In this course a graduate introduction to the vast field of Partial Differential Equations (PDE for short) will be given. The first part of the course will be about classical approaches to construct explicit solutions to basic PDE. In particular, we will look at transport, wave, heat, and Laplace equations and basic properties of their solutions. In the second part of the course a more abstract approach to the existence of solutions of some PDE will be presented. In particular, we will discuss the so-called generalized functions and introduce the notions of weak solutions and Sobolev spaces. If time permits, a spectral problem for the Laplace operator will be discussed.

• Classes: MWF 10:00am-10:50am, NDSU Walster Hall, Room 315
• Office hours: MWF 11:00pm-11:50pm (Minard 408E32)
• Syllabus
• Textbook: Partial Differential Equations in Action: From Modelling to Theory (UNITEXT) 3rd ed. 2016 Edition by Sandro Salsa (Amazon)

• Partial Differential Equations: An Accessible Route Through Theory and Applications (Graduate Studies in Mathematics) by Andras Vasy (Amazon)
• Evans L. C. Partial Differential Equations: Second Edition, Graduate Studies in Mathematics, Publisher: American Mathematical Society, 2010 (Amazon)
• Lectures on Partial Differential Equations (Universitext) 2004th Edition by Vladimir I. Arnold (Amazon)