Mathematics and Mechanics - The Interplay: Volume I: The Basics

ISBN-13: 9783662632055 / Angielski / Twarda / 2021 / 1019 str.

Luigi Morino

Recenzje

"This exhaustive and accurate volume, as well as the whole trilogy it belongs to, is essentially a gift for all the people who 'enjoy math and mechanics with their applications' under the honest promise that 'the journey will be rewarding'." (Enzo Bonacci, zbMATH 1491.00005, 2022)

Spis treści

Part I The beginning - Precalculus.- Part II Calculus and dynamics of a particle in one dimension.- Part III Multivariate calculus and mechanics in three dimensions.

Blurb

Mathematics plays an important role in mechanics and other human endeavours. Validating examples in this first volume include, for instance: the connection between the golden ratio (the “divine proportion" used by Phidias and many other artists and enshrined in Leonardo's Vitruvian Man, shown on the front cover), and the Fibonacci spiral (observable in botany, e.g., in the placement of sunflower seeds); is the coast of Tuscany infinitely long?; the equal-time free fall of a feather and a lead ball in a vacuum; a simple diagnostic for changing your car's shocks; the Kepler laws of the planets; the dynamics of the Sun-Earth-Moon system; the tides' mechanism; the laws of friction and a wheel rolling down a partially icy slope; and many more.

The style is colloquial. The emphasis is on intuition - lengthy but intuitive proofs are preferred to simple non-intuitive ones. The mathematical/mechanical sophistication gradually increases, making the volume widely accessible. Intuition is not at the expense of rigor. Except for grammar-school material, every statement that is later used is rigorously proven. Guidelines that facilitate the reading of the book are presented.

The interplay between mathematics and mechanics is presented within a historical context, to show that often mechanics stimulated mathematical developments - Newton comes to mind. Sometimes mathematics was introduced independently of its mechanics applications, such as the absolute calculus for Einstein's general theory of relativity. Bio-sketches of all the scientists encountered are included and show that many of them dealt with both mathematics and mechanics.