerical solution methods, their strong-weak, positive-negative aspects and the criteria for determining the numerical solution method to be used depending on the characteristics of the mathematical problem.
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Content
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Mathematical preliminaries about numerical computation, Numerical solution of nonlinear equations and systems of equations, Numerical solutions of systems of linear equations, direct solution methods and iterative methods, Matrix eigenvalue problem and numerical solution methods, Interpolation, Curve fitting, Numerical differentiation and Numerical integration.
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Program Learning Outcomes |
Level of Contribution |
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1
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Having advanced theoretical and applied knowledge in the basic areas of mathematics
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3
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2
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Ability of abstract thinking
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-
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3
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To be able to use the acquired mathematical knowledge in the process of defining, analyzing and separating the problem encountered into solution stages.
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1
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4
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Associating mathematical achievements with different disciplines and applying them in real life
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4
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5
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Ability to work independently in a problem or project that requires knowledge of mathematics
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-
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6
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Ability to work harmoniously and effectively in national or international teams and take responsibility
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-
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7
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Having the skills to critically evaluate and advance the knowledge gained from different areas of mathematics
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3
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8
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To be able to determine what kind of knowledge learning the problem faced and to direct this knowledge learning process.
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-
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9
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To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time
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-
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10
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Ability to verbally and in writing convey thoughts on mathematical issues, and solution proposals to problems, to experts or non-experts.
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2
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11
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Being able to produce projects and organize events with social responsibility awareness
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-
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12
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Being able to follow publications in the field of mathematics and exchange information with colleagues by using a foreign language at least at the European Language Portfolio B1 General Level
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-
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13
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Ability to use computer software (at least at the Advanced Level of European Computer Use License), information and communication technologies for solving mathematical problems, transferring ideas and results
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-
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14
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Being conscious of acting in accordance with social, scientific, cultural and ethical values
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-
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