MTM3502 – Partial Differential Equations (Spring 2023-2024)

Instructor Information

• Instructors: Coşkun Güler (Gr. 1) and Gökhan Göksu (Gr. 2)

• E-mail (CG): cguler [at] yildiz [dot] edu [dot] tr

• E-mail (GG): gokhan [dot] goksu [at] yildiz [dot] edu [dot] tr

• Course Web Site: gokhangoksu.github.io/MTM3502

General Information

• Schedule: Monday, 09:00-12:00

• Classroom: KMB-320

• Office Hours: Friday, 14:00-17:00 (and/or by appointment)

Expectations and Goals

• Teaching the general theory of partial differential equations along with basic concepts and techniques, understanding the strong relationship between partial differential equations and physical events, and laying the groundwork for more advanced topics.

Course Materials

• Textbook:

  • J. N. Sharma and K. Singh (2000). Partial Differential Equations for Engineers and Scientist, Alpha Science.

  • T. Myint-U and L. Debnath (2007). Linear Partial Differential Equations for Scientists and Engineers, Birkhäuser.

• Optional Materials (in Turkish):

  • K. Koca (2008). Kısmi Türevli Denklemler, Gazi Kitabevi.

Tentative Course Schedule

• Week 1 (19.02.2024): Basic Concepts and Definitions
  [Slide]

• Week 2 (26.02.2024): Solutions of First Order Linear, Semi-/Quasi-Linear PDEs: Lagrange's Method, Integral Surfaces Passing Through a Given Curve
  [Slide]

• Week 3 (04.03.2024): Surfaces Orthogonal to a Given System of Surfaces, Compatibility of First Order PDEs, Classification of the Solutions of First Order PDEs
  [Slide]

• Week 4 (11.03.2024): Solution of Nonlinear PDEs of First Order: The Method of Charpit, Cauchy’s Method of Characteristics
  [Slide]

• Week 5 (18.03.2024): The Method of Integrating Factors for First Order Linear PDEs
  [Slide]

• Week 6 (25.03.2024): Classification of Second Order Linear PDEs, Canonical Forms of Hyperbolic PDEs
  [Slide]

• Week 7 (01.04.2024): Second Order Linear PDEs with Constant Coefficients and Operator Factorization
  [Slide]

• Week 8 (08.04.2024): No Class (Eid al-Fitr Week)
  [No Class]

• Week 9 (18.04.2024, 17:00-19:00): Midterm
  [Midterm]

• Week 10 (22.04.2024): Second Order Linear PDEs: Canonical Forms of Parabolic PDEs, Canonical Forms of Elliptic PDEs
  [Slide]

• Week 11 (29.04.2024): The Cauchy Problem: Homogeneous and Nonhomogeneous Wave Equations
  [Slide]

• Week 12 (06.05.2024): TBA
  [Slide]

• Week 13 (13.05.2024): TBA
  [Slide]

• Week 14 (20.05.2024): TBA
  [Slide]

Course Evaluation

• Midterm: 60 %

• Final: 40 %