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There are many ordinary/partial differential equations/systems describing various phenomena in physics, mechanics, chemistry, biology, sociology, etc. We study how to write out the equations and the related boundary conditions. What does ``well-posedeness\" mean? Various kinds of PDE and the main properties of their solutions are considered. How does one determine the solutions and what does "determine" mean? What are the reasons behind blow-up phenomena? Some methods of analytical and numerical solutions will be considered as well. Prerequisites: 1 semester "Advanced Calculus", 1 semester "Linear Algebra". Optional: 2 semester "Advanced Calculus", 2 semester "Linear Algebra", 1 semester "Functions of Complex Variables", elements of the functional analysis and the ordinary differential equations theory. Curriculum:
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