Posts Tagged 'Numerical Analysis'

Staying Put or Going with the Flow

The atmospheric temperature at a fixed spot may change in two ways. First, heat sources or sinks may increase or decrease the thermal energy; for example, sunshine may warm the air or radiation at night may cool it. Second, warmer or cooler air may be transported to the spot by the air flow in a process called advection. Normally, the two mechanisms act together, sometimes negating and sometimes reinforcing each other. What is true for temperature is also true for other quantities: pressure, density, humidity and even the flow velocity itself. This last effect may be described by saying that “the wind blows the wind” [TM132 or search for “thatsmaths” at irishtimes.com].

Ophelia-20171016-1200

Hurricane Ophelia approaching Ireland, 16 October 2017, 1200Z. Image from https://earth.nullschool.net/

Continue reading ‘Staying Put or Going with the Flow’

Marvellous Merchiston’s Logarithms

Log tables, invaluable in science, industry and commerce for 350 years, have been consigned to the scrap heap. But logarithms remain at the core of science, as a wide range of physical phenomena follow logarithmic laws  [TM103 or search for “thatsmaths” at irishtimes.com].

realcalc

Android app RealCalc with natural and common log buttons indicated.

Continue reading ‘Marvellous Merchiston’s Logarithms’

Simulating the Future Climate

The Earth’s climate is changing, and the consequences may be very grave. This week, That’s Maths in The Irish Times ( TM040  ) is about computer models for simulating and predicting the future climate.

Continue reading ‘Simulating the Future Climate’

French Curves and Bézier Splines

A French curve is a template, normally plastic, used for manually drawing smooth curves. These simple drafting instruments provided innocent if puerile merriment to generations of engineering students, but they have now been rendered obsolete by computer aided design (CAD) packages, which enable us to construct complicated curves and surfaces using mathematical functions called Bézier splines.

French-Curve Continue reading ‘French Curves and Bézier Splines’

Singularly Valuable SVD

In many fields of mathematics there is a result of central importance, called the “Fundamental Theorem” of that field. Thus, the fundamental theorem of arithmetic is the unique prime factorization theorem, stating that any integer greater than 1 is either prime itself or is the product of prime numbers, unique apart from their order.

The fundamental theorem of algebra states that every non-constant polynomial has at least one (complex) root. And the fundamental theorem of calculus shows that integration and differentiation are inverse operations, uniting differential and integral calculus.

The Fundamental Theorem of Linear Algebra
Continue reading ‘Singularly Valuable SVD’

The Lambert W-Function

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In a recent post ( The Power Tower ) we described a function defined by iterated exponentiation:

\displaystyle y(x) = {x^{x^{x^{.^{.^{.}}}}}}

It would seem that when {x>1} this must blow up. Surprisingly, it has finite values for a range of x>1. Continue reading ‘The Lambert W-Function’

Carving up the Globe

This week, That’s Maths (TM007) describes various ways of dividing up the sphere. This is an important problem in geometry, biology, chemistry, astronomy, meteorology and climate modelling. Continue reading ‘Carving up the Globe’


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