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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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Introduction, Mathematical Modeling, Error Analysis, Computer Programming, Excel and High Level Languages
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2
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Equation Roots: Graphical Method, Bisection, False Position, Simple Fixed-Point, Newton Raphson, Secant Methods Nonlinear sets of equations
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3
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Sets of Linear Equations: Gauss Elimination Method, Gauss-Seidel Method, Gauss-Jordan Method, Thomas Algorithm, L-U Decomposition, Matrix Inverse
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4
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Curve Fitting: Least Squares Methods, Linear Regression, Polynomial Regression, Multiple Linear Regression, Nonlinear Regression
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5
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Interpolation; Newton Finite-Difference Interpolation Polynomials, Lagrange Interpolation Polynomials
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6
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Numerical Differentiation and Integration: Newton-based Integration Formulas; Trapezoidal Rule, Simpson`s Rules, Multivariable Integrals
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7
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Genelleştirilmiş İntegraller, Sayısal Türev, Yüksek Doğruluklu Türev Formülleri, Kısmi Türev
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8
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Adi Diferansiyel Denklemler: Euler Yöntemi
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9
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Improved Euler (Heun) Method, Runge-Kutta Methods
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10
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Solution of Ordinary Differential Equation Systems Boundary Value and Eigenvalue Problems
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11
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Finite Difference Method: Solution methods of Elliptic Equations, Laplace Equation, Boundary Conditions, Control Volume Approach
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12
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Solution methods of parabolic equations: Heat-conduction equation, Open methods Closed methods, Cranck-Nicolson method, Two dimensional problems
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13
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Solution methods of Hyperbolic Equations
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14
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Examples for Partial Differential Equation Solutions
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Prerequisites
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None
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Language of Instruction
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Turkish
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Responsible
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Dr. Battal Doğan
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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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1. Steven C. Chapra ve Raymond P. Canale, 2010, Numerical Methods for Engineers, Sixth Ed., McGraw-Hill International Edition
2. J. Douglas Faires ve Richard Burden, 2003, Numerical Methods, Third Edition, Thomson
Brooks/Cole Thomson Learning
3. John H. Mathews, Numerical Methods for Mathematics, Science and Engineering,
Prentice-Hall International Edition.
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Supplementary Book
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-
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Goals
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To gain the ability to develop and apply solution models to an engineering problem using analytical and numerical methods.
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Content
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Mathematical modeling, Linear Equation Sets and Solution Methods, Curve fitting, Numerical Differentiation and Integration, Ordinary Dif. Equations and Solution Methods, Partial Dif. derivative and solution approaches
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Program Learning Outcomes |
Level of Contribution |
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1
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Acquires information by carrying out scientific research in the field of Civil Engineering, evaluates the findings and makes comments
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4
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2
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Complements the restricted or incomplete information and applies it, unifies the multidisciplinary information
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4
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3
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Designs and implements a system meeting the requirements in the field of Civil Engineering
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4
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4
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Makes an interpretation of a problem in the field of Civil Engineering, develops models for solutions and applies innovative methods in these solutions
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2
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5
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Has comprehensive knowledge on the contemporary applied method and techniques used in the field of Civil Engineering and their limitations
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4
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6
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Undertakes and implements analytic, simulation or experimental types of research and has the ability to solve the complex problems encountered there
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2
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7
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Can participate and assume responsibility in multidisciplinary task forces
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2
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8
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Observes the scientific, professional and ethical rules during data collection, its introduction and interpretation
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2
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9
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Be aware of recent advances and developments in the field of Civil Engineering, learns, analyses and applies them wherever needed
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1
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10
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Publishes his/her research findings verbally and in written forms in national and international arena
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-
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