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polya g mathematical methods science 2ed 1998

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Textbook in PDF format 'Mathematics, taught and learned appropriately, improves the mind and implants good habits of thought.' This tenet underlies all of Professor Polya's works on teaching and problem-solving. This book captures some of Pуlya's excitement and vision. In it he provides enlightenment for all those who have ever wondered how the laws of nature were worked out mathematically. The distinctive feature of the present book is the stress on the history of certain elementary chapters of science; these can be a source of enjoyment and deeper understanding of mathematics even for beginners who have little, or perhaps no, knowledge of physics. Introduction From the History of Astronomy: Measurement and Successive Approximation Measurement The Tunnel Measuring: Triangulating How Far Away is the Moon? Why Teach Triangulation? Astronomical measurements Aristarchus of Samos Radius of Earth: Eratosthenes Rival Cosmologies The Orbit of Venus Tycho Brahe and Kepler The Mars year The Orbit of Mars A Word to the Perceptive Reader Newton’s Problem of a Comet’s Path Successive approximation First Application Extraction of SquareRoots Newton’s method of successive approximation The General Method of Newton √a ∛a 5√a From the History of Statics Stevinus and Archimedes Inclined Plane Lever Vectors Inclined Plane Pulley Lever Archimedes' Application of his Law of the Lever ( - ) * ( - ) = ( + ) Von Mises. Flight Triangle From the History of Dynamics Galileo Heavier Bodies Fall Faster? Not "Why?", But "How?" How do Heavy Bodies Fall? Dynamics of the Inclined Plane Conservation of Energy Law of Inertia A Cannon Ball's Trajectory Newton Apples, Cannon Balls, and the Moon Never Smoke Without Fire That the Planets do Accelerate Towards the Sun What is the Law of Universal Gravitation? Uniform Circular Motion: Hamilton's Hodograph On Newton's Discovery of the Law of Universal Gravitation Scientific Attitude: Verification Hindsight and Foresight The Pendulum The Dimensions Test Simple Pendulum's Time of Swing Determination of g by Pendulum Experiment The Conical Pendulum Escape velocity Go-Around Velocity Apropos Go-Away Velocity The Force of Gravity That Kepler's Third Law is a Newton's Law of Gravitation Consequence Planetary Mass Go-Away Velocity Ratio of Escape and Orbital Velocities Physical Reasoning in Mathematics Differential Equations and Their Use in Science First examples Rotating Fluid Galileo: Free Fall Catenary Fall with Friction Approximate formulae: Power series Introduction Calculation of ∛28 Fall with Friction Again How Deep is a Well? Pendulum: Small Oscillations Physical analogy What is a differential equation? Example Vector Fields Direction Fields

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Polya G. Mathematical Methods in Science 2ed 1998.pdf 7.6 MB

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polya g mathematical methods science 2ed 1998

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