MAT5143
Mathematical Physics  MAT4143/5153
Course description
Mathematical Physics tentative topics list. This course is aimed at physics majors who wish to deepen their understanding or mathematical methods used in physics. This course is also suitable for Mathematics majors, who can deepen their understanding of applications and proofs of major theorems in Functional Analysis.
Textbooks:
 Needham, T. (1997). Visual Complex Analysis. United Kingdom: Clarendon Press.
 Grimshaw, R. (1993). Nonlinear Ordinary Differential Equations (1st ed.). Routledge.
 R. Courant and D. Hilbert, Methods of Mathematical Physics. Vol. II: Partial Differential Equations, Wiley Classics Library, John Wiley & Sons Inc., New York, 1989.
 Bender, C. and Orszag, S. Advanced Mathematical Methods for Scientists and Engineers. McGraw Hill.
 Kreyszig, E. (1989). Introductory Functional Analysis with Applications. Wiley.
 Methods of Applied Mathematics. Todd Arbogast and Jerry L. Bona. Department of Mathematics, and Institute for Computational Engineering and Sciences, University of Texas at Austin, 2008.
 P. J. Olver , Applications of Lie Groups to Differential Equations, Second Edition, Graduate Texts in Mathematics, vol. 107, SpringerVerlag, New York, 1993.
 Rutherford Aris, Vectors, Tensors and the Basic Equations of Fluid Mechanics. Dover Publications
Topics List
Date  Sections  Topics  Prerequisite Skills  Student Learning Outcomes 

Week 1 

Complex Analysis Part I 
 
Week 2 

Complex Analysis Part II 
 
Week 3 

Complex Analysis Part III 
 
Week 4 

Tensor Calculus Basics I 
 
Week 5 

Tensor Caluclus Basics II 
 
Week 6 

Applied Functional Analysis Part I 
 
Week 7 

Applied Functional Analysis Part II 
 
Week 8 

Applied Functional Analysis Part III 
 
Week 9 

Overview about ordinary differential equations I 
 
Week 10 
Overview about ordinary differential equations II 
 
Week 11 

PDE's of Mathematical Physics 
 
Week 12 
Introduction to Lie Groups and Symmetries I 

 
Week 13 

Introduction to Lie Groups and Symmetries II 
 
Week 14 

KdV equation, completely integrable systems 

