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Mathematical methods in science [[electronic resource] /] / by George Polya; edited by Leon Bowden
| Mathematical methods in science [[electronic resource] /] / by George Polya; edited by Leon Bowden |
| Autore | Polya George |
| Pubbl/distr/stampa | Washington, DC, : Mathematical Association of America, 1977 |
| Descrizione fisica | 1 online resource (247 p.) |
| Disciplina | 530 |
| Altri autori (Persone) | BowdenLeon |
| Collana | Anneli Lax New Mathematical Library |
| Soggetto topico |
Mathematics
Science - Mathematics |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-88385-941-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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""
""5 (�) · (�) = (+)""""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 Hodograph""""6 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"" ""3 Direction Fields"" |
| Record Nr. | UNINA-9910465747703321 |
Polya George
|
||
| Washington, DC, : Mathematical Association of America, 1977 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematical methods in science / / by George Polya; edited by Leon Bowden
| Mathematical methods in science / / by George Polya; edited by Leon Bowden |
| Autore | Polya George |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Washington, DC, : Mathematical Association of America, 1977 |
| Descrizione fisica | 1 online resource (xi, 234 pages) : digital, PDF file(s) |
| Disciplina | 530.1/5 |
| Altri autori (Persone) | BowdenLeon |
| Collana | Anneli Lax New Mathematical Library |
| Soggetto topico |
Mathematics
Science - Mathematics |
| ISBN | 0-88385-941-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. From the history of astronomy: measurement and successive approximation. -- Measurement ; Astronomical measurements ; Successive approximation ; Newton's method of successive approximation -- 2. From the history of statics. -- Stevinus and Archimedes ; Vectors -- 3. From the history of dynamics. -- Galileo ; Newton ; The pendulum ; Escape velocity -- 4. Physical reasoning in mathematics. -- 5. Differential equations and their use in science. -- First examples ; Approximate formulae: power series ; Physical analogy ; What is a differential equation? |
| Record Nr. | UNINA-9910809573803321 |
|
Polya George
|
||
| Washington, DC, : Mathematical Association of America, 1977 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematical methods in science / / by George Pólya ; edited by Leon Bowden [[electronic resource]]
| Mathematical methods in science / / by George Pólya ; edited by Leon Bowden [[electronic resource]] |
| Autore | Pólya George <1887-1985, > |
| Pubbl/distr/stampa | Washington : , : Mathematical Association of America, , 1977 |
| Descrizione fisica | 1 online resource (xi, 234 pages) : digital, PDF file(s) |
| Disciplina | 530.1/5 |
| Collana | Anneli Lax New Mathematical Library |
| Soggetto topico |
Mathematics
Science - Mathematics |
| ISBN | 0-88385-941-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. From the history of astronomy: measurement and successive approximation. -- Measurement ; Astronomical measurements ; Successive approximation ; Newton's method of successive approximation -- 2. From the history of statics. -- Stevinus and Archimedes ; Vectors -- 3. From the history of dynamics. -- Galileo ; Newton ; The pendulum ; Escape velocity -- 4. Physical reasoning in mathematics. -- 5. Differential equations and their use in science. -- First examples ; Approximate formulae: power series ; Physical analogy ; What is a differential equation? |
| Record Nr. | UNINA-9910791741103321 |
|
Pólya George <1887-1985, >
|
||
| Washington : , : Mathematical Association of America, , 1977 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The role of mathematics in science [[electronic resource] /] / by M.M. Schiffer and Leon Bowden
| The role of mathematics in science [[electronic resource] /] / by M.M. Schiffer and Leon Bowden |
| Autore | Schiffer Menahem |
| Pubbl/distr/stampa | Washington, DC, : Mathematical Association of America, 1984 |
| Descrizione fisica | 1 online resource (220 p.) |
| Disciplina | 501 |
| Altri autori (Persone) | BowdenLeon |
| Collana | Anneli Lax New Mathematical Library |
| Soggetto topico |
Exponential functions
Mathematical analysis |
| Soggetto genere / forma | Electronic books. |
| ISBN | 0-88385-945-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""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 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 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 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 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? 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 Velocities""""6.3 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"" ""7.10 Relativity in More than One Space Dimension"" |
| Record Nr. | UNINA-9910461903503321 |
|
Schiffer Menahem
|
||
| Washington, DC, : Mathematical Association of America, 1984 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The role of mathematics in science / / by M.M. Schiffer and Leon Bowden [[electronic resource]]
| The role of mathematics in science / / by M.M. Schiffer and Leon Bowden [[electronic resource]] |
| Autore | Schiffer Menahem |
| Pubbl/distr/stampa | Washington : , : Mathematical Association of America, , 1984 |
| Descrizione fisica | 1 online resource (xi, 207 pages) : digital, PDF file(s) |
| Disciplina | 501.51 |
| Collana | Anneli Lax New Mathematical Library |
| Soggetto topico |
Mathematical physics
Mathematics Science |
| ISBN | 0-88385-945-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
The beginnings of mechanics: Archimedes' law of the lever ; First application: the centroid of a triangle ; Second application: the area under a parabola ; Third application: the law of the crooked lever ; Galileo: the law of the inclined plane ; Stevin: the law of the inclined plane ; Insight and outlook -- Growth functions: The exponential law of growth ; Maxwell's derivation of the law of errors ; Differential and / or functional equations ; The problem of predicting population growth ; Cusanus' recursive formula for [pi] ; Arithmetic and geometric means -- The role of mathematics in optics: Euclid's optics ; Heron: the shortest path principle ; Archimedes' symmetry proof ; Ptolemy and refraction ; Kepler and refraction ; Fermat: the quickest path principle ; Newton's mechanistic theory of light ; Fermat versus Newton: experimentum crucis ; To recapitulate ; The role of science in mathematics ; Some practical applications of conics ; Conical ingenuity: the reflecting telescope.
