View author publications . This states that, in a steady flow, the sum of all forms of energy in a fluid along a streamline is the same at all points on that streamline. This function is a modified exponential model so that you have rapid initial growth (as in a normal exponential function), but then a growth slowdown with time. The major applications are as listed below. In recent years, there has been subject so far-reaching of research in derivative and differential equation because of its performance in numerous branches of pure and applied mathematics. %PDF-1.5 % Now customize the name of a clipboard to store your clips. They are used in many applications like to explain thermodynamics concepts, the motion of an object to and fro like a pendulum, to calculate the movement or flow of electricity. It involves the derivative of a function or a dependent variable with respect to an independent variable. Q.2. Often the type of mathematics that arises in applications is differential equations. which can be applied to many phenomena in science and engineering including the decay in radioactivity. 0 Academia.edu uses cookies to personalize content, tailor ads and improve the user experience. Now lets briefly learn some of the major applications. The degree of a differential equation is defined as the power to which the highest order derivative is raised. Ordinary differential equations are applied in real life for a variety of reasons. In addition, the letter y is usually replaced by a letter that represents the variable under consideration, e.g. The Simple Pendulum - Ximera Due in part to growing interest in dynamical systems and a general desire to enhance mathematics learning and instruction, the teaching and learning of differential equations are moving in new directions. This is useful for predicting the behavior of radioactive isotopes and understanding their role in various applications, such as medicine and power generation. 2Y9} ~EN]+E- }=>S8Smdr\_U[K-z=+m`{ioZ They can describe exponential growth and decay, the population growth of species or the change in investment return over time. :dG )\UcJTA (|&XsIr S!Mo7)G/,!W7x%;Fa}S7n 7h}8{*^bW l' \ Video Transcript. Does it Pay to be Nice? 2) In engineering for describing the movement of electricity (i)\)At \(t = 0,\,N = {N_0}\)Hence, it follows from \((i)\)that \(N = c{e^{k0}}\)\( \Rightarrow {N_0} = c{e^{k0}}\)\(\therefore \,{N_0} = c\)Thus, \(N = {N_0}{e^{kt}}\,(ii)\)At \(t = 2,\,N = 2{N_0}\)[After two years the population has doubled]Substituting these values into \((ii)\),We have \(2{N_0} = {N_0}{e^{kt}}\)from which \(k = \frac{1}{2}\ln 2\)Substituting these values into \((i)\)gives\(N = {N_0}{e^{\frac{t}{2}(\ln 2)}}\,.