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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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Review of Power Series
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R1: Section 5.1
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2
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Series Solutions Near an Ordinary Point
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R1: Section 5.2, 5.3
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3
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Euler Equations; Regular Singular Points
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R1: Section 5.4
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4
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Series Solutions Near a Regular Singular Point
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R1: Section 5.5, 5.6
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5
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Bessel`s Equation
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R1: Section 5.7
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6
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Definition of the Laplace Transform and Solution of Initial Value Problems
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R1: Section 6.1, 6.2
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7
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Step Functions
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R1: Section 6.3
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8
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Differential Equations with Discontinuous Forcing Functions
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R1: Section 6.4
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9
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Impulse Functions and The Convolution Integral
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R1: Section 6.5, 6.6
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10
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Review of Matrices and Linear Algebraic Equations
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R1: Section 7.1, 7.2, 7.3
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11
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Basic Theory of Systems of First Order Linear Equations
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R1: Section 7.4
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12
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Homogeneous Linear Systems with Constant Coefficients and Complex Eigenvalues
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R1: Section 7.5, 7.6
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13
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Fundamental Matrices and Repeated Eigenvalues
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R1: Section 7.7, 7.8
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14
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Nonhomogeneous Linear Systems
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R1: Section 7.9
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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. Boyce, W. E., & Diprima, R. C. (2010). Ordinary Differential Equations and Boundary Value Problems. John Willey and Sons. Inc.
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Supplementary Book
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SR1. Bronson, R., & Costa, G. B. (2014). Schaum`s outline of differential equations. McGraw-Hill Education.
SR2. Edwards, C. H., Penney, D. E., & Calvis, D. T. (2016). Differential equations and boundary value problems. Pearson Education Limited.
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Goals
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The goal of this course is to teach solution methods of linear and nonlinear differential equations, to introduce Laplace transformation, to study boundary value problems and to find solutions by using series.
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Content
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Series Solutions of Second Order Linear Equations, The Laplace Transform, Systems of First Order Linear Equations
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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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2
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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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3
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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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3
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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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2
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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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2
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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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