# applications of differential equations

Download Free PDF. The practical importance is given by the fact that the most important time dependent scienti c, social and economical problems are described by di erential, partial di erential and stochastic di erential equations. APPLICATIONS OF DIFFERENTIAL EQUATIONS 2 the colony to grow. The differential equation together with the boundary conditions constitutes a boundary value problem. Differential Equations have already been proved a significant part of Applied and Pure Mathematics since their introduction with the invention of calculus by Newton and Leibniz in the mid-seventeenth century. This paper. One of the fundamental examples of differential equations in daily life application is the Malthusian Law of population growth. Separable Equations So, since the differential equations have an exceptional capability of foreseeing the world around us, they are applied to describe an array of disciplines compiled below;-, explaining the exponential growth and decomposition, growth of population across different species over time, modification in return on investment over time, find money flow/circulation or optimum investment strategies, modeling the cancer growth or the spread of a disease, demonstrating the motion of electricity, motion of waves, motion of a spring or pendulums systems, modeling chemical reactions and to process radioactive half life. PDF. 6) The motion of waves or a pendulum can also … An object is dropped from a height at time t = 0. Let us consider the RL (resistor R and inductor L) circuit shown above. PDF. The theory of differential equations has become an essential tool of economic analysis particularly since computer has become commonly available. Hyperbola: Conic Sections. Let M(t) be the amount of a product that decreases with time t and the rate of decrease is proportional to the amount M as follows. Exponential Growth For exponential growth, we use the formula; G(t)= G0 ekt Let G0 is positive and k is constant, then G(t) increases with time G0 is the value when t=0 G is the exponential growth model. Modeling is an appropriate procedure of writing a differential equation in order to explain a physical process. Rep:? Models such as these are executed to estimate other more complex situations. 4) Movement of electricity can also be described with the help of it. We can describe the differential equations applications in real life in terms of: 1. dp/dt = rp represents the way the population (p) changes with respect to time. If you try and use maths to describe the world around you — say the growth of a plant, the fluctuations of the stock market, the spread of diseases, or physical forces acting on an object — you soon find yourself dealing with derivatives offunctions. 3) They are used in the field of medical science for modelling cancer growth or the spread of disease in the body. 12. However, the above cannot be described in the polynomial form, thus the degree of the differential equation we have is unspecified. How to Solve Linear Differential Equation? In medicine for modelling cancer growth or the spread of disease 2) In engineering for describing the movement of electricity 3) In chemistry for modelling chemical reactions 4) In economics to find optimum investment strategies 5) In physics to describe the motion of waves, pendulums or chaotic systems . The theory of differential equations is quite developed and the methods used to study them vary significantly with the type of the equation. 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