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Syllabus ( MATH 204 )


   Basic information
Course title: Differential Equations II
Course code: MATH 204
Lecturer: Prof. Dr. Coşkun YAKAR
ECTS credits: 6
GTU credits: 3 (3+0+0)
Year, Semester: 2, Spring
Level of course: First Cycle (Undergraduate)
Type of course: Compulsory
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: none
Professional practice: No
Purpose of the course: Teach Solution Methods of Differential Equations, Mathematical Applications in Science and Engineering and Mathematical Modelling.

   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Explain the basic concepts of Differential Equations.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    3. Ability to work in interdisciplinary research teams effectively.
    4. Using technology as an efficient tool to understand mathematics and apply it.

    Method of assessment

    1. Written exam
  2. Obtain and Explain the Fundamental Definitions, Concepts, Theorems, Stability and Applications of Differential Equations.

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    2. Ability to work in interdisciplinary research teams effectively.
    3. Using technology as an efficient tool to understand mathematics and apply it.
    4. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment
  3. Gain Experience on Differential Equations

    Contribution to Program Outcomes

    1. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    2. Being fluent in English to review the literature, present technical projects, and write journal papers.
    3. Using technology as an efficient tool to understand mathematics and apply it.

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
Week 1: Improper Integrals; Definition of Laplace Transforms;
Week 2: Properties of Laplace Transforms; Inverse Laplace Transforms;
Week 3: Convolution and the Unit Step Function; Solution of Linear Differential Equations with Constant Coefficients by Laplace Transforms;
Week 4: Solution of systems of LDEs with Constant Coefficient by Laplace Transforms.
Week 5: Linear differential equations with variable coefficients: Change of Dependent Variable; Reduction of Order; Reduction to the Canonical Form; Change of Independent Variable; Methods Based on Factorization of the Operator.Nonlinear DEs of order two and higher: Without Dependent Variable; Without Independent Variable; Homogeneous Eqs., Total Deqs; Sarrus Method;
Week 6: Midterm exam I
Week 7: Variation of parameters.Integration in series: Analytic Functions; Ordinary and Singular Points; Power-Series Solution about an Ordinary Point;
Week 8: Regular Singular Points and the Method of Frobenius; The Expansion for Large Values of x.The Legendre, Bessel and Hypergeometric equations: Elementary and Transcendental Functions; The Legendre Equation; The Bessel Equation; The Hypergeometric Equation.Boundary value problems: Initial Value Problems; Existence and Uniqueness Theorems; Second Order Boundary Value Problems; Uniqueness of Solutions;
Week 9: Eigenvalue Problems; Sturm-Liouville Problems; Properties of Sturm-Liouville Problems;
Week 10: Systems of linear first order differential equations: Linear Systems of ODEs; Homogeneous LS with Constant Coefficients; Distinct Real Eigenvalue;
Week 11: Repeated Eigenvalue, Complex Eigenvalue; Nonhomogeneous Linear Systems; Variation of Parameters;
Week 12: Midterm exam II
Week 13: Linear and nonlinear method of variation of parameters. Theory of differential and integral inequalities;
Week 14: Qualitative and quantitative theory;
Week 15*: Basic stability theory and Lyapunovs second method;
Week 16*: Final exam
Textbooks and materials:
Recommended readings: Diferansiyel Denklemler Teorisi(E. Hasonov,G. Uzgören, İ. A. Büyükaksoy).
Differential Equations with BVP(D.G, Zill,M.R,Cullen)
Ordinary Differential Equations(V. Lakshmikantham,V. Raghavendra).
Nonlinear Variation of Parameters for Dynamical Systems(S.G., Deo, V. Lakshmikantham)
Stability Analysis of Dynamical Systems (V.Lakshmikantham)
  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 6,12 40
Other in-term studies: 0
Project: 0
Homework: 2,3,4,6,7,8,9,10,11,13 5
Quiz: 5,11 5
Final exam: 16 50
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 3 14
Practice, Recitation: 0 0
Homework: 3 10
Term project: 0 0
Term project presentation: 0 0
Quiz: 1 2
Own study for mid-term exam: 8 2
Mid-term: 2 2
Personal studies for final exam: 10 1
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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