last - MATH2860U: Chapter 12 1 BOUNDARY-VALUE PROBLEMS IN...

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MATH2860U: Chapter 12 1 BOUNDARY-VALUE PROBLEMS IN RECTANGULAR COORDINATES Separable Partial Differential Equations (Section 12.1, pg. 433) Recall: While we have spent the course studying ordinary differential equations, we did also introduce partial differential equations at the start of the course. Definition: A linear second-order partial differential equation is of the form G Fu Eu Du Cu Bu Au y x yy xy xx Examples: For each of the following, identify its order and whether or not it is linear. If it is linear, is it homogeneous? 0 9 10 8 x y x xy u u u u ) sin( 4 xy u u y xxy x y xx u u u 7 And now, a little bit more terminology regarding PDEs: Definition: The linear 2 nd -order partial differential equation 0 Fu Eu Du Cu Bu Au y x yy xy xx where A , B , C , D , E , and F are real constants, is said to be hyperbolic if 0 4 2 AC B parabolic if 0 4 2 AC B elliptic if 0 4 2 AC B
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MATH2860U: Chapter 12
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