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Definition
| Has more than 1 independent variable x,y and a dependent variable that is a function of the independent variables u(x,y...) whose solution is a function u(x,y...) |
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Term
| Given a linear operator what is the definition of linearity? |
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Definition
L(u+v) = Lu + Lv
L(cu) = cLu |
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Term
| What is a homogenous and inhomogenous differential equation? |
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Definition
Homogenous: u = 0
Inhomogenous: u = g
Let g be a function of independent variables. |
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Term
| T/F: In a linear function, if u and v are both solutions, so is (u+v). |
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Definition
| True, it is an advantage of linearity. |
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Term
| T/F: If u1, u2, ... un are all solutions, so is any other linear combination. |
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Definition
| True, it is an advantage of linearity. |
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Term
| For an ODE of order m you get _ arbitrary constants. |
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Definition
| For an ODE of order m you get m arbitrary constants. |
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| If you add a homogenous linear solution to an inhomogenous linear solution, is the solution still homogenous? |
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Definition
No, the solution becomes inhomogenous. If linear, then:
Homogenous + inhomogenous = inhomogenous |
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