Learning and teaching mathematics using simulations :: plus 2000 examples from physics /
This is a unique, comprehensive and documented collection of simulations in mathematics and physics: More than 2000 simulations, offered on our webpage for comfortable use online. The book, written by an experienced teacher and practitioner, contains a complete introduction to mathematics and the do...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English German |
| Veröffentlicht: |
Berlin ; Boston :
De Gruyter,
©2011.
|
| Schriftenreihe: | De Gruyter textbook.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This is a unique, comprehensive and documented collection of simulations in mathematics and physics: More than 2000 simulations, offered on our webpage for comfortable use online. The book, written by an experienced teacher and practitioner, contains a complete introduction to mathematics and the documentation to the simulations. This is a great way to learn mathematics and physics. Suitable for courses in Mathematics for Engineering and Sciences. |
| Beschreibung: | 1 online resource (238 pages) |
| ISBN: | 9783110250077 3110250071 128339992X 9781283399920 |
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| 240 | 1 | 0 | |a Mathematik mit Simulationen lehren und lernen. |l English |
| 245 | 1 | 0 | |a Learning and teaching mathematics using simulations : |b plus 2000 examples from physics / |c Dieter Röss. |
| 260 | |a Berlin ; |a Boston : |b De Gruyter, |c ©2011. | ||
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| 520 | |a This is a unique, comprehensive and documented collection of simulations in mathematics and physics: More than 2000 simulations, offered on our webpage for comfortable use online. The book, written by an experienced teacher and practitioner, contains a complete introduction to mathematics and the documentation to the simulations. This is a great way to learn mathematics and physics. Suitable for courses in Mathematics for Engineering and Sciences. | ||
| 505 | 0 | |a Introduction; Goal and structure of the digital book; Directories; Usage and technical conventions; Example of a simulation: The Möbius band; Physics and mathematics; Mathematics as the ``Language of physics''; Physics and calculus; Numbers; Natural numbers; Whole numbers; Rational numbers; Irrational numbers; Algebraic numbers; Transcendental numbers; and the quadrature of the circle, according to Archimedes; Real numbers; Complex numbers; Representation as a pair of real numbers; Normal representation with the ``imaginary unit i''; Complex plane; Representation in polar coordinates. | |
| 505 | 8 | |a Simulation of complex addition and subtractionSimulation of complex multiplication and division; Extension of arithmetic; Sequences of numbers and series; Sequences and series; Sequence and series of the natural numbers; Geometric series; Limits; Fibonacci sequence; Complex sequences and series; Complex geometric sequence and series; Complex exponential sequence and exponential series; Influence of limited accuracy of measurements and nonlinearity; Numbers in mathematics and physics; Real sequence with nonlinear creation law: Logistic sequence. | |
| 505 | 8 | |a Complex sequence with nonlinear creation law: FractalsFunctions and their infinitesimal properties; Definition of functions; Difference quotient and differential quotient; Derivatives of a few fundamental functions; Powers and polynomials; Exponential function; Trigonometric functions; Rules for the differentiation of combined functions; Derivatives of further fundamental functions; Series expansion: the Taylor series; Coefficients of the Taylor series; Approximation formulas for simple functions; Derivation of formulas and errors bounds for numericaldifferentiation. | |
| 505 | 8 | |a Interactive visualization of Taylor expansionsGraphical presentation of functions; Functions of one to three variables; Functions of four variables: World line in the theory of relativity; General properties of functions y=f(x); Exotic functions; The limiting process for obtaining the differential quotient; Derivatives and differential equations; Phase space diagrams; Antiderivatives; Definition of the antiderivative via its differential equation; Definite integral and initial value; Integral as limit of a sum; The definition of the Riemann integral; Lebesgue integral. | |
| 505 | 8 | |a Rules for the analytical integrationNumerical integration methods; Error estimates for numerical integration; Series expansion (2): the Fourier series; Taylor series and Fourier series; Determination of the Fourier coefficients; Visualizing the calculation of coefficients and spectrum; Examples of Fourier expansions; Complex Fourier series; Numerical solution of equations and iterative methods; Visualization of functions in the space of real numbers; Standard functions y=f(x); Some functions y=f(x) that are important in physics; Standard functions of two variables z=f(x, y); Waves in space. | |
| 650 | 0 | |a Mathematics |x Study and teaching |x Simulation methods. | |
| 650 | 0 | |a Physics |x Study and teaching |x Simulation methods. | |
| 650 | 0 | |a Mathematics |v Textbooks. | |
| 650 | 0 | |a Physics |v Textbooks. | |
| 650 | 6 | |a Mathématiques |x Étude et enseignement |x Méthodes de simulation. | |
| 650 | 6 | |a Physique |x Étude et enseignement |x Méthodes de simulation. | |
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| 776 | 0 | 8 | |i Print version: |a Röss, Dieter. |t Learning and Teaching Mathematics using Simulations : Plus 2000 Examples from Physics. |d Berlin : Walter de Gruyter, ©2011 |z 9783110250053 |
