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Syllabus ( MATH 305 )


   Basic information
Course title: Partial Differential Equations
Course code: MATH 305
Lecturer: Assoc. Prof. Dr. Feray HACIVELİOĞLU
ECTS credits: 6
GTU credits: 3 (3+0+0)
Year, Semester: 3, Fall
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: The methods of solutions, applications to engineering and other sciences, Heat and Wave equations, Boundary-value problems
   Learning outcomes Up

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

  1. Transfer the mathematical applications to engineering and other applied sciences

    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. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    3. Ability to work in interdisciplinary research teams effectively.
    4. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment
  2. Perceive the solution methods of partial 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. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.

    Method of assessment

    1. Written exam
  3. Gain the capability of mathematical modeling

    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. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.

    Method of assessment

    1. Homework assignment
   Contents Up
Week 1: Quasi-linear and linear Partial Differential Equations (PDE) of first order
Week 2: Series solutions of PDE, the Cauchy- Kovalevskaya theorem
Week 3: Characteristics, classification and caninical forms of linear PDE of second order
Week 4: Conception of the well-posed and ill-posed boundary-value problems
Week 5: Hyperbolic type PDE, Wave equation, energetic inequalities
Week 6: Uniqueness of the solutions of Cauchy problem and mixed problem
Week 7: MIDTERM EXAM I. The D’Alembert, Kirchhoff and Poisson formulas
Week 8: General scheme of Fourier method, application to the mixed problem for one-dimensipnal wave equation
Week 9: Elliptic type PDE, Helmholtz, Laplace and Poisson equations
Week 10: Uniqueness of the solutions of the interior and exterior boundary-value problems for Laplace equation
Week 11: Green’s functions, existence of the solutions of the boundary-value problems for Laplace equation
Week 12: MIDTERM EXAM II. Parabolic type PDE, Heat and diffusion equations, Principle of maximum in the bounded domains
Week 13: Existence and uniqueness of the solution for Cauchy problem for heat equation
Week 14: Existence and uniqueness of the solution for mixed problem for heat equation
Week 15*: *
Week 16*: Final Exam
Textbooks and materials:
Recommended readings: Introduction to Partial Differential Equations with Applications (E.C. Zachmanoglu, D.W,Thoe),
Lectures on Partial Differential Equations (I G Petrovsky)
  * 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: 7, 12 40
Other in-term studies: 0
Project: 0
Homework: 1, 2, 3, 4, 5, 6, 9, 10, 13, 14 10
Quiz: 0
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: 0 0
Own study for mid-term exam: 8 2
Mid-term: 4 2
Personal studies for final exam: 8 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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