Lecture 1 Notes

E has as many derivatives as appear in the equation

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Unformatted text preview: t + y = sin(t) dt 2 dy t + y 2 = sin(t) dt r2 = rP − P K <--- Nonlinear <--- Linear <--- Linear Classifying DEs (Section 1.3) • Linearity - a DE is linear if it is linear in the unknown function and all its derivatives. • (A) Linear or (B) nonlinear: dP = rP dt ￿ P 1− K ￿ d4 w EI 4 = q dx 2 dy t + y = sin(t) dt 2 dy t + y 2 = sin(t) dt r2 = rP − P K <--- Nonlinear <--- Linear <--- Linear <--- Nonlinear More definitions - solutions More definitions - solutions • Solution to a DE on some interval A More definitions - solutions • Solution to a DE on some interval A • a function that is suitable differentiable everywhere in A (i.e. has as many derivatives as appear in the equation) and, More definitions - solutions • Solution to a DE on some interval A • a function that is suitable differentiable everywhere in A (i.e. has as many derivatives as appear in the equation) and, • satisfies the equation. More definitions - solutions • Solution to a DE on some interval A ...
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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.

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