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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 to numerical analysis, error concept and error types, Taylor and Maclaurin series
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R1-Chapter 1, R2-Chapter 2, R3-Chapter 1
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2
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The solution of linear equation systems by numerical methods, matrix concepts, matrix types, matrix transposition, matrix operations, elementary row operations, the inverse of matrices
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R4-Chapter 3, R5-Chapter 7
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3
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Determinant calculation (Sarrus method), minor and cofactor calculation, determinant calculation with cofactor, determinant properties
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R4-Chapter 3, R5-Chapter 7
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4
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Solution method of linear equation systems, positive and semi-positive definite matrices, Cholesky factorization method, Jacobi iteration method, Gauss Seidel iteration method
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R4-Chapter 3, R5-Chapter 7
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5
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Numerical solution of nonlinear equations, division by two method, interpolation method, Newton Raphson method
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R6-Chapter 6, R7-Chapter 3, R3-Chapter 6, Chapter 8
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6
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Secant method, Repetition method, Least squares method
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R6-Chapter 6, R7-Chapter 3, R3-Chapter 6, Chapter 8
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7
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Interpolation, linear interpolation method, curvilinear interpolation method, Lagrange interpolation method
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R3-Chapter 7, R2-Chapter 9
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8
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Numerical differential, Taylor series method, Euler method
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R1-Chapter 10, R2-Chapter 9
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9
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Picard iteration method, Range Kunta method
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R1-Chapter 10, R2-Chapter 9
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10
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Second order Range Kunta method, Heun method
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R1-Chapter 10, R2-Chapter 9
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11
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Midpoint method, Ralston method
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R1-Chapter 10, R2-Chapter 9
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12
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Third order Range Kunta method, Fourth order Range Kunta method
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R1-Chapter 10, R2-Chapter 9
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13
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Numerical integral, trapezoid rule
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R1-Chapter 8, R2-Chapter 8
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14
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Simpson 1/3, Simpson 3/8
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R1-Chapter 8, R2-Chapter 8
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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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Asst. Prof. Dr. Pembe Merve KARABULUT
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Instructors
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1-)Doktor Öğretim Üyesi Pembe Merve Karabulut
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Assistants
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-
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Resources
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R1-Uzun, İ. (2004). Mühendis nümerik çözüm yöntemleri. (3. Baskı). Beta Yayıncılık. İstanbul. R2-Karagöz, İ. (2014). Sayısal analiz ve mühendislik uygulamaları. (4. Baskı). Nobel Akademik Yayıncılık. Ankara. R3-Bakioğlu, M. (2011). Sayısal analiz. Birsen Yayınevi. İstanbul. R4-Tapramaz, R. (2005). Sayısal çözümleme. Literatür Yayınları:76. İstanbul. R5-Çağal, B. (1989). Sayısal analiz. Birsen Yayınevi. İstanbul. R6-Amirali, G. & Duru, H. (2002). Nümerik analiz. Pegem Yayıncılık. Ankara. R7-Bayram, M. (2009). Nümerik analiz. Birsen Yayınevi. İstanbul.
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Supplementary Book
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SR-Hacısalihoğlu, H.H. (2005). Temel ve genel matematik cilt: 2. (5. Baskı). Ertem Matbaacılık. Ankara. AR2-Süli, E. & Mayers, D. (2008). An introduction to numerical analysis. Cambridge University Press. New York. AR3-Bakioğlu, M., Kadıoğlu, F., Barlas, B. & Yanık, A. (2011). Sayısal analiz problemleri. Birsen Yayınevi. İstanbul.
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Goals
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To gain the ability to apply numerical methods in the solution of engineering problems, to gain the ability to apply the knowledge acquired in engineering courses (strength, fluid mechanics, heat transfer, etc.) and in working life.
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Content
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Introduction to numerical analysis, matrix and determinant, systems of linear equations, inverse of matrix, systems of nonlinear equations, interpolation, curve fitting, numerical derivative, numerical integration, numerical solutions of differential equations.
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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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-
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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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-
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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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-
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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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-
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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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-
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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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