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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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Some Basic Mathematical Models; Direction Fields, Solutions of Some Differential Equations
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R1-Chapter 1.1 & 1.2
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2
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Classification of Differential Equations, Historical Remarks
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R1-Chapter 1.3 & 1.4
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3
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Linear Equations; Method of Integrating Factors, Separable Equations
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R1-Chapter 2.1 & 2.2
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4
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Modeling with First Order Equations, Differences Between Linear and Nonlinear Equations
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R1-Chapter 2.3 & 2.4
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5
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Autonomous Equations and Population Dynamics, Exact Equations and Integrating Factors
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R1-Chapter 2.5 & 2.6
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6
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Numerical Approximations: Euler?s Method, The Existence and Uniqueness Theorem, First Order Difference Equations
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R1-Chapter 2.7 & 2.8
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7
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First Order Difference Equations
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R1-Chapter 2.9
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8
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Homogeneous Equations with Constant Coefficients, Solutions of Linear Homogeneous Equations; the Wronskian
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R1-Chapter 3.1 & 3.2
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9
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Complex Roots of the Characteristic Equation, Repeated Roots; Reduction of Order
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R1-Chapter 3.3 & 3.4
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10
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Nonhomogeneous Equations; Method of Undetermined Coefficients, Variation of Parameters
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R1-Chapter 3.5 & 3.6
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11
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Mechanical and Electrical Vibrations, Forced Vibrations
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R1-Chapter 3.7 & 3.8
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12
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General Theory of nth Order Linear Equations, Homogeneous Equations with Constant Coefficients
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R1-Chapter 4.1 & 4.2
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13
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The Method of Undetermined Coefficients
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R1-Chapter 4.3
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14
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The Method of Variation of Parameters
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R1-Chapter 4.4
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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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Dr. Emel BOLAT YEŞİLOVA
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Instructors
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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-Lecture notes
SR2-Bronson, R., & Costa, G. B. (2014). Schaum`s outline of differential equations. McGraw-Hill Education.
SR3-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 introduce differential equations, to teach solving methods, to study existence and uniqueness of solutions of initial value problems, to find exact solutions and to examine these solutions.
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Content
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Differential equation, order, degree, solutions and obtaining differential equations, initial and boundary value problems, mathematical models, differential equations by solving derivative: separable equations , homogeneous equations and equations reducible to this form, exact differential equations, integrating factor, linear, Bernoulli and Riccati differential equations, substitution, existence and uniqueness theorems, Clairaut and Lagrange equations, theory of linear differential equations, second order linear homogeneous equations with constant coefficiens, the method of undetermined coefficients, the method of variation of parameters, Cauchy-Euler equation
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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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4
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2
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Ability of abstract thinking
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3
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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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4
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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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-
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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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-
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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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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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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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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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-
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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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-
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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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14
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Being conscious of acting in accordance with social, scientific, cultural and ethical values
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