Time: 09:00
Location: ENG Z15



KOC University and ITU, Istanbul, Turkey

Brian Cantwell, Stanford University

Date : May 24 and 25, 2017

Time :09:00 - 17:00

Place: ENG Z15



Course summary

This short course is based on the course AA218 given at Stanford University. The course is designed to introduce students to the powerful methods of symmetry analysis with application to the reduction, simplification and solution of differential equations. The methods can be used to find the symmetries of almost any system of linear or nonlinear differential equations and this knowledge can be used to enhance understanding of the solutions.  In many cases, symmetries can be used to solve the equations. The main goal is to develop skill in the use of symmetry methods through problem solving and one-on-one instruction. Topic areas: solution methods for nonlinear ordinary differential equations and partial differential equations, reduction of order and reduction of dimension, symmetries of the classical equations of mathematical physics including the heat equation, wave equation, Navier-Stokes, Euler and Maxwell's equations will be discussed. The methods developed will be used to solve in class problems from dynamics, heat conduction, laminar boundary layers, turbulence and nonlinear wave propagation. Primary course material can be found at:

Mathematica Software for finding symmetries, and related AA218 course notes can be downloaded directly from this site.

Text - Introduction to Symmetry Analysis, Cambridge Press


Brian J. Cantwell (PhD, Caltech 1976) is the Edward C. Wells Professor in the school of engineering at Stanford University. He has been a member of the Stanford faculty since 1978 and served as department chairman from 2001 to 2008. In his research, Professor Cantwell uses similarity methods to investigate the space-time structure of turbulent flow. Research topics have included experimental and numerical investigations of variable density and reacting flows. Since 1998 his research has concentrated on a new class of fast burning fuels for application to hybrid propulsion. Recent research has led to a new area of interdisciplinary study that joins propulsion research with environmental biotechnology. In this research, the focus is on terrestrial applications where energy is derived from waste nitrogen. Teaching duties have included courses on propulsion, compressible flow, turbulence, similarity methods and experimentation. He was given the excellence in teaching award by the Stanford student chapter of the AIAA in 1984 and 1988. He is a Fellow of the American Physical Society, a Fellow of the AIAA, a Fellow of the Royal Aeronautical Society, a member of Sigma Xi, and a member of the National Academy of Engineering. He is the author of four books including a textbook on symmetry analysis published by Cambridge Press in September 2002.


Please contact Özge Çelik (  for registration untill May 23.