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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
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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
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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.
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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.
