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Calculus: Numerical analysis...?Calculus: **Numerical** **Analysis** As early as the time of Archimedes in 3rd century BCE, integral and differential studies began when Archimedes used a method of approximation in calculating bounded areas and volumes of particular solids. Since no algorithm had yet come up during such endeavor, German astronomer Johann Kepler (1571 – 1630) reformed conventions set by Archimedes and promoted new techniques of approximation. By rotating a segment of conic section about an axis, Kepler managed to determine a volume of solid and this became his chief contribution to integral calculus. A contemporary Italian priest, Bonaventura Cavalieri (1598-1647), supplicated this work with fresh concept through an...

13 Pages(3250 words)Essay

Numerical Precision...? **Numerical** Precision **Numerical** precision Floating point numbers Floating point numbers arethe most common way of representing real numbers in computers in recent times. The numbers are mostly represented in a scientific notation which includes a base number and an exponent. For instance, 123.46 can also be expressed as 1.23456 x 102. Floating point numbers range from 1,000,000,000,000 to 0.0000000000000001. In the expression of floating point numbers, they are expressed in a normalized manner in which the radix point is put after the non-zero digit Storage in memory Floating point numbers are stored in computer memory in 4 bytes i.e. 32 bits. Floating point numbers is composed of two components that is,...

4 Pages(1000 words)Assignment

Numerical Precision...? **Numerical** Precision **Numerical** precision. Floating-point arithmetic is reflected as an obscure issue by alot of persons because it is universal in a computer scheme. Every language almost has a floating-point data type, meaning computers that consist from PCs to supercomputers of floating-point accelerators, compilers would oftenly be needed to compile floating-point procedures and then almost every operating system should answer to floating-point exclusions like excess. This paper discusses the aspects of floating-point computer scientist should know to avoid some petty mistakes than can rather cost him a lot. Goldberg (1991) states that discrete mathematics is what distinguishes old computers from scientific computing. He adds... in the...

5 Pages(1250 words)Research Paper

Computer Numerical Control...
Computer **Numerical** Control
Computer **Numerical** Control (CNC) popularly known as **Numerical** Control (NC) is the automatic control that is integrated into mechanical tools and equipments used in manufacturing mass products. These automated instructions are abstractly encoded into a program that is used as a language by the tools. These machines were introduced in the 1940s and their gross use was initiated in the 1950s although these did not use the modern computation language that is afforded by computer programs. However, in the modern times, the machines have been well developed so that little man power is needed. End to end designs of the components have been highly developed and the...

3 Pages(750 words)Essay

Civil Engineering Numerical Analysis...Civil Engineering **Numerical** **Analysis** The governing equation for the given problem is ; ; The solution to the above equations can be determined using the Galerkin Method. According to Galerkin method the solution of for the above equation is obtained using a test function v.
with u =0 and v=0 at x =0 and integrating by parts following equations are obtained
(1)
Thus this indicates that for u(x) as the solution for displacement in the bar the left hand side of this equation. The linear interpolation functions chosen 3 node bar elements given as shown below
1 2 3
The unknown U is defined across the problem domain using the interpolation functions N1, N2 and N3 as U= N1U1 + N2 U2 + N3 U3.
The interpolation...

2 Pages(500 words)Assignment

Computer Numerical Control...Computer **Numerical** Control
Computer **Numerical** Control (CNC) popularly known as **Numerical** Control (NC) is the automatic control that is integrated into mechanical tools and equipments used in manufacturing mass products. These automated instructions are abstractly encoded into a program that is used as a language by the tools. These machines were introduced in the 1940s and their gross use was initiated in the 1950s although these did not use the modern computation language that is afforded by computer programs. However, in the modern times, the machines have been well developed so that little man power is needed. End to end designs of the components have been highly developed and the...

3 Pages(750 words)Essay

History of Numerical Control development...HISTORY OF **NUMERICAL** CONTROL DEVELOPMENT Development and implementation of the **Numerical** Control process Introduction
**Numerical** control is the automation of operated by commands that are abstractly programmed and encoded on a medium of storage. If not automated machine tools are just controlled in a manual way by way of levers or hand wheels or automated mechanically through cams only. The United States air force is credited for the development of **numerical** control.1They saw the need of developing methods of manufacturing that are more efficient for modern aircraft. With the coming of the Second World War those components that were used for fabricating jet aircraft turned to be more complex thereby needing more machining. Most... of this...

2 Pages(500 words)Essay

Numerical Understanding in Preschool...Harris Kamran Developmental Psychology Case Study 27 March **Numerical** understanding in preschool This paper purports to address a problem related to the preschool funding in Iowa, with the aim of demonstrating to the legislators that preschool education, especially in mathematics and in the development of **numerical** sense in children, most of whom hail from low-income families, is crucial to their continued development and understanding in later years of mathematical tasks (Siegler, 2009), thereby opposing the decision to cut down on preschool funding. Scientific data and research to substantiate the stance is taken from Siegler’s paper ...

3 Pages(750 words)Essay

Numerical integral...Mathematics 13 November **Numerical** Integral The history of integrals s back to the 17th century. The basis of integrals was formed in about 1635 by an Italian mathematician known as Cavalieri. His work was the fundamental modern step towards the branch of calculus. However, the development of integrals has had many contributions by different mathematicians. Before the development of integral calculus by Gottfried Wilheim Von Leibnz and Sir Isaac Newton, several other mathematicians had made several developments using the ideas of Archimedes of Syracuse (Elroy 63). Cavalieri was one of the pioneer proponents of the idea that quantities too small cannot be divided into halves, in a concept known as the concept of...

2 Pages(500 words)Research Paper

Numerical Problem...**NUMERICAL** PROBLEM Du Pont **analysis** is a financial ratio that is based on the return on equity ratio. It analyses the ability of a firm to increase its return on equity by analyzing total asset turnover, profit margin and financial leverage.
Return on Equity= profit margin x Total Asset Turnover x financial leverage factor
ROE= 3.8%x2.1x302= 25.5%
2.
Ratio
Formula
Calculation
Return on assets (ROA)
Net income/total assets
1218/9869= 12.3%
Current ratio
Current assets/current liabilities
3945/3456= 1.14
Days cash on hand
Cash/ ([operating expense - depreciation expense]/365).
2737/(27395-367-385)/365
= 37.50days= 38days
Average collection period
(365*net premiums receivables)/premiums...

1 Pages(250 words)Speech or Presentation