The aim of this unit is to introduce some fundamental concepts of the theory of partial differential equations (PDEs) arising in Physics, Chemistry, Biology and Mathematical Finance. The focus is mainly on linear equations but some important examples of nonlinear equations and related phenomena re introduced as well. After an introductory lecture, we proceed with firstorder PDEs and the method of characteristics. Here, we also nonlinear transport equations and shock waves are discussed. Then the theory of the elliptic equations is presented with an emphasis on eigenvalue problems and their application to solve parabolic and hyperbolic initial boundaryvalue problems. The Maximum principle and Harnack's inequality will be discussed and the theory of Green's functions.
Unit details and rules
Unit code  MATH3978 

Academic unit  Mathematics and Statistics Academic Operations 
Credit points  6 
Prohibitions
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MATH3078 or MATH4078 
Prerequisites
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A mark of 65 or greater in 6cp from (MATH2X21 or MATH2X65 or MATH2067) and a mark of 65 or greater 6cp from (MATH2X22 or MATH2X61) 
Corequisites
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None 
Assumed knowledge
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[MATH2X61 and MATH2X65] or [MATH2X21 and MATH2X22] 
Available to study abroad and exchange students  Yes 
Teaching staff
Coordinator  FloricaCorina Cirstea, florica.cirstea@sydney.edu.au 

Lecturer(s)  FloricaCorina Cirstea, florica.cirstea@sydney.edu.au 