APM346H1 Differential Equations
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چکیده
Types of Partial Differential Equations • Transport equation: u x x , y u y x , y =0 , where u x= ∂u ∂ x , u y= ∂u ∂ y , and u x , y=? . • Shockwave equation: u x x , y u x , yu y x , y=0 . • The vibrating string equation: u tt x , t =c 2 u xx x , t , where ut= ∂ u ∂ t 2 and u xx= ∂ u ∂ x . The wave equation: utt x , y , z , t =c 2 u xx x , y , z , t u yy x , y , z , t u zz x , y , z , t .
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