Differential equation

Research question: To what extent is the maths behind the double pendulum correct and what are its limitations due to chaos theory. Chaos theory is the idea, in simple terms, that certain natural events and occurrences are unpredictable in their behaviour. Examples of this are: weather, turbulent flow in certain liquids and even the double pendulum. These things can be explored and determined mathematically just how unpredictable they are and under what conditions they may become predictable,…

[Tas1965], Martin and Drew [Mar1989], whose theory was based on Donnell’s equations, and the work done by Chao [Cha1960] whose analysis was based on Timoshenko’s buckling equations. All the theories discussed above are based on the classical shell theory where the Love-Kirchhoff assumptions are used. The Love-Kirchhoff assumptions amount to treating shells as infinitely rigid…

generated initially by differential connection [31]–[33] between two HSC dc-dc converter [16] (cf. Fig. 2a), which was generated as a bidirectional version of the HSC boost dc-dc converter [34], [35]. The unidirectional dc-dc version can be seen as an integration between a conventional boost dc-dc converter and a voltage multiplier circuit [36]. Some known characteristics of a dc-dc converter are necessary to ensure the generation of a dc-ac converter through differential connection. The HSC…

function, ("Black–Scholes Model"). Black–Scholes Equation The Black–Scholes equation is a partial differential equation, which describes the price of the option over time. The equation is: The Black-Scholes PDE can be transformed into the heat equation with following change of variables: , , Placing the partial derivatives into the Black-Scholes PDE, we could get: , We can clearly see that the first part of the equation is actually the heat equation. More changes of variables are…

rate of water through a pump, and to better understand how flow meters work. In this experiment, the relationship of the plot between the orifice and Venturi meter pressure differential showed many correlation with each other. The volumetric flow rate had a square root relationship with the previous stated pressure differentials. The error in this lab was also extremely low appearing at around 0.000004%. Introduction The objective and purpose of experiment six was to use flow meters to…

In an efficient market, optimal allocation of resources, ideally should keep agents from earning abnormal profits due to the interest rate and exchange rate differential, because these will be priced appropriately to reflect all the available information. The test for market efficiency then should reject any claims for abnormal arbitrage situations that may arise out of forward premium rate deviation beyond the…

dynamics based on their fitness. When the prey spots a potential attacker, it alarms the others with a chance of survival that depends on the rate of the sentinels. A way to analyze this proposed dynamic is by constructing a model of a partial differential equation system considering the existence of altruistic vigilance. In which I would like to understand the pattern formation for the two species given the presence of guards and its influences on the population dynamics for preys and…

com/46558-laws-of-motion.html. Newton is known for his work in gravity and the motion of planets. Isaac Newton based his discoveries off of Descartes and changed the modern era of scientific thinking. In mathematics, Newton created integral and differential calculus, and in optics, he created the first telescope. His most influential and famous contribution came from his three laws that describe the motion of objects on the earth. The first law Newton created was based off of Descartes, but the…

Sophie Germain is one of France’s greatest female mathematician prior to revolutionary war, she was the daughter of Ambroise-François Germain and Marie-Madeleine Gruguelu. Her father worked as a part time deputy to the State-General. In his speeches he gave he referred to himself as a merchant and ardently defended the rights of the Third Estate, which he was there to represent. Somewhat later in his life time he became one of the directors of the Banque de France or in English the Bank of…

of all mathematical theorems, and as many as 400 different geometrical, some algebraic, some involving advanced differential equations, etc. proofs now exist, some geometrical, some algebraic, some involving advanced differential equations. Pythagoreans were interested in philosophy, but especially in music and mathematics, two ways of making order out of chaos.…