The role of mathematics in science / by M.M. Schiffer and Leon Bowden.

Format:

Book

Author/Creator:

Schiffer, Menahem.

Contributor:

Bowden, Leon.

Series:

Anneli Lax New Mathematical Library

Anneli Lax New Mathematical Library ; 30

Language:

English

Subjects (All):

Exponential functions.

Mathematical analysis.

Physical Description:

1 online resource (xi, 207 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Washington, DC : Mathematical Association of America, 1984.

Language Note:

English

Summary:

The Role of Mathematics in Science aims to illustrate the many ways in which mathematical methods have helped discovery in science. It is aimed at a group of readers who are interested in mathematics beyond the level of high school. The authors occasionally use some calculus and more intricate arguments. The book should appeal to college students and general readers with some background in mathematics. The authors state that, 'If we succeed in giving an impression of the beauty and power of mathematical reasoning in science, the purpose of our work will have been achieved.' This book includes the laws of levers and inclined planes, the laws of exponential versus limited population growth, ray optics, and relativity.

Contents:

The beginnings of mechanics: Archimedes' law of the lever ; First application: the centroid of a triangle ; Second application: the area under a parabola ; Third application: the law of the crooked lever ; Galileo: the law of the inclined plane ; Stevin: the law of the inclined plane ; Insight and outlook

Growth functions: The exponential law of growth ; Maxwell's derivation of the law of errors ; Differential and / or functional equations ; The problem of predicting population growth ; Cusanus' recursive formula for [pi] ; Arithmetic and geometric means

The role of mathematics in optics: Euclid's optics ; Heron: the shortest path principle ; Archimedes' symmetry proof ; Ptolemy and refraction ; Kepler and refraction ; Fermat: the quickest path principle ; Newton's mechanistic theory of light ; Fermat versus Newton: experimentum crucis ; To recapitulate ; The role of science in mathematics ; Some practical applications of conics ; Conical ingenuity: the reflecting telescope.

Mathematics with matrices-transformations: Why use matrices? ; Plane analytic geometry and vector addition ; The dot product ; To relate coordinate geometry and vector algebra ; The law of cosines revisited ; Linear transformations of the plane ; Rotations ; Composite transformations and inverses ; Composition and matrix multiplication ; Rotations and the addition formulas of trigonometry ; Reflections ; Rigid motions (isometries) ; Orthogonal matrices ; Coordinate transformations ; A matter of notation

What is time? Einstein's transformation problem: The Michelson-Morley experiment ; What time is it? ; Einstein's space-time transformation problem ; Einstein's solution ; Rods contract and clocks slow down

Relativistic addition of velocities: Einstein's law of relativistic addition ; Rescaling velocities ; Experimental verification of Einstein's law ; Rescaled velocities revisited

Energy: The two body impact problem in classical mechanics ; The two body impact problem in the theory of relativity ; Admissible energy functions ; More about admissible energy functions ; Proof that V is admissible ; Energy and momentum ; The dependence of mass on velocity ; Energy and matter ; The Lorentz transformation and the momentum-energy vector ; Relativity in more than one space dimension ; Relativity and electrodynamics.

Notes:

Includes index.

Description based on print version record.

ISBN:

0-88385-945-9

OCLC:

929120121