Mathematics with matrices-transformations: Why use matrices? ; Plane analytic geometry and vector addition ; The dot product ; To relate coordinate geometry and vector algebra ; The law of cosines revisited ; Linear transformations of the plane ; Rotations ; Composite transformations and inverses ; Composition and matrix multiplication ; Rotations and the addition formulas of trigonometry ; Reflections ; Rigid motions (isometries) ; Orthogonal matrices ; Coordinate transformations ; A matter of notation -- What is time? Einstein's transformation problem: The Michelson-Morley experiment ; What time is it? ; Einstein's space-time transformation problem ; Einstein's solution ; Rods contract and clocks slow down -- Relativistic addition of velocities: Einstein's law of relativistic addition ; Rescaling velocities ; Experimental verification of Einstein's law ; Rescaled velocities revisited -- Energy: The two body impact problem in classical mechanics ; The two body impact problem in the theory of relativity ; Admissible energy functions ; More about admissible energy functions ; Proof that V is admissible ; Energy and momentum ; The dependence of mass on velocity ; Energy and matter ; The Lorentz transformation and the momentum-energy vector ; Relativity in more than one space dimension ; Relativity and electrodynamics. |
| Record Nr. | UNINA-9910790363403321 |
|
Schiffer Menahem
|
||
| Washington : , : Mathematical Association of America, , 1984 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The role of mathematics in science / / by M.M. Schiffer and Leon Bowden
| The role of mathematics in science / / by M.M. Schiffer and Leon Bowden |
| Autore | Schiffer Menahem |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Washington, DC, : Mathematical Association of America, 1984 |
| Descrizione fisica | 1 online resource (xi, 207 pages) : digital, PDF file(s) |
| Disciplina | 501.51 |
| Altri autori (Persone) | BowdenLeon |
| Collana | Anneli Lax New Mathematical Library |
| Soggetto topico |
Exponential functions
Mathematical analysis |
| ISBN | 0-88385-945-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
The beginnings of mechanics: Archimedes' law of the lever ; First application: the centroid of a triangle ; Second application: the area under a parabola ; Third application: the law of the crooked lever ; Galileo: the law of the inclined plane ; Stevin: the law of the inclined plane ; Insight and outlook -- Growth functions: The exponential law of growth ; Maxwell's derivation of the law of errors ; Differential and / or functional equations ; The problem of predicting population growth ; Cusanus' recursive formula for [pi] ; Arithmetic and geometric means -- The role of mathematics in optics: Euclid's optics ; Heron: the shortest path principle ; Archimedes' symmetry proof ; Ptolemy and refraction ; Kepler and refraction ; Fermat: the quickest path principle ; Newton's mechanistic theory of light ; Fermat versus Newton: experimentum crucis ; To recapitulate ; The role of science in mathematics ; Some practical applications of conics ; Conical ingenuity: the reflecting telescope.
Mathematics with matrices-transformations: Why use matrices? ; Plane analytic geometry and vector addition ; The dot product ; To relate coordinate geometry and vector algebra ; The law of cosines revisited ; Linear transformations of the plane ; Rotations ; Composite transformations and inverses ; Composition and matrix multiplication ; Rotations and the addition formulas of trigonometry ; Reflections ; Rigid motions (isometries) ; Orthogonal matrices ; Coordinate transformations ; A matter of notation -- What is time? Einstein's transformation problem: The Michelson-Morley experiment ; What time is it? ; Einstein's space-time transformation problem ; Einstein's solution ; Rods contract and clocks slow down -- Relativistic addition of velocities: Einstein's law of relativistic addition ; Rescaling velocities ; Experimental verification of Einstein's law ; Rescaled velocities revisited -- Energy: The two body impact problem in classical mechanics ; The two body impact problem in the theory of relativity ; Admissible energy functions ; More about admissible energy functions ; Proof that V is admissible ; Energy and momentum ; The dependence of mass on velocity ; Energy and matter ; The Lorentz transformation and the momentum-energy vector ; Relativity in more than one space dimension ; Relativity and electrodynamics. |
| Record Nr. | UNINA-9910828719903321 |
|
Schiffer Menahem
|
||
| Washington, DC, : Mathematical Association of America, 1984 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||