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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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Washington, D.C. :
Mathematical Association of America,
©1984.
|
| Schriftenreihe: | New mathematical library ;
v. 30. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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 arguments. The book should appeal to college students and general readers with some background in mathematics. The authors state that, 'If we succeed in giving an impression of the beauty and power of mathematical reasoning in science, the purpose of our work will have been achieved.' This book includes the laws of levers and inclined planes, the laws of exponential versus limited population growth, ray optics, and relativity. |
| Beschreibung: | 1 online resource (xi, 207 pages) : illustrations |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9780883859452 0883859459 |
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| 490 | 1 | |a New mathematical library ; |v v. 30 | |
| 504 | |a Includes bibliographical references and index. | ||
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| 505 | 0 | |a 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. | |
| 505 | 0 | |a 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. | |
| 520 | |a 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 arguments. The book should appeal to college students and general readers with some background in mathematics. The authors state that, 'If we succeed in giving an impression of the beauty and power of mathematical reasoning in science, the purpose of our work will have been achieved.' This book includes the laws of levers and inclined planes, the laws of exponential versus limited population growth, ray optics, and relativity. | ||
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| 538 | |a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn762969534 |
|---|---|
| _version_ | 1816881777363386369 |
| adam_text | |
| any_adam_object | |
| author | Schiffer, Menahem |
| author2 | Bowden, Leon |
| author2_role | |
| author2_variant | l b lb |
| author_GND | http://id.loc.gov/authorities/names/nr95012463 http://id.loc.gov/authorities/names/n77012445 |
| author_facet | Schiffer, Menahem Bowden, Leon |
| author_role | |
| author_sort | Schiffer, Menahem |
| author_variant | m s ms |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | Q172 |
| callnumber-raw | Q172.5.M3 S3 1984 |
| callnumber-search | Q172.5.M3 S3 1984 |
| callnumber-sort | Q 3172.5 M3 S3 41984 |
| callnumber-subject | Q - General Science |
| classification_rvk | SG 700 |
| classification_tum | MAT 005f |
| collection | ZDB-4-EBA |
| contents | 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. |
| ctrlnum | (OCoLC)762969534 |
| dewey-full | 501.51 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 501 - Philosophy and theory |
| dewey-raw | 501.51 |
| dewey-search | 501.51 |
| dewey-sort | 3501.51 |
| dewey-tens | 500 - Natural sciences and mathematics |
| discipline | Allgemeine Naturwissenschaft Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn762969534 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:06Z |
| institution | BVB |
| isbn | 9780883859452 0883859459 |
| language | English |
| oclc_num | 762969534 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xi, 207 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Mathematical Association of America, |
| record_format | marc |
| series | New mathematical library ; |
| series2 | New mathematical library ; |
| spelling | Schiffer, Menahem. http://id.loc.gov/authorities/names/nr95012463 The role of mathematics in science / by M.M. Schiffer and Leon Bowden. Washington, D.C. : Mathematical Association of America, ©1984. 1 online resource (xi, 207 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier New mathematical library ; v. 30 Includes bibliographical references and index. Print version record. 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. 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 arguments. The book should appeal to college students and general readers with some background in mathematics. The authors state that, 'If we succeed in giving an impression of the beauty and power of mathematical reasoning in science, the purpose of our work will have been achieved.' This book includes the laws of levers and inclined planes, the laws of exponential versus limited population growth, ray optics, and relativity. Use copy Restrictions unspecified star MiAaHDL Electronic reproduction. [Place of publication not identified]: HathiTrust Digital Library. 