Mathematical-analysis Sentence Examples

The practical problems of fluid motion, which are amenable to mathematical analysis when viscosity is taken into account, are excluded from treatment here, as constituting a separate branch called "hydraulics" (q.v.).

If an iron ship be swung when upright for deviation, and the mean horizontal and vertical magnetic forces at the compass positions be also observed in different parts of the world, mathematical analysis shows that the deviations are caused partly by the permanent magnetism of hard iron, partly by the transient induced magnetism of soft iron both horizontal and vertical, and in a lesser degree by iron which is neither magnetically hard nor soft, but which becomes magnetized in the same manner as hard iron, though it gradually loses its magnetism on change of conditions, as, for example, in the case of a ship, repaired and hammered in dock, steaming in an opposite direction at sea.

Instead of observing the deviation solely for the purposes of correcting the indications of the compass when disturbed by the iron of the ship, the practice is to subject all deviations to mathematical analysis with a view to their mechanical correction.

It can only be contrived by means of complicated mathematical analysis.

Wallis having meanwhile published other works and especially a comprehensive treatise on the general principles of calculus (Mathesis universalis, 1657), he might take this occasion of exposing afresh the new-fangled methods of mathematical analysis and reasserting his own earlier positions.

Oliver Heaviside after 1880 rendered much assistance by reducing Maxwell's mathematical analysis to more compact form and by introducing greater precision into terminology (see his Electrical Papers, 1892).

The extraordinary advances made by him in this branch of knowledge were owing to his happy method of applying mathematical analysis to physical problems. As a pure mathematician he was, it is true, surpassed in profundity by more than one among his pupils and contemporaries; and in the wider imaginative grasp of abstract geometrical principles he cannot be compared with Fermat, Descartes or Pascal, to say nothing of Newton or Leibnitz.

His familiarity with the methods of mathematical analysis and a certain refinement of taste in their application have resulted in great beauty of form.

Speculations concerning a calculus of reasoning had at different times occupied Boole's thoughts, but it was not till the spring of 1847 that he put his ideas into the pamphlet called Mathematical Analysis of Logic. Boole afterwards regarded this as a hasty and imperfect exposition of his logical system, and he desired that his much larger work, An Investigation of the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probabilities (1854), should alone be considered as containing a mature statement of his views.

Many teachers use the Funderstanding coaster as a practical lesson in physics or engineering, and students can use the resulting measurements for mathematical analysis.

So also any exhaustive survey of the temperature and salinity of the sea at a great number of points on and below the surface reveals a complexity of conditions that may defy mathematical analysis and could not easily be predicted.