Abstract: This paper is concerned with quick survey on differential equations which includes main types of differential equations and its applications. The differential equations are useful for modeling and simulating phenomena and understanding how they operate. The solution to a differential equation is a function or a class of functions, its not just a value or a set of values. Key words: Differential Equations, ordinary differential equations I. INTRODUCTION A differential condition is a scientific condition that relates some capacity with its subsidiaries. In applications, the capacities as a rule speak to physical amounts, the subsidiaries speak to their rates of progress, and the condition characterizes a connection between the two. …show more content…
Contained in this book was Fourier's proposition of his warmth condition for conductive dispersion of warmth. This halfway differential condition is presently educated to each understudy of scientific material science. III. TYPES OF DIFFERENTIAL EQUATIONS There were mainly four types of differential equations listed below. A. Ordinary differential equations B. Partial differential equations C. Linear differential equations D. Non-linear differential equations Now we will discuss briefly about above different types of differential equations. A. ORDINARY DIFFERENTIAL EQUATIONS In mathematics, an ordinary differential equation (ODE) is a differential equationcontaining at least one elements of one autonomous variable and its subsidiaries. The term customary is utilized as a part of stand out from the term halfway differential condition which might be as for more than one autonomous variable. Given F, a function of x, y, and derivatives of y. Then an equation of the form is called an explicit ordinary differential equation of order n
An exponential equation is a type of transcendental equation, or equation that can be solved for one factor in terms of another. An exponential function f with base a is denoted by f (x) = ax, where a is greater than 0, a can not equal 1, and x is any real number. The base 1 is excluded because 1 to any power yields 1. For example, 1 to the fourth power is 1×1×1×1, which equals 1. That is a constant function which is not exponential, so 1 is not allowed to be the base of an exponential equation. Otherwise, the base of a can be any number that is greater than 0 and isn’t 1, and x can be any real number. The equation for the parent function of an exponential functions follows as so:
4. A) The functions for the problem would look like p=800*0.95*t and 0=50*1.15*t. P represents the pine
The objective of this experiment was to identify a metal based on its specific heat using calorimetry. The unknown metals specific heat was measured in two different settings, room temperature water and cold water. Using two different temperatures of water would prove that the specific heat remained constant. The heated metal was placed into the two different water temperatures during two separate trials, and then the measurements were recorded. Through the measurements taken and plugged into the equation, two specific heats were found. Taking the two specific heats and averaging them, it was then that
Typical analysis such as analytical analysis (PDE, ODE etc), numerical analysis (finite element analysis) might not be so attractive in the settings of my research problem above. One of the big disadvantages for typical analysis in my research problem is that typical analysis is computationally intractable due to the high dimensions in the above problems. Secondly, typical analysis is usually not as flexible and adaptable as Monte Carlo simulations. Some analytical analysis such as PDE does not even fit the setting of the above research problems, as it is empirical by its natural.
method can be produced and a graph of the function can be made. From the graph,
idea was that electrical current flow was similar to that of heat flow, and by
In Newtonian physics, free fall is any motion of a body where its weight is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it and it moves along a geodesic. The present article only concerns itself with free fall in the Newtonian domain.
Differential analysis is useful in many situations faced by the management and it has to choice between different alternatives for each situation to make the necessary decision. Some of these situations are as follows:
Calculus is defined as, "The branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two main types are differential calculus and integral calculus." (Oxford Dictionary). Contrary to any other type of math, calculus allowed Newton and other scientists to process the different motions and dynamic changes in world, such as the orbit of planets in space. Newton first became interested in the subject of mathematics while he was an undergraduate at Cambridge University. Although he did not focus on any of his math classes during his time as an undergraduate because it focused on Greek mathematics, he instead learned
The argument in this paper that even though the onus of the discovery of calculus lies with Isaac Newton, the credit goes to Leibniz for the simple fact that he was the one who published his works first. Appending to this is the fact that the calculus wars that ensue was merely and egotistic battle between humans succumbing to their bare primal instincts. To commence, a brief historical explanation must be given about both individuals prior to stating their cases.
