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 first-order 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 boundary-value problems. The Maximum principle and Harnack's inequality will be discussed and the theory of Green's functions.
Unit details and rules
Academic unit | Mathematics and Statistics Academic Operations |
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Credit points | 6 |
Prerequisites
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(A mark of 65 or greater in 12cp of 2000 level units) or [12cp from (MATH3061 or MATH3066 or MATH3063 or MATH3076 or MATH3961 or MATH3962 or MATH3963 or MATH3968 or MATH3969 or MATH3971 or MATH3974 or MATH3976 or MATH3977 or MATH3979)] |
Corequisites
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None |
Prohibitions
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MATH3078 or MATH3978 |
Assumed knowledge
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(MATH2X61 and MATH2X65) or (MATH2X21 and MATH2X22) |
Available to study abroad and exchange students | Yes |
Teaching staff
Coordinator | Daniel Hauer, daniel.hauer@sydney.edu.au |
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Lecturer(s) | Daniel Hauer, daniel.hauer@sydney.edu.au |