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  • Course Information
    • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Nonlinear Dynamical Systems MATH409 FALL-SPRING 3+0 E 6
    Learning Outcomes
    1-Solves linear or decoupled system of ODEs
    2-Calculates fixed points or periodic orbits of systems
    3-Sketches the phase portraits
  • ECTS / WORKLOAD
    • ActivityPercentage

    (100)

    		NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14342
    Classroom study (Pre-study, practice)14798
    Assignments0000
    Short-Term Exams (exam + preparation) 10144
    Midterm exams (exam + preparation)30188
    Project0000
    Laboratory 0000
    Final exam (exam + preparation) 6011616
    0000
    Total Workload (hours)   168
    Total Workload (hours) / 30 (s)     5,6 ---- (6)
    ECTS Credit   6
  • Course Content
    • Week Topics Study Metarials
    1 Review of ODEs and Dynamical Systems R2 - Chapter 1.1
    2 An overview of XPPAUT R2 - Chapter 1.2
    3 An overview of MATLAB/Octave R2 - Chapter 1.3
    4 One dimensional flows, Fixed points, Stability R1 - Chapter 2
    5 Linear stability analysis, Existence and uniqueness R1 - Chapter 2
    6 Introduction to numerical methods R1 - Chapter 2
    7 Introduction to bifurcation theory, Saddle-node bifurcation, Transcritical bifurcation R1 - Chapter 3
    8 Pitchfork bifurcation, Cusp catastrophe R1 - Chapter 3
    9 Flows on circle R1 - Chapter 4
    10 Two dimensional flows, Classification of linear systems R1 - Chapter 5
    11 Phase plane analysis R1 - Chapter 6
    12 Limit cycles R1 - Chapter 7
    13 Bifurcations in 2D systems, Hopf bifurcation R1 - Chapter 8
    14 Quasi-periodicity, Poincare maps R1 - Chapter 8
    Prerequisites -
    Language of Instruction English
    Responsible Dr. Harun BALDEMİR
    Instructors -
    Assistants -
    Resources R1 - Strogatz, S. H. (2018). Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. CRC Press. R2 - Lecture Notes
    Supplementary Book SR1 - Ermentrout, B. (2002). Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students. Society for Industrial and Applied Mathematics. SR2 - Lynch, S. (2004). Dynamical systems with applications using MATLAB. Boston: Birkhäuser.
    Goals This course aims to introduce the main features of dynamical systems as models in applied marthematics.
    Content ODEs and dynamical systems, XPPAUT, MATLAB/Octave, 1 dimensional flows, fixed points, stability, linear stability analysis, existence and uniqueness, numerical methods, bifurcation theory, saddle-node bifurcation, transcritical bifurcation, pitchfork bifurcation, cusp catastrophe, flows on circle, 2 dimensional flows, classification of linear systems, phase plane analysis, limit cycles, bifurcations in 2D systems, Hopf bifurcation, quasi-periodicity, Poincare maps
  • Program Learning Outcomes
    • Program Learning Outcomes Level of Contribution
    1 Having advanced theoretical and applied knowledge in the basic areas of mathematics 3
    2 Ability of abstract thinking -
    3 To be able to use the acquired mathematical knowledge in the process of defining, analyzing and separating the problem encountered into solution stages. 4
    4 Associating mathematical achievements with different disciplines and applying them in real life 4
    5 Ability to work independently in a problem or project that requires knowledge of mathematics -
    6 Ability to work harmoniously and effectively in national or international teams and take responsibility -
    7 Having the skills to critically evaluate and advance the knowledge gained from different areas of mathematics 4
    8 To be able to determine what kind of knowledge learning the problem faced and to direct this knowledge learning process. -
    9 To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time -
    10 Ability to verbally and in writing convey thoughts on mathematical issues, and solution proposals to problems, to experts or non-experts. -
    11 Being able to produce projects and organize events with social responsibility awareness -
    12 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 -
    13 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 -
    14 Being conscious of acting in accordance with social, scientific, cultural and ethical values -
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