PHY 711 Classical Mechanics and Mathematical Methods 11-11:50 AM MWF Olin 107 Plan for Lecture 37 Review of mathematical methods – More comments on complex numbers Topics concerning matrices 12/02/2016 PHY 711 Fall 2016 -- Lecture 37

12/02/2016 PHY 711 Fall 2013 -- Lecture 34 PHY 711 Fall 2016 -- Lecture 37 2

12/02/2016 PHY 711 Fall 2016 -- Lecture 37

12/02/2016 PHY 711 Fall 2016 -- Lecture 37

Evaluating contour integrals in the presence of poles z4 z1 z2 z3 12/02/2016 PHY 711 Fall 2016 -- Lecture 37

A function is “meromorphic” in a region of the complex plane if it is analytic except for poles in that region 12/02/2016 PHY 711 Fall 2016 -- Lecture 37

Useful theorem: 12/02/2016 PHY 711 Fall 2016 -- Lecture 37

C P P Z 12/02/2016 PHY 711 Fall 2016 -- Lecture 37

Some useful properties of matrices 12/02/2016 PHY 711 Fall 2016 -- Lecture 37

Singular value decomposition 12/02/2016 PHY 711 Fall 2016 -- Lecture 37

Singular value decomposition -- continued 12/02/2016 PHY 711 Fall 2016 -- Lecture 37

12/02/2016 PHY 711 Fall 2016 -- Lecture 37

12/02/2016 PHY 711 Fall 2016 -- Lecture 37

Example: = = 12/02/2016 PHY 711 Fall 2016 -- Lecture 37

Note that SVD can be applied to rectangular matrices UT 12/02/2016 PHY 711 Fall 2016 -- Lecture 37