Solution Of Differential Calculus By Das And Mukherjee Pdf 13 WORK
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Given a circuit with the equation L·R. in circuit elements as below: l The equation will be solved in the form of a first order differential equation 2 2 The capacitor could be considered as a mass of. equation: dv/dt = -5 v, with initial condition: v(0) = 1. Solution: We solve the first order differential equation by the Euler method. The Euler method consists in calculating the derivative dv/dt v(t) and the new value v(t + 1). As we know. the difference between dv/dt v(t) and v(t + 1) (dv/dt v(t)) is smaller and smaller as time increases. In our case we have dv/dt v(t) = -5 v(t). The new value v(t + 1) is therefore v(t) + 1 5 v(t). The differential equation becomes dv/dt v(t) - v(t) = -5 v(t). The equation is solved using the Euler method which means we need a computer to solve the equation. In this case the Euler method is implemented in Java. The function call takes two arguments: v(t) the current value of the function at the t-th step and t the current number of steps. In our case, the initial value v(0) is one. We have the initial value v(1) of the function so we can start. The variables names can be changed according to the needs. The first time the function is called the equation is solved, then the new value of v(t + 1) is calculated and the new equation is solved again, and so on. Once we have the two functions, then we can use the function voltize() to apply voltage to the circuit and the function current() to check the current in the circuit. 7. First test:The result is as expected as the circuit is applied to a 3 volts battery. 5 seconds later it is applied to a 5 volts battery. 12 seconds later it is applied to the 9 volts battery. And finally, at the 23 seconds it is applied to the 18 volts battery. The current is applied between the battery and the ground and measured using the function current(). function voltize() { // Place the battery and ground the equation: dv/dt = -5 v, with initial condition: v(0 847798691e