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The Navier–Stokes equations, in their full and simplified forms, help with the design of aircraft and cars, the study of blood flow, the design of power stations, the analysis of pollution, and many other problems. Coupled with Maxwell's equations, they can be used to model and study magnetohydrodynamics.
Mathematicians have always had differing opinions regarding the distinction between pure and applied mathematics. One of the most famous (but perhaps misunderstood) modern examples of this debate can be found in G.H. Hardy's 1940 essay A Mathematician's Apology. It is widely believed that Hardy considered applied mathematics to be ugly and dull.
[6] [7] [a] The parentheses can be omitted if the input is a single numerical variable or constant, [2] as in the case of sin x = sin(x) and sin π = sin(π). [ a ] Traditionally this convention extends to monomials ; thus, sin 3 x = sin(3 x ) and even sin 1 / 2 xy = sin( xy /2) , but sin x + y = sin( x ) + y , because x + y is not a ...
The metal-promoted [6+4] cycloaddition using a cycloheptatriene–metal complex is a stepwise, photolytic process that lacks the periselectivity issues of the purely thermal [6+4] cycloaddition. The mechanism has been debated, but likely proceeds through a hapticity change in the metal-triene complex followed by coordination of the diene ...
If the fluid is flowing out of a reservoir, the sum of all forms of energy is the same because in a reservoir the energy per unit volume (the sum of pressure and gravitational potential ρ g h) is the same everywhere. [6]: Example 3.5 and p.116 Bernoulli's principle can also be derived directly from Isaac Newton's second Law of Motion. When ...
Simpson's rules are used to calculate the volume of lifeboats, [6] and by surveyors to calculate the volume of sludge in a ship's oil tanks. For instance, in the latter, Simpson's 3rd rule is used to find the volume between two co-ordinates. To calculate the entire area / volume, Simpson's first rule is used. [7]
Image source: Getty Images. By the time a business has been around for 10 years, there's a dismal 70% failure rate. However, that means 3 out of 10 new business owners are still going strong a ...
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include: