Download
1 / 19
871 likes | 2.28k Views
Introduction to Partial Differential Equations. http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates. 9/19/2014. http://numericalmethods.eng.usf.edu. 1. For more details on this topic Go to http://numericalmethods.eng.usf.edu
E N D
Introduction to Partial Differential Equations http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates 9/19/2014 http://numericalmethods.eng.usf.edu 1
For more details on this topic • Go to http://numericalmethods.eng.usf.edu • Click on Keyword • Click on Introduction to Partial Differential Equations
You are free • to Share – to copy, distribute, display and perform the work • to Remix – to make derivative works
Under the following conditions • Attribution — You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). • Noncommercial — You may not use this work for commercial purposes. • Share Alike — If you alter, transform, or build upon this work, you may distribute the resulting work only under the same or similar license to this one.
What is a Partial Differential Equation ? • Ordinary Differential Equations have only one independent variable • Partial Differential Equations have more than one independent variable subject to certain conditions: where uis the dependent variable, and x and y are the independent variables.
Spherical Ball Hot Water Example of an Ordinary Differential Equation • Assumption: Ball is a lumped system. • Number of Independent variables: One (t)
Spherical Ball Hot Water Example of an Partial Differential Equation • Assumption: Ball is not a lumped system. • Number of Independent variables: Four (r,θ,φ,t)
Classification of 2nd Order Linear PDE’s where are functions of ,and is a function of
Classification of 2nd Order Linear PDE’s can be: • Elliptic • Parabolic • Hyperbolic
Classification of 2nd Order Linear PDE’s: Elliptic If ,then equation is elliptic.
Classification of 2nd Order Linear PDE’s: Elliptic Example: where, giving therefore the equation is elliptic.
Classification of 2nd Order Linear PDE’s: Parabolic If ,then the equation is parabolic.
Classification of 2nd Order Linear PDE’s: Parabolic Example: where, giving therefore the equation is parabolic.
Classification of 2nd Order Linear PDE’s: Hyperbolic If ,then the equation is hyperbolic.
Classification of 2nd Order Linear PDE’s: Hyperbolic Example: where, giving therefore the equation is hyperbolic.
The End http://numericalmethods.eng.usf.edu
Acknowledgement This instructional power point brought to you by Numerical Methods for STEM undergraduate http://numericalmethods.eng.usf.edu Committed to bringing numerical methods to the undergraduate
For instructional videos on other topics, go to http://numericalmethods.eng.usf.edu/videos/ This material is based upon work supported by the National Science Foundation under Grant # 0717624. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
