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Syllabus ( MATH 435 )


   Basic information
Course title: Applied Partial Differential Equations
Course code: MATH 435
Lecturer: Prof. Dr. Coşkun YAKAR
ECTS credits: 6
GTU credits: 3 (3+0+0)
Year, Semester: 4, 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: Math 203, Math 204, Math 305
Professional practice: No
Purpose of the course: Examine Applications of Partial Differential Equations
   Learning outcomes Up

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

  1. Explain the basic concepts 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
  2. Interpret the Stability results and Applications 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.
    4. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Homework assignment
  3. Develop awareness for the 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.
    4. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
Week 1: Derivation of the equations of mathematical physics.
Week 2: Free oscillations of a string and the wave equation. Oscillations of a string in an elastic medium and Klein-Gordon equation. Kirchhoff lows for the currents in wires; the wave equation and Klein-Gordon equation.
Week 3: Equations of acoustics. Thermal conductivity equation and diffusion equation. Schroedinger equation.
Week 4: Possible physical reasons of the nonlinearities in the equations of mathematical physics. Steady states and Helmholtz equations.
Week 5: Oscillations of the membranes. Initial-value problems, boundary-value problems and mixed problems. Physical analogies. Well-posed problems in Hadamars terminology. The uniqueness theorem.
Week 6: MIDTERM EXAM II and solutions
Week 7: Equations of the hyperbolic type. Method of the propagating waves. D’Alembert’s formula for the wave equation and its generalization for Klein-Gordon equation.
Week 8: Integral equation for oscillations. Examples of solutions. Propagation of the discontinuities along the characteristics. Problem with data on the characteristics.
Week 9: Method of successive approximations. Separation of variables method.
Week 10: Adjoint differential operators. Integral form of solution. Physical interpretation of the Riemann function.
Week 11: Equations of the parabolic type. Formulation of the boundary value problems. Principle of maximal value. Theorem of uniqueness.
Week 12: MIDTERM EXAM II and solutions
Week 13: Method of separation of variables. Homogeneous boundary value problem. Function of a source. Boundary value problems with discontinuous initial conditions. Inhomogeneous heat equation and boundary value problems. Problems on the infinite line. Problems without initial conditions.
Week 14: Equations of the elliptic type. Problems reducible to the Laplace equation. General properties of the harmonic functions. Solutions by separation of variables for the simplest domains. Source functions. Potential theory. Pivotal problems reducible to the Helmholtz equation. Problems for infinite domain. Principle of radiation. Principle of limiting absorption. Principle of limiting amplitude.
Week 15*: -
Week 16*: FINAL EXAM
Textbooks and materials: Partial Differential Equations with Boundary Value Problems by Larry C. Andrews.
Recommended readings: Partial Differential Equations. Lawrence C. Evans
Applied Partial Differential Equations
Paul DuChateau, David Zachmann
Applied Partial Differential Equations
Richard Haberman
Applied Partial Differential Equations
John R. Ockendon, Sam Howison, John Ockendon, Andrew Lacey, Alexander Movchan
  * 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, 7, 8, 9, 10,13,14,15 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: 6 2
Mid-term: 6 2
Personal studies for final exam: 8 1
Final exam: 3 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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