INTRODUCTION OF EULER METHOD
1.1 Ordinary Differential Equations
• A most general form of an ordinary differential equation (ode) is given by f( x, y, y', . . ., y(m) ) = 0
Where x is the independent variable and y is a function of x. y', y'' . . . y(m) are respectively, first, second and mth derivatives of y with respect to x.
Some definitions:
• the highest derivative in the ode is called the order of the ode.
• the degree of the highest order derivative in the ode is called the degree of the ode.
• the differential equation is linear if no product of the dependent variable y(x) with itself or with any one of its derivatives occur in the equation otherwise is non-linear.
• The
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Consider the following initial value problem:
dy/dx = x2 - 1, y(0) = 1
• Suppose we want to use Euler's Method to graph an estimate for the initial value problem with f(x,y) = x2 - 1 given above, on the interval 0 ≤ x ≤ 2.
• From the initial value condition, we know that when x =0, y = 1, so we will start at the initial point (x0, y0) = (0, 1).
• The tangent line at this point is y = 1 - x. If we use a "step size" of h = 1, then our x coordinates will be x0 = 0, x1 = 1, and x2 = 2, and Euler's Method will give us estimates for the y values corresponding to them.
• For this step size, Euler's Method takes just two steps: x0 = 0, y0 = 1 (The initial point) x1 = 1, y1 = 1 + 1*f(0, 1) = 0 x2 = 2, y2 = 0 + 1*f(1, 0) = 0
• So for h = 1, Euler's Method is estimating that our solution curve goes through the three points: (0, 1), (1, 0), and (2, 0).
• What if we used a smaller step size, say h = 0.5? Then we would get y values corresponding to x0 = 0, x1 = 0.5, x2 = 1, x3 = 1.5, and x4 =
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4.APPLICATION OF EULER METHOD
• A first-order explicit Euler method with Higdon absorbing boundary condition is presented to simulate GPR wave propagation in 2-D pavement structure
• The Euler Method for Real-time Simulation, like flight simulation
• In Simulation of 3D-deformable Objects Using Stable and Accurate using Euler Method
• This method is also used for Robot fault detection and control
• Euler method is used in natural gas during transportation in pipeline
5.APPLICATION OF EULER METHOD
• Application : The Euler Method for Real-time Simulation
5.1 What is The Application?
• They developed an experimental flight simulator. Its cockpit is shown in
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:
[-2, -1], [0, 1] and [1, 2]. Looking at the root in the interval [1,
Both passages concern the same topic, the Okefenokee Swamp. Yet, through the use of various techniques, the depictions of the swamp are entirely different. While Passage 1 relies on simplicity and admiration to publicize the swamp, Passage 2 uses explicitness and disgust to emphasize the discomfort the swamp brings to visitors.
ee, searching for a ‘perfect’ love has never mattered to me. It’s never been about someone who would match this silly list of criteria or be exactly who I always dreamed of. I haven’t spent my life wishing for a prince or a man to save me. I haven’t hoped that I’d find this ideal man who could have all the answers and never leave me wondering.
“Hell-raiser, razor-feathered risers, windhover over Peshawar,”(Majmudar Lines 1-3) That was the first stanza of the poem “Ode to a Drone” by Amit Majmudar. This poem is written by a Muslim American who grew up in Cleveland, Ohio. The first stanza is the beginning to an ode to a drone, but immediately, you know he is not praising the drone for being powerful, he is explaining how it is unnecessarily destructive. A drone is an unmanned flying vehicle that shoots missiles or drops bombs on targets in modern warfare. Modern warfare today is taking place in the Middle East which is a transcontinental region centered on Western Asia and Egypt. Many terrorist groups such as ISIS, which is the largest threat right now.
In the previous section, the governing equation of the dynamic and stability behavior of the nanobeam are derived. The Eq. (19) and Eq. (20) are the fourth order partial differential equations which are obtained as the governing equation of the vibration and buckling of the nanobeam, respectively. If it is not impossible to solve these equations as analytically, it is very hard to solve these equations as exact solutions. For this purpose, for computing the vibration frequencies and the buckling loads, the differential quadrature method is selected. The real reason of this selection is because that this method is one of the useful methods to solve the ordinary and partial boundary value and initial
Kate wanted a relationship for a long time - and finally, she had met Aaron and they started dating. They went on a couple of dates and had a great time together. Aaron recently graduated from university, so he wanted to take a few months off, before applying for a steady job. This change also gave Aaron an opportunity to shake off some of his romantic dust and find new ways for Kate and him to spend time together. At first, Kate was delighted with Aaron’s sense of romance and creativity, but as time went by, she barely found time for herself anymore. Kate didn 't want to hurt Aaron so she “played along”, and only a few weeks later (after she had tried to find *ANY* way to keep him busy…) Kate finally decided to bring up the subject. Aaron
indicates towards a fraud. On eof the most important qualities or benefits of this model is that it understands the pattern in the data and generates the result. Once the result is generated the model checks as to how close was the result from the actual results. Based on this analysis the model adjusts its weights to give an accurate result the next time. Once this model has been trained to give accurate results, it can be used to analyze other data as well. Even when Neural Networks are widely accepted, they are not really used that much in the marketing industry merely by the fact that data preparation for this model is very complex time consuming as compared to the Regression Analysis. The marketers are much comfortable using the Regression Analysis over Neural Networks because of the ease of interpreting the results in the Regression Analysis.
The DESTEP analysis consists of following factors: Demographic, Economic, Social, Technological, Environmental, and Political. Outcome of this analysis is derived from new collected data and obtained data from the previous section, country analysis. At the end of this chapter a conclusion concerning the macro environment of Thailand is made.
The derivative of a function is the rate of change of that function. It shows how fast or how slow the function is changing. This can be useful in determining things such as instantaneous rates of change, velocity, acceleration and maximum profits. A good way to explain the concept of a derivative is to do it graphically. To illustrate, think of a drag car race. The track is only ¼ of a mile long, or 1320 feet. The dragster crosses the finish line in six seconds. How fast was the dragster going when it crossed the finish line? The dragster traveled 1320 feet in 6 seconds, so the average speed of the dragster is 1320 divided by 6 which equals 220 feet per second, or 150 miles per hour. The following graph represents the dragster’s position function as the red curve. The position function for the dragster is 36 2/3 x^2. The green line is the secant line connecting the dragster’s starting point and end point. The slope of this secant line is the average speed of the dragster, 220 feet per second, or 150 miles per hour.
Many accounts support the possibility for objects genuinely to persist yet change their intrinsic, natural properties. Intuitively we think that it would be possible: the assumption that this claim is true, Loux argues, ‘underlies some of our most fundamental beliefs about ourselves and the world around us’ (1998: 203). In this essay I shall focus solely on the account of David Lewis’s ‘Doctrine of Temporal Parts’ that it is possible for objects to persist through change by having different temporal parts. By briefly examining intrinsics and extrinsics and the problem of change you will be able to see how successful Lewis’s solution is to this problem, before viewing some weaknesses of the account and then ultimately concluding that Lewis solution successfully achieves the possibility that objects genuinely persist yet change their intrinsic, natural properties.
slope. I think that out of all the variables, this is the one which is
Lumen Learning. (n.d.). Managerial Accounting. Chapter 10: Differential Analysis (or Relevant Costs) Retrieved from: https://courses.lumenlearning.com/managacct/chapter/differential-analysis-and-its-application-to-managerial-decision-making/
Simple linear regression is a model with a single regressor x that has a relationship with a response y that is a straight line. This simple linear regression model can be expressed as
... resultant speed and, by the definition of the tangent, to determine the angle of which the object is launched into the air.