This is an undergraduate course on linear partial differential equations (PDEs) and associated boundary and boundary-initial value problems. Special emphasis is placed on fundamental concepts,solution methods and applications of PDEs to problems in Mechanical Engineering

• Sturm-Liouville Theory.
• Expansions in series of eigen-functions. Fourier series.
• Introduction to Scientific
• Computing with Mathematica.
• Classification of PDEs,
• Characteristic Curves – the Method of
  Characteristics.
• Elliptic Equations (Laplace, Poisson), the Methods of Separation of Variables and Finite Fourier Transform.
• Dirichlet & Neumann Problems.
• Applications to various coordinate systems.
• Solving Parabolic Equations (Heat Transfer) with the Method of Separation of Variables.
• Solving Hyperbolic Equations (Wave Equation) with the Method of Separation of Variables.
• Integral Fourier Transform.
• Heat Transfer and Wave Propagation in Infinite and Semi-Infinite Space.
• The Green’s Function Method.

Suggested Literature:
1. Σ. Τραχανάς, “Μερικές Διαφορικές Εξισώσεις”
2. Μυλωνάς, Ν. & Σχοινάς, Χ., Διαφορικές Εξισώσεις, Μετασχηματισμοί και Μιγαδικές Συναρτήσεις, Εκδόσεις Τζιόλα, 2015.
3. Σταυρακάκης, Ν., Διαφορικές Εξισώσεις: Συνήθεις και Μερικές, Εκδόσεις Σταυρακάκης, 2015.
4. Haberman Richard (2004). Applied Partial Differential Equations, With Fourier Series and Boundary Value Problems (Fourth ed.). NJ: Pearson/PrenticeHall.
5. Strauss W.A. (2008). Partial Differential Equations, An Introduction. Hoboken, NJ: Wiley.
6. Pinchover Y. and Rubistein J. (2005). An Introduction to Differential Equations. Cambridge: Cambridge University Press.

Related Academic Journals:

• Journal of Engineering Mathematics
• SIAM Journal on Applied Mathematics

Greek

Lectures