Differential equation has its application in different area of knowledge of mankind. A few such examples are: the motion of a projectile, rocket, planet or satellite, the charge or current in an electric circuit, the reactions of chemicals, the rate of growth of a population, spring mass systems, bending of beams, the conduction of heat in a rod or in a slab etc. The mathematical formulations of all of the problems give rise to differential equations. Basically, most of the differential equations involving physical phenomena are nonlinear. It is simple to solve the differential equations which are linear but the solution of nonlinear equations are laborious and in some cases it is impossible to solve them analytically. In such circumstances the investigators attempt to fit the studied oscillatory processes into linear schemes, neglecting the nonlinear terms or convert the nonlinear equations into linear equations by imposing some conditions.
Calculus, the mathematical study of change, can be separated into two departments: differential calculus, and integral calculus. Both are concerned with infinite sequences and series to define a limit. In order to produce this study, inventors and innovators throughout history have been present and necessary. The ancient Greeks, Indians, and Enlightenment thinkers developed the basic elements of calculus by forming ideas and theories, but it was not until the late 17th century that the theories and concepts were being specified. Originally called infinitesimal calculus, meaning to create a solution for calculating objects smaller than any feasible measurement previously known through the use of symbolic manipulation of expressions. Generally accepted, Isaac Newton and Gottfried Leibniz were recognized as the two major inventors and innovators of calculus, but the controversy appeared when both wanted sole credit of the invention of calculus. This paper will display the typical reason of why Newton was the inventor of calculus and Leibniz was the innovator, while both contributed an immense amount of knowledge to the system.
Ever wonder how scientists figure out how long it takes for the radiation from a nuclear weapon to decay? This dilemma can be solved by calculus, which helps determine the rate of decay of the radioactive material. Calculus can aid people in many everyday situations, such as deciding how much fencing is needed to encompass a designated area. Finding how gravity affects certain objects is how calculus aids people who study Physics. Mechanics find calculus useful to determine rates of flow of fluids in a car. Numerous developments in mathematics by Ancient Greeks to Europeans led to the discovery of integral calculus, which is still expanding. The first mathematicians came from Egypt, where they discovered the rule for the volume of a pyramid and approximation of the area of a circle. Later, Greeks made tremendous discoveries. Archimedes extended the method of inscribed and circumscribed figures by means of heuristic, which are rules that are specific to a given problem and can therefore help guide the search. These arguments involved parallel slices of figures and the laws of the lever, the idea of a surface as made up of lines. Finding areas and volumes of figures by using conic section (a circle, point, hyperbola, etc.) and weighing infinitely thin slices of figures, an idea used in integral calculus today was also a discovery of Archimedes. One of Archimedes's major crucial discoveries for integral calculus was a limit that allows the "slices" of a figure to be infinitely thin. Another Greek, Euclid, developed ideas supporting the theory of calculus, but the logic basis was not sustained since infinity and continuity weren't established yet (Boyer 47). His one mistake in finding a definite integral was that it is not found by the sums of an infinite number of points, lines, or surfaces but by the limit of an infinite sequence (Boyer 47). These early discoveries aided Newton and Leibniz in the development of calculus. In the 17th century, people from all over Europe made numerous mathematics discoveries in the integral calculus field. Johannes Kepler "anticipat(ed) results found… in the integral calculus" (Boyer 109) with his summations. For instance, in his Astronomia nova, he formed a summation similar to integral calculus dealing with sine and cosine. F. B. Cavalieri expanded on Johannes Kepler's work on measuring volumes. Also, he "investigate[d] areas under the curve" ("Calculus (mathematics)") with what he called "indivisible magnitudes.
This equation states that for an incompressible, non-viscous fluid with constant density flowing through a channel, the mass and volume of the fluid are conserved. As a result, the rate of fluid volume flow has to be constant at different points where the cross-sectional area differs.