Mathematical Methods in Science /

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If you have ever wondered how the laws of nature were worked out mathematically, this is the book for you. Above all, it captures some of Pólya's excitement and vision.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Pólya, George
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2012.
Colección:Anneli Lax new mathematical library.
Temas:
Mathematics.
Science > Mathematics.
Mathematics
Mathématiques.
Sciences > Mathématiques.
SCIENCE > Physics > Mathematical & Computational.
Science > Mathematics
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Front Cover
  • Mathematical Methods in Science
  • Copyright Page
  • Contents
  • INTRODUCTION
  • CHAPTER 1. From the History of Astronomy: Measurement and Successive Approximation
  • SECTION 1 MEASUREMENT
  • 1 The Tunnel
  • 2 Measuring: Triangulating
  • 3 How Far Away is the Moon?
  • 4 Why Teach Triangulation?
  • SECTION 2 ASTRONOMICAL MEASUREMENTS
  • 1 Aristarchus of Samos
  • 2 Radius of Earth: Eratosthenes
  • 3 Rival Cosmologies
  • 4 The Orbit of Venus
  • 5 Tycho Brahe and Kepler
  • 6 The Mars Year
  • 7 The Orbit of Mars
  • 8 A Word to the Perceptive Reader9 Newtonâ€?s Problem of a Cometâ€?s Path
  • SECTION 3 SUCCESSIVE APPROXIMATION
  • 1 First Application
  • 2 Extraction of Square Roots
  • SECTION 4 NEWTONâ€?S METHOD OF SUCCESSIVE APPROXIMATION
  • 1 The General Method of Newton
  • 2 Newtonâ€?s Formula
  • 3 â?ša
  • 4 3â?ša
  • 5 5â?ša
  • CHAPTER 2. From the History of Statics
  • SECTION 1 STEVINUS AND ARCHIMEDES
  • 1 Inclined Plane
  • 2 Lever
  • SECTION 2 VECTORS
  • 1 Inclined Plane
  • 2 Pulley
  • 3 Lever
  • 4 Archimedes' Application of his Law of the Lever
  • 5 (â€?) · (â€?) = (+)6 Von Mises' Flight Triangle
  • CHAPTER 3. From the History of Dynamics
  • SECTION 1 GALILEO
  • 1 Heavier Bodies Fall Faster?
  • 2 Not Why?, But How?
  • 3 How do Heavy Bodies Fall?
  • 4 Dynamics of the Inclined Plane
  • 5 Conservation of Energy
  • 6 Law of Inertia
  • 7 A Cannon Ball's Trajectory
  • SECTION 2 NEWTON
  • 1 Apples, Cannon Balls, and the Moon
  • 2 Never Smoke Without Fire
  • 3 That the Planets do Accelerate Towards the Sun
  • 4 What is the Law of Universal Gravitation?
  • 5 Uniform Circular Motion: Hamilton's Hodograph6 On Newton's Discovery of the Law of Universal Gravitation
  • 7 Scientific Attitude: Verification
  • 8 Hindsight and Foresight
  • SECTION 3 THE PENDULUM
  • 1 The Dimensions Test
  • 2 Simple Pendulum's Time of Swing
  • 3 Determination of g by Pendulum Experiment
  • 4 The Conical Pendulum
  • SECTION 4 ESCAPE VELOCITY
  • 1 Go-Around Velocity
  • 2 Apropos Go-Away Velocity
  • 3 The Force of Gravity
  • 4 That Kepler's Third Law is a Consequence of Newton's Law of Gravitation
  • 5 Planetary Mass
  • 6 Go-Away Velocity
  • 7 Ratio of Escape and Orbital VelocitiesCHAPTER 4. Physical Reasoning in Mathematics
  • CHAPTER 5. Differential Equations and Their Use in Science
  • SECTION 1 FIRST EXAMPLES
  • 1 Rotating Fluid
  • 2 Galileo: Free Fall
  • 3 Catenary
  • 4 Fall with Friction
  • SECTION 2 APPROXIMATE FORMULAE: POWER SERIES
  • Introduction
  • 1 Calculation of 3â?š28
  • 2 Fall with Friction Again
  • 3 How Deep is a Well?
  • 4 Pendulum: Small Oscillations
  • SECTION 3 PHYSICAL ANALOGY
  • SECTION 4 WHAT IS A DIFFERENTIAL EQUATION?
  • 1 Example
  • 2 Vector Fields

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