Designing, Making and Testing a Sundial Introduction: The sundial is the oldest know device for measuring time. The first confirmed uses of it where by the Babylonians in around 2000BC. However it is safe to say that shadows have been used as a rough measure of time ever since primitive man discovered that as the day progresses the shadows of trees and rocks get shorter and then longer again. The sundials used by the Babylonians were hollow half spheres, set with edges flat and with
In real engineering problems like heat transfer from cylinder, cylinder head, etc. and fluid flow requires lots of experimental effort for the analysis. It is very time consuming and costly process. Computational fluid dynamics, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computational fluid dynamics analysis is nothing but the simulation process which involves heat flow as well as fluid flow on the basis of computer
In classical fluid dynamics, the Navier-Stokes equations for incompressible viscous fluids and its special (limiting) case the Euler equations for inviscid fluids are sets of non-linear partial differential equations that describes the spatiotemporal evolution of a fluid (gas). Both equations are derived from conservative principles and they model the behavior of some macroscopic variables namely: mass density, velocity and temperature. The evolution of a fluid (gas) can also be described by the
II.3 Partial Adjustment Valuation (PAV) Theory In order to relate among subsystems of the system analyzed by the RBV theory, it is necessary to provide logical relationships that might utilize several mathematical theories such as the structure equation model. This research tries to employ the partial adjustment valuation (PAV) theory to correlate logically the system. Accordingly, the subsequent explanation depicts it as follows. The origin of PAV theory was initiated by Nerlove (1958) and further
ABSTRACT A partial differential equation is a differential equation that contain unknown multivariable functions and their partial derivatives while ordinary differential equations contains function of a single variables and their derivatives. Therefore, an ordinary differential equation is a special case of partial differential equation but the behaviour of a solution is quite different. It is much more complicated in the case of partial differential equation because it has more than one independent
Cubic equations were known since ancient times, even from the Babylonians. However they did not know how to solve all cubic equations. There are many mathematicians that attempted to solve this “impossible equation”. Scipione del Ferro in the 16th century, made progress on the cubic by figuring out how to solve a 3rd degree equation that lacks a 2nd degree. He passes the solution onto his student, Fiore, right on his deathbed. In 1535 Niccolò Tartaglia figures out how to solve x3+px2=q and later
ABSTRACT A partial differential equation is a differential equation that contain unknown multivariable functions and their partial derivatives while ordinary differential equations contains function of a single variables and their derivatives. Therefore, an ordinary differential equation is a special case of partial differential equation but the behaviour of a solution is quite different. It is much more complicated in the case of partial differential equation because it has more than one independent
Maxwell’s Equations are a set of four equations that govern all of electromagnetism. The equations show a unification of the electric and magnetic fields and are often considered one of the greatest unifications in physics, describing one of the four fundamental interactions, the electromagnetic force. The unification of the electric and magnetic forces in the 19th century by Maxwell’s Equations led to several scientific advancements – including an entire new branch of physics, electromagnetism
and the vertical and horizontal components. Projectile Motion Projectile motion is the force that acts upon an object that is released or thrown into the air. Once the object is in the air, the object has two significant forces acting upon it at the time of release. These forces are also known as horizontal and vertical forces. These forces determine the flight path and are affected by gravity, air resistance, angle of release, speed of release, height of release and spin Useful for the military, projectile
At this time of the year eighth graders are reviewing for Standardized Testing. One of the things they need practice on is their algebra skills, such as solving linear equations. The focus of this lesson was on solving linear equations with one variable. There are various standards that deal with solving equations, but for these students I narrowed it down to single-variable equations: Solve linear equations. The Alabama standard used from this lesson was 8. EE.7.b Solve linear equations with rational
other instruments found in the lab. The thermometer only reaches 45 degrees celsius; therefore, thermodynamic equations need to be applied in order to find the original temperature of the hot water. We also had access to deionized water that was approximately room temperature. Two equations were used in this experiment to determine the initial temperature of the hot water. The first equation
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
key tool to study nonlinear difference equations which arise in the mathematical modelling of real-world phenomena. It is not expected that explicit solutions can be found for the solutions of nonlinear difference equations; however, some nonlinear equations can be transformed into equivalent linear equations by a change of dependent variable. In this work, we transform a discrete logistic equation, which is a nonlinear difference equation, into a linear equation and we determine its explicit solution
theory in which he proposed in 1867, he suggested that the surface area produced by crushing is directly proportional to the energy consumed. Rittinger formulated an equation in which energy consumed is in the form of Rittinger. Below is the Energy Rittinger equation ERittinger=CRittinger(1/P_80 -1/f_80 )………………………………………………………………..Equation 2.1 Where Rittinger E is the energy input, Rittinger C is a material constant, 80 p is the size which 80 % of the product passes, and 80 f is the size which 80 % of
Evaluating Volterra Integro-Differential Equations in terms of Global, Polynomial and Numerical Equations in Boundary Conditions The integro-differential equations are originated from different mathematical models for many scientific phenomena. Nonlinear integro-differential equations are also can be seen in various applications of various scientific fields that are modeled by nonlinear phenomena.[3] The solutions using in integro-differential equations have an important role in lots of engineering
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
As the time goes by, the value and the prices of the product will changes base on the society and the temporal finance situation. People will have the chance to buy the same products in different prices in different period of time due to the changing situation of the society. To let the people purchase products in a fair price as well as they can earn profit at the same time, businesses will need to consider the impact to the prices of product that effected by society. In Linear Algebra in the Financial
to a winning strategy. Either an effective serve will not be returned, leading to a point, or it will be returned with minimal strength, providing the serving team with the advantage. One aim of a good serve is to provide the receivers with little time as possible to react. Forces and angles are the two main factors at play when relating volleyball with math (Papageōrgiou & Spitzley, 2003). In short, in order to relate volleyball with math, the force needed to make the ball move a certain height
space. It is stated that in order to escape Earth’s gravitational pull, one must travel with velocity of 11.2km/s and is also known as the ‘escape velocity. Which is why in this exploration, I am going to explore and research on Tsiolkovsky rocket equation to discover what it takes travel into outer space and to our moon by observing the Saturn V’s ideal velocity during when it first took Neil Armstrong onto the moon and whether or not it takes that much speed in order to escape Earth’s gravity. Forces
could be calculated using a low-density expansion in powers of $sqrt{na^3}$, where $n$ is the number density. For example the energy density has the expansion begin{equation} frac{E}{N} = frac{2 pi na {hbar}^2}{m} Bigg( 1 + frac{128}{15sqrt{pi}}sqrt{na^3} + frac{8(4pi-3sqrt{3})}{3}na^3 (ln(na^3)+c) + ... Bigg) label{en} end{equation} The first term in this expansion is the mean-field approximation and was calculated by Bogoliubov cite{Bog}. The corrections to the mean-field approximation can be