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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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Linear equation systems, solution methods of linear equation systems, representation of linear equation systems with matrices
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R1-Chapter 3, R2-Chapter 14
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2
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Basic matrix concepts, matrix types, transpose of matrices, mathematical operations on matrices
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R1-Chapter 6, R2-Chapter 8, R5-Chapter 9
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3
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Elementary row operations, inverse of matrices
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R3-Chapter 6, R4-Chapter 9, Chapter 10
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4
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Determinant calculation, minor and cofactor calculation, determinant properties
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R3-Chapter 6, R4-Chapter 11
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5
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Solution cases of linear equation systems, Gauss and Gauss Jordan elimination methods
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R1-Chapter 3, Chapter 4, R6-Chapter 3
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6
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Cramer method, Inverse matrix method, echelon and reduced echelon matrices
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R1-Chapter 3, Chapter 4, R6-Chapter 3
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7
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A = LU decomposition, homogeneous linear equation systems
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R1-Chapter 3, Chapter 4, R6-Chapter 3
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8
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Finding eigenvalues and eigenvectors in matrices, diagonalization, Cayley-Hamilton theorem
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R1-Chapter 5, R7-Chapter 8
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9
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Vectors, unit vector, unit base vectors, multiplication of vectors
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R4-Chapter 7
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10
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Perpendicularity and parallelism conditions of vectors, finding the angle between two vectors, finding the orthogonal projection vector
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R4-Chapter 7
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11
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Finding triangle area in plane, finding triangle area in space, finding parallel edge area in space
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R4-Chapter 7
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12
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Vector space, subspace, linear combination, linear dependence and linear independence,
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R4-Chapter 7
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13
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Elongation, base, size
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R4-Chapter 7
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14
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Linear transformation matrix, linear transformation kernel, linear transformation image, linear transformation space and rank
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R4-Chapter 7
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Prerequisites
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Language of Instruction
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Turkish
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Responsible
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Asst. Prof. Dr. Mehmet Ali BİBERCİ
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Instructors
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Assistants
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Resources
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R1-Tapramaz, R. (2005). Sayısal çözümleme. Literatür Yayınları:76, İstanbul.
R2-Bakioğlu, M. (2011). Sayısal analiz. Birsen Yayınevi, İstanbul.
R3-Çağal, B. (1989). Sayısal analiz. Birsen Yayınevi, İstanbul.
R4-Hacısalihoğlu, H.H. (2005). Temel ve genel matematik Cilt: 2. (5. Baskı). Ertem Matbaacılık, Ankara.
R5-Süli, E. & Mayers, D. (2008). An introduction to numerical analysis. Cambridge University Press, New York.
R6-Karagöz, İ. (2014). Sayısal analiz ve mühendislik uygulamaları. (4. Baskı). Nobel Akademik Yayıncılık, Ankara.
R7-Bayram, M. (2009). Nümerik analiz. Birsen Yayınevi, İstanbul.
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Supplementary Book
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AR1-Uzun, İ. (2004). Mühendis nümerik çözüm yöntemleri. (3. Baskı). Beta Yayıncılık, İstanbul.
AR2-Amirali G. & Duru, H. (2002) Nümerik analiz. Pegem Yayıncılık, Ankara.
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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Create the necessary information for more advanced mathematics topics.
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Content
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Matrices: Definition of matrix, Types of matrices, matrix equality, Sum and difference of matrices, The product of scaler and matrix and their properties , Transpose of matrix and its properties - Some Special Matrices and Matrix Applications - Elementary row and column operations in matrices, Reduced rows echelon form, Rank of a matrix, The inverse of a square matrix, - Determinants: The determinant of a square matrix, Laplace`s expansion, Properties of determinants -Sarrus rule, Additional matrix, Calculation of the inverse of a matrix with the aid of additional matrix - Systems of Linear Equations: Solving systems of linear equations with the aid of equivalent matrices, Linear homogeneous equations, -Cramer`s method, The solution with the help of coefficients matrix -Vectors: Vector definition, the sum of vectors, the difference, the analytical expression vectors, scalar product of vectors, properties of the scalar multiplication Scalar product and its features, the mixed multiplication and properties, and properties of double vector product, -Vector spaces: Definition of vector spaces and theorems. Subspaces. Span concept and fundamental theorems. Linear dependence and linear independence of vectors and some theorems about linear dependence and linear independence. -Bases and dimension concepts and fundamental theorems. Definition of coordinates and transition matrices and some theorems. -Eigenvalues and Eigenvectors: The Calculation of Eigenvalues and Eigenvectors of a square matrix, - The calculation of Inverse and power of a square matrix with the help of the Cayley-Hamilton theorem.
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Program Learning Outcomes |
Level of Contribution |
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1
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Apply theoretical and practical knowledge in the fields of Mathematics, Science and Engineering to Mechanical Engineering.
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3
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2
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Engineering graduates with skills and professional background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations.
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4
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3
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Engineering graduates with the necessary technical, academic and practical knowledge and application confidence in the design and assessment of machines or mechanical systems or industrial processes with considerations of productivity, feasibility and environmental and social aspects.
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4
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Use the techniques, skills, and modern engineering tools necessary for mechanical engineering practice.
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4
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5
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Design and conduct experiments individually or in groups, as well as analyze and interpret data for mechanical engineering problems.
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6
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Ability of identifying the potential resources for information or knowledge regarding a given engineering issue.
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7
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The abilities and performance to participate multi-disciplinary groups together with the effective oral and official communication skills and personal confidence.
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8
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Communicate effectively in oral and written forms with a good command of at least one foreign language, preferably English.
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9
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Engineering graduates with motivation to life-long learning and having known significance of continuous education beyond undergraduate studies for science and technology.
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10
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Engineering graduates with well-structured responsibilities in profession and ethics.
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11
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Engineering graduates who are aware of the importance of safety and healthiness in the project management, workshop environment as well as related legal issues.
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12
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Consciousness for the results and effects of engineering solutions on the society and universe, awareness for the developmental considerations with contemporary problems of humanity.
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