Author Shiffer, M. M
Title Role of Mathematics in Science
Imprint Washington : American Mathematical Society, 1965
©1984
book jacket
Descript 1 online resource (220 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Anneli Lax New Mathematical Library ; v.30
Anneli Lax New Mathematical Library
Note 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 Errors -- 2.3 Differential and/or Functional Equations -- 2.4 The Problem of Predicting Population Growth -- 2.5 Cusanus' Recursive Formula for π -- 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 Newton's Mechanistic Theory of Light -- 3.8 Fermat Versus Newton: Experimentum Crucis -- 3.9 To Recapitulate -- 3.10 The Role of Science in Mathematics -- 3.11 Some Practical Applications of Conics -- 3.12 Conical Ingenuity -- the Reflecting Telescope -- Chapter 4. Mathematics with Matrices-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 Trigonometry -- 4.11 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? Einstein's Transformation Problem -- 5.1 The Michelson-Morley Experiment -- 5.2 What Time Is It? -- 5.3 Einstein's Space-Time Transformation Problem -- 5.4 Einstein's Solution -- 5.5 Rods Contract and Clocks Slow Down -- Chapter 6. Relativistic Addition of Velocities -- 6.1 Einstein's Law of Relativistic Addition -- 6.2 Rescaling Velocities -- 6.3 Experimental Verification of Einstein'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 Φ( 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 -- 7.10 Relativity in More than One Space Dimension -- 7.11 Relativity and Electrodynamics -- Epilogue -- Index -- Back Cover
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Shiffer, M. M. Role of Mathematics in Science Washington : American Mathematical Society,c1965 9780883856307
Subject Exponential functions.;Mathematical analysis
Electronic books
Alt Author Bowden, Leon
Bowden, Leon