Mathematics and the Physical World (eBook)

Morris Kline (Autor)

eBook Download: EPUB

2012
512 Seiten
Dover Publications (Verlag)
978-0-486-13631-8 (ISBN)

Infos

Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.

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"e;Kline is a first-class teacher and an able writer. . . . This is an enlarging and a brilliant book."e; ― Scientific American"e;Dr. Morris Kline has succeeded brilliantly in explaining the nature of much that is basic in math, and how it is used in science."e; ― San Francisco ChronicleSince the major branches of mathematics grew and expanded in conjunction with science, the most effective way to appreciate and understand mathematics is in terms of the study of nature. Unfortunately, the relationship of mathematics to the study of nature is neglected in dry, technique-oriented textbooks, and it has remained for Professor Morris Kline to describe the simultaneous growth of mathematics and the physical sciences in this remarkable book. In a manner that reflects both erudition and enthusiasm, the author provides a stimulating account of the development of basic mathematics from arithmetic, algebra, geometry, and trigonometry, to calculus, differential equations, and the non-Euclidean geometries. At the same time, Dr. Kline shows how mathematics is used in optics, astronomy, motion under the law of gravitation, acoustics, electromagnetism, and other phenomena. Historical and biographical materials are also included, while mathematical notation has been kept to a minimum. This is an excellent presentation of mathematical ideas from the time of the Greeks to the modern era. It will be of great interest to the mathematically inclined high school and college student, as well as to any reader who wants to understand ― perhaps for the first time ― the true greatness of mathematical achievements.

Inhalt

1: THE WHY AND WHEREFORE2: DISCOVERY AND PROOF3: THE SCIENCE OF ARITHMETIC4: THE DEEPER WATERS OF ARITHMETIC5: "NUMBERS, KNOWN AND UNKNOWN"6: THE LAWS OF SPACE AND FORMS7: THE DIMENSIONS OF THE HEAVENLY SPHERES8: THE REVOLUTIONS OF THE HEAVENLY SPHERES9: THE SCIENTIFIC REVOLUTION10: THE WEDDING OF CURVE AND EQUATION11: EXPLANATION VERSUS DESCRIPTION12: VERTICAL MOTION13: MOTION ON AN INCLINED PLANE14: THE MOTION OF PROJECTILES15: FROM PROJECTILE TO PLANET AND SATELLITE16: DEDUCTIONS FROM THE LAW OF GRAVITATION17: MORE LIGHT ON LIGHT18: THE MATHEMATICS OF OSCILLATORY MOTION19: OSCILLATIONS OF THE AIR20: OLD FOES WITH NEW FACES21: MATHEMATICAL OSCILLATIONS OF THE ETHER22: THE DIFFERENTIAL CALCULUS23: THE INTEGRAL CALCULUS24: DIFFERENTIAL EQUATIONS-THE HEART OF ANALYSIS25: FROM CALCULUS TO COSMIC PLANNING26: NON-EUCLIDEAN GEOMETRIES27: MATHEMATICS AND NATURE INDEX

Produkt-Details

• Erscheint lt. Verlag: 15.3.2012
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 140 x 140 mm
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Schlagworte: advanced concepts • Algebras • arabs • arithmetic • arts students • babylonians • Bolyai • books on arts students • books on college maths • books on elementary maths • books on integral calculus • books on mathematical approaches • books on mathematical discoveries • books on mathematical topics • books on math knowledges • books on math textbooks • books on modern mathematics • books on musical sounds • books on non-euclidean geometries • books on projective geometries • books on renaissance painters • books on school mathematics • circumference • classical greek • college math • copernican theory • Derivation • Descartes • Differential • Dover • Edward Gibbon • egyptians • elementary math • Equation • Eratosthenes • Euclidean Geometry • explaining math • Formulas • Galileo • geometries • Gravitation • Greeks • hated math • hate math • heaps praise • Historical background • Historical Development • Integral calculus • Kepler • Liberal Arts • lobachevsky • math concepts • Mathematical approach • mathematical concepts • mathematical discoveries • Mathematical Theory • mathematical thinking • mathematical topics • Mathematicians • math history • math knowledge • math teacher • math textbooks • mind allows • Modern Mathematics • Motion • musical sounds • Newton • Non-Euclidean geometry • nonmathematician • non-mathematicians • Physics • Plato • Projectiles • Projective Geometry • pythagoreans • quadratic equations • RADIUS • renaissance painters • school math • school mathematics • somewhat embarrassed • Sound Waves • taught math • teaching company • Thinkers • tremendously • trigonometric • Trigonometry • understand math • Velocity • Western Culture
• ISBN-10: 0-486-13631-0 / 0486136310
• ISBN-13: 978-0-486-13631-8 / 9780486136318