wk13 - QMA PASS Week 13 Review of Lecture 21-22 Derek &...

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QMA PASS Week 13 Derek & Jessica Review of Lecture 21-22 - 1 - Introduction to Differential Equations The simplest form of differential equation is expressed as: dx dy = f(x) To find solution simple integrate both sides with respect to x Hence, dx dy = ) ( x f Thus, y = ) ( x f The general form of a separable differential equation looks like this: dx dy = f(x)g(y) The above ‘general form’ can be further expressed as: ) ( y g dy = f(x)dx Integrate LHS with respect to y and RHS with respect to x: ) ( y g dy = dx x f ) ( This is identical to: ) ( 1 y g dy = dx x f ) ( Example: Solve the separable differential equation: (1+x 3 ) dx dy + 6x 2 y = 0 Exponential Growth S(t) is a variable that grows exponentially as a function of time: kS dt dS = where k is the growth rate. This differential equation has the general solution: kt Ae S = where A is the value of S when t = 0; k is the rate of growth Example : S dt dS 2 . 0 = When t = 0, S = 10,000 Find S when t = 4.
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QMA PASS Week 13 Derek & Jessica Review of Lecture 21-22 - 2 - Lecture 22 Limited Growth )] ( [ ) ( t N M K dt t dN - = b Integrating gives
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This note was uploaded on 04/02/2012 for the course ECON 1101 taught by Professor Julia during the Three '08 term at University of New South Wales.

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wk13 - QMA PASS Week 13 Review of Lecture 21-22 Derek &...

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