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11/17/2015 1 Introduction to Partial Differential Equations Transforming Numerical.

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Presentation on theme: "11/17/2015 1 Introduction to Partial Differential Equations Transforming Numerical."— Presentation transcript:

1 11/17/2015 http://numericalmethods.eng.usf.edu 1 Introduction to Partial Differential Equations http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates

2 For more details on this topic  Go to http://numericalmethods.eng.usf.eduhttp://numericalmethods.eng.usf.edu  Click on Keyword  Click on Introduction to Partial Differential Equations

3 You are free to Share – to copy, distribute, display and perform the work to Remix – to make derivative works

4 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.

5 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 u is the dependent variable, and x and y are the independent variables.

6 Example of an Ordinary Differential Equation Assumption: Ball is a lumped system. Number of Independent variables: One (t) Hot Water Spherical Ball

7 Example of an Partial Differential Equation Assumption: Ball is not a lumped system. Number of Independent variables: Four (r, θ, φ,t) Hot Water Spherical Ball

8 Classification of 2 nd Order Linear PDE’s where are functions of,and is a function of

9 Classification of 2 nd Order Linear PDE’s can be: Elliptic Parabolic Hyperbolic

10 Classification of 2 nd Order Linear PDE’s: Elliptic If,then equation is elliptic.

11 Classification of 2 nd Order Linear PDE’s: Elliptic Example: where, giving therefore the equation is elliptic.

12 Classification of 2 nd Order Linear PDE’s: Parabolic If,then the equation is parabolic.

13 Classification of 2 nd Order Linear PDE’s: Parabolic Example: where, giving therefore the equation is parabolic.

14 Classification of 2 nd Order Linear PDE’s: Hyperbolic If,then the equation is hyperbolic.

15 Classification of 2 nd Order Linear PDE’s: Hyperbolic Example: where, giving therefore the equation is hyperbolic.

16 THE END http://numericalmethods.eng.usf.edu

17 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 Acknowledgement

18 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.

19 The End - Really


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