2023. MiAaHDL Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL digitized 2023. HathiTrust Digital Library committed to preserve pda MiAaHDL Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Mathematics. http://id.loc.gov/authorities/subjects/sh85082139 Science. http://id.loc.gov/authorities/subjects/sh85118553 Mathematics https://id.nlm.nih.gov/mesh/D008433 Science https://id.nlm.nih.gov/mesh/D012586 Physique mathématique. Mathématiques. Sciences. mathematics. aat applied mathematics. aat sciences (philosophy) aat science (modern discipline) aat 31.81 mathematical physiscs. (NL-LeOCL)081545460 bcl SCIENCE Philosophy & Social Aspects. bisacsh MATHEMATICS General. bisacsh Mathematical physics fast Mathematics fast Science fast Geschichte gnd Naturwissenschaften gnd Mathematik gnd Physik gnd http://d-nb.info/gnd/4045956-1 Mathematische fysica. gtt Mathematics. nli Mathématiques. ram Physique mathématique. ram Science Mathematics Bowden, Leon. http://id.loc.gov/authorities/names/n77012445 Print version: Schiffer, M.M. Role of mathematics in science. Washington, D.C. : Mathematical Association of America, ©1984 9780883856307 (DLC) 84060251 (OCoLC)11049727 New mathematical library ; v. 30. http://id.loc.gov/authorities/names/n42017890 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=452153 Volltext |
| spellingShingle | Schiffer, Menahem The role of mathematics in science / New mathematical library ; 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. Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Mathematics. http://id.loc.gov/authorities/subjects/sh85082139 Science. http://id.loc.gov/authorities/subjects/sh85118553 Mathematics https://id.nlm.nih.gov/mesh/D008433 Science https://id.nlm.nih.gov/mesh/D012586 Physique mathématique. Mathématiques. Sciences. mathematics. aat applied mathematics. aat sciences (philosophy) aat science (modern discipline) aat 31.81 mathematical physiscs. (NL-LeOCL)081545460 bcl SCIENCE Philosophy & Social Aspects. bisacsh MATHEMATICS General. bisacsh Mathematical physics fast Mathematics fast Science fast Geschichte gnd Naturwissenschaften gnd Mathematik gnd Physik gnd http://d-nb.info/gnd/4045956-1 Mathematische fysica. gtt Mathematics. nli Mathématiques. ram Physique mathématique. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082129 http://id.loc.gov/authorities/subjects/sh85082139 http://id.loc.gov/authorities/subjects/sh85118553 https://id.nlm.nih.gov/mesh/D008433 https://id.nlm.nih.gov/mesh/D012586 (NL-LeOCL)081545460 http://d-nb.info/gnd/4045956-1 |
| title | The role of mathematics in science / |
| title_auth | The role of mathematics in science / |
| title_exact_search | The role of mathematics in science / |
| title_full | The role of mathematics in science / by M.M. Schiffer and Leon Bowden. |
| title_fullStr | The role of mathematics in science / by M.M. Schiffer and Leon Bowden. |
| title_full_unstemmed | The role of mathematics in science / by M.M. Schiffer and Leon Bowden. |
| title_short | The role of mathematics in science / |
| title_sort | role of mathematics in science |
| topic | Mathematical physics. http://id.loc.gov/authorities/subjects/sh85082129 Mathematics. http://id.loc.gov/authorities/subjects/sh85082139 Science. http://id.loc.gov/authorities/subjects/sh85118553 Mathematics https://id.nlm.nih.gov/mesh/D008433 Science https://id.nlm.nih.gov/mesh/D012586 Physique mathématique. Mathématiques. Sciences. mathematics. aat applied mathematics. aat sciences (philosophy) aat science (modern discipline) aat 31.81 mathematical physiscs. (NL-LeOCL)081545460 bcl SCIENCE Philosophy & Social Aspects. bisacsh MATHEMATICS General. bisacsh Mathematical physics fast Mathematics fast Science fast Geschichte gnd Naturwissenschaften gnd Mathematik gnd Physik gnd http://d-nb.info/gnd/4045956-1 Mathematische fysica. gtt Mathematics. nli Mathématiques. ram Physique mathématique. ram |
| topic_facet | Mathematical physics. Mathematics. Science. Mathematics Science Physique mathématique. Mathématiques. Sciences. mathematics. applied mathematics. sciences (philosophy) science (modern discipline) 31.81 mathematical physiscs. SCIENCE Philosophy & Social Aspects. MATHEMATICS General. Mathematical physics Geschichte Naturwissenschaften Mathematik Physik Mathematische fysica. |
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