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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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Translation of points and axes in the plane
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R1-Chapter 5.1, 5.2
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2
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Function of rotation in plane and rotation of axes
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R1-Chapter 5.3, 5.4
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3
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Complex numbers and properties of complex numbers
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R2-Chapter 2.1
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4
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Relationship of complex numbers with rotation in the plane
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R2-Chapter 2.1
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5
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Discovery of quaternions and usage areas of them
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R2-Chapter 8.4
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6
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Quaternions and basic operations on them
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R2-Chapter 8.1
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7
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The inner product and norm in quaternions
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R2-Chapter 8.1
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8
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Complex expression of quaternions, Polar representation of quaternions
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R2-Chapter 8.1
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9
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De Moivre and Euler formula for quaternions
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R2-Chapter 8.1
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10
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Real matrix representation of quaternions
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R2-Chapter 8.2
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11
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Complex matrix representation of quaternions
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R2-Chapter 8.2
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12
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De Moivre and Euler formula for the matrix corresponding to the quaternions
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R2-Chapter 8.2
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13
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The relationship of quaternions with rotation in 3-dimensional space
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R3-Chapter 4
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14
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Rotation matrix corresponding to the unit quaternion
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R3-Chapter 4
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Prerequisites
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-
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Language of Instruction
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Turkish
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Responsible
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Asst. Prof. Dr. Kahraman Esen ÖZEN
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Instructors
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1-)Doktor Öğretim Üyesi Kahraman Esen Özen
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Assistants
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-
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Resources
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R1. Balcı, M. (2021). Analitik Geometri, Palme Yayınevi, Ankara
R2. Yüce, S. (2020). Sayılar ve Geometri, 1. Baskı. Pegem Akademi, Ankara
R3. Özdemir, M. (2020). Kuaterniyonlar ve Geometri, 1. Baskı. Altın Nokta Yayınevi, İzmir
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Supplementary Book
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SR1. Hacısalihoğlu, H. H. (1983). Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Üniversitesi Fen Edebiyat Fakültesi, Ankara
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Goals
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To give the basic properties of quaternions and to explain their relationship with rotation in space.
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Content
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Quaternions and basic operations on them, Complex expression of quaternions, Polar representation of quaternions, Real matrix representation of quaternions, The relationship of quaternions with rotation in 3-dimensional space, Rotation matrix corresponding to the unit quaternion
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Program Learning Outcomes |
Level of Contribution |
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1
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Improve and deepen the gained knowledge in Mathematics in the speciality level
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-
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2
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Use gained speciality level theoretical and applied knowledge in mathematics
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3
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3
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Perform interdisciplinary studies by relating the gained knowledge in Mathematics with other fields.
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2
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4
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Analyze mathematical problems by using the gained research methods
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3
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5
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Conduct independently a study requiring speciliaty in Mathematics
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-
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6
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Develop different approaches and produce solutions by taking responsibility to problems encountered in applications
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2
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7
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Evaluate the gained speciality level knowledge and skills with a critical approach and guide the process of learning
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-
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8
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Transfer recent and own research related to mathematics to the expert and non-expert shareholders written, verbally and visually
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-
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9
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Uses computer software and information technologies related to the field of mathematics at an advanced level.
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-
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10
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Have the awareness of acting compatible with social, scientific, cultural and ethical values during the process of collecting, interpreting, applying and informing data related to Mathematics
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-
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