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Unformatted text preview: ial differential equation (PDE)  a DE that involves derivatives of a function
with respect to more than one independent variable. ∂u
∂2u
Heat/diffusion equation:
=D 2
∂t
∂x
Wave equation: ∂2u
∂2u
2
=c
2
∂t
∂ x2 Classifying DEs (Section 1.3) Classifying DEs (Section 1.3)
• Order of a DE  order of the highest derivative in the equation. Classifying DEs (Section 1.3)
• Order of a DE  order of the highest derivative in the equation.
2 • e.g. Heat/diffusion equation: ∂u
∂u
=D 2
∂t
∂x Classifying DEs (Section 1.3)
• Order of a DE  order of the highest derivative in the equation.
2 • e.g. Heat/diffusion equation: ∂u
∂u
=D 2
∂t
∂x • First order in time (t), second order in space (x). Classifying DEs (Section 1.3)
• Order of a DE  order of the highest derivative in the equation.
2 • e.g. Heat/diffusion equation: ∂u
∂u
=D 2
∂t
∂x • First order in time (t), second order in space (x). • Order (in time): Logistic equation:
dP
= rP
dt P
1−
K (A) ﬁrst order (B) second order
(C)...
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This note was uploaded on 02/12/2014 for the course MATH 256 taught by Professor Ericcytrynbaum during the Spring '13 term at UBC.
 Spring '13
 EricCytrynbaum
 Math, Differential Equations, Logic, Equations, Partial Differential Equations

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