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First order differential equations: Euler's method
Finally, we consider ?nding the numerical solution for a ?rst order differential equation given an initial value. We consider the Euler's method, which is the most basic procedure for ?nding the approximate solution of an initial value problem stated as:
dy/dx = f(x, y),
given the initial value
y(x0) = y0
where x0 and y0 are given parameters (numbers). The derivation of the Euler can be geometrical (by looking at the tangent) or by considering Taylor expansions and taking only ?rst order terms or alternatively by considering the basic de?nition of derivative in terms of limit theorem.
Let us consider the geometric form of the derivation for the Euler's method.
The characteristic properties of an aquifer can be used to calculate groundwater velocities, v groundwater (L/T), according to: where KH (L/T) is the hydraulic conductivit
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1. Design a suitable phase-lead controller. You should explain in detail how your design has been developed. Your solution should include Bode plots constructed both manually and
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