The Role of Mathematics in Science /

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 argum...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Schiffer, M. M., Bowden, Leon
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2012.
Colección:Anneli Lax new mathematical library.
Temas:
Exponential functions.
Mathematical analysis.
Fonctions exponentielles.
Analyse mathématique.
Exponential functions
Mathematical analysis
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Front Cover
  • The Role of Mathematics in Science
  • Copyright Page
  • Contents
  • Preface
  • Introduction
  • Chapter 1. The Beginnings of Mechanics
  • 1.1 Archimedes' Law of the Lever
  • 1.2 First Application: The Centroid of a Triangle
  • 1.3 Second Application: The Area Under a Parabola
  • 1.4 Third Application: The Law of the Crooked Lever
  • 1.5 Galileo: The Law of the Inclined Plane
  • 1.6 Stevin: The Law of the Inclined Plane
  • 1.7 Insight and Outlook
  • Chapter 2. Growth Functions
  • 2.1 The Exponential Law of Growth
  • 2.2 Maxwell's Derivation of the Law of Errors2.3 Differential and/or Functional Equations
  • 2.4 The Problem of Predicting Population Growth
  • 2.5 Cusanus' Recursive Formula for Ï€
  • 2.6 Arithmetic and Geometric Means
  • Chapter 3. The Role of Mathematics in Optics
  • 3.1 Euclid's Optics
  • 3.2 Heron: The Shortest Path Principle
  • 3.3 Archimedes' Symmetry Proof
  • 3.4 Ptolemy and Refraction
  • 3.5 Kepler and Refraction
  • 3.6 Fermat: The Quickest Path Principle
  • 3.7 Newtonâ€?s Mechanistic Theory of Light
  • 3.8 Fermat Versus Newton: Experimentum Crucis
  • 3.9 To Recapitulate3.10 The Role of Science in Mathematics
  • 3.11 Some Practical Applications of Conics
  • 3.12 Conical Ingenuity; the Reflecting Telescope
  • Chapter 4. Mathematics with Matricesâ€?Transformations
  • 4.1 Why Use Matrices?
  • 4.2 Plane Analytic Geometry and Vector Addition
  • 4.3 The Dot Product
  • 4.4 To Relate Coordinate Geometry and Vector Algebra
  • 4.5 The Law of Cosines Revisited
  • 4.6 Linear Transformations of the Plane
  • 4.7 Rotations
  • 4.8 Composite Transformations and Inverses
  • 4.9 Composition and Matrix Multiplication
  • 4.10 Rotations and the Addition Formulas of Trigonometry4.11 Reflections
  • 4.12 Rigid Motions (Isometries)
  • 4.13 Orthogonal Matrices
  • 4.14 Coordinate Transformations
  • 4.15 A Matter of Notation
  • Chapter 5. What is Time? Einsteinâ€?s Transformation Problem
  • 5.1 The Michelson-Morley Experiment
  • 5.2 What Time Is It?
  • 5.3 Einsteinâ€?s Space-Time Transformation Problem
  • 5.4 Einsteinâ€?s Solution
  • 5.5 Rods Contract and Clocks Slow Down
  • Chapter 6. Relativistic Addition of Velocities
  • 6.1 Einsteinâ€?s Law of Relativistic Addition
  • 6.2 Rescaling Velocities6.3 Experimental Verification of Einsteinâ€?s Law
  • 6.4 Rescaled Velacities Revisited
  • Chapter 7. Energy
  • 7.1 The Two Body Impact Problem in Classical Mechanics
  • 7.2 The Two Body Impact Problem in the Theory of Relativity
  • 7.3 Admissible Energy Functions
  • 7.4 More About Admissible Energy Functions
  • 7.5 Proof that Î?(V) Is Admissible
  • 7.6 Energy and Momentum
  • 7.7 The Dependence of Mass on Velocity
  • 7.8 Energy and Matter
  • 7.9 The Lorentz Transformation and the Momentum-Energy Vector

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