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| contents | Introduction; Goal and structure of the digital book; Directories; Usage and technical conventions; Example of a simulation: The Möbius band; Physics and mathematics; Mathematics as the ``Language of physics''; Physics and calculus; Numbers; Natural numbers; Whole numbers; Rational numbers; Irrational numbers; Algebraic numbers; Transcendental numbers; and the quadrature of the circle, according to Archimedes; Real numbers; Complex numbers; Representation as a pair of real numbers; Normal representation with the ``imaginary unit i''; Complex plane; Representation in polar coordinates. Simulation of complex addition and subtractionSimulation of complex multiplication and division; Extension of arithmetic; Sequences of numbers and series; Sequences and series; Sequence and series of the natural numbers; Geometric series; Limits; Fibonacci sequence; Complex sequences and series; Complex geometric sequence and series; Complex exponential sequence and exponential series; Influence of limited accuracy of measurements and nonlinearity; Numbers in mathematics and physics; Real sequence with nonlinear creation law: Logistic sequence. Complex sequence with nonlinear creation law: FractalsFunctions and their infinitesimal properties; Definition of functions; Difference quotient and differential quotient; Derivatives of a few fundamental functions; Powers and polynomials; Exponential function; Trigonometric functions; Rules for the differentiation of combined functions; Derivatives of further fundamental functions; Series expansion: the Taylor series; Coefficients of the Taylor series; Approximation formulas for simple functions; Derivation of formulas and errors bounds for numericaldifferentiation. Interactive visualization of Taylor expansionsGraphical presentation of functions; Functions of one to three variables; Functions of four variables: World line in the theory of relativity; General properties of functions y=f(x); Exotic functions; The limiting process for obtaining the differential quotient; Derivatives and differential equations; Phase space diagrams; Antiderivatives; Definition of the antiderivative via its differential equation; Definite integral and initial value; Integral as limit of a sum; The definition of the Riemann integral; Lebesgue integral. Rules for the analytical integrationNumerical integration methods; Error estimates for numerical integration; Series expansion (2): the Fourier series; Taylor series and Fourier series; Determination of the Fourier coefficients; Visualizing the calculation of coefficients and spectrum; Examples of Fourier expansions; Complex Fourier series; Numerical solution of equations and iterative methods; Visualization of functions in the space of real numbers; Standard functions y=f(x); Some functions y=f(x) that are important in physics; Standard functions of two variables z=f(x, y); Waves in space. |
| ctrlnum | (OCoLC)775864413 |
| dewey-full | 510.71 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.71 |
| dewey-search | 510.71 |
| dewey-sort | 3510.71 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| genre | Textbooks fast |
| genre_facet | Textbooks |
| id | ZDB-4-EBA-ocn775864413 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:14Z |
| institution | BVB |
| isbn | 9783110250077 3110250071 128339992X 9781283399920 |
| language | English German |
| oclc_num | 775864413 |
| open_access_boolean | |
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| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (238 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | De Gruyter, |
| record_format | marc |
| series | De Gruyter textbook. |
| series2 | De Gruyter Textbook |
| spelling | Röss, Dieter, 1932- https://id.oclc.org/worldcat/entity/E39PBJhhqYVhcmhjfdT4DXVHmd http://id.loc.gov/authorities/names/n85801829 Mathematik mit Simulationen lehren und lernen. English Learning and teaching mathematics using simulations : plus 2000 examples from physics / Dieter Röss. Berlin ; Boston : De Gruyter, ©2011. 1 online resource (238 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter Textbook This is a unique, comprehensive and documented collection of simulations in mathematics and physics: More than 2000 simulations, offered on our webpage for comfortable use online. The book, written by an experienced teacher and practitioner, contains a complete introduction to mathematics and the documentation to the simulations. This is a great way to learn mathematics and physics. Suitable for courses in Mathematics for Engineering and Sciences. Introduction; Goal and structure of the digital book; Directories; Usage and technical conventions; Example of a simulation: The Möbius band; Physics and mathematics; Mathematics as the ``Language of physics''; Physics and calculus; Numbers; Natural numbers; Whole numbers; Rational numbers; Irrational numbers; Algebraic numbers; Transcendental numbers; and the quadrature of the circle, according to Archimedes; Real numbers; Complex numbers; Representation as a pair of real numbers; Normal representation with the ``imaginary unit i''; Complex plane; Representation in polar coordinates. Simulation of complex addition and subtractionSimulation of complex multiplication and division; Extension of arithmetic; Sequences of numbers and series; Sequences and series; Sequence and series of the natural numbers; Geometric series; Limits; Fibonacci sequence; Complex sequences and series; Complex geometric sequence and series; Complex exponential sequence and exponential series; Influence of limited accuracy of measurements and nonlinearity; Numbers in mathematics and physics; Real sequence with nonlinear creation law: Logistic sequence. Complex sequence with nonlinear creation law: FractalsFunctions and their infinitesimal properties; Definition of functions; Difference quotient and differential quotient; Derivatives of a few fundamental functions; Powers and polynomials; Exponential function; Trigonometric functions; Rules for the differentiation of combined functions; Derivatives of further fundamental functions; Series expansion: the Taylor series; Coefficients of the Taylor series; Approximation formulas for simple functions; Derivation of formulas and errors bounds for numericaldifferentiation. Interactive visualization of Taylor expansionsGraphical presentation of functions; Functions of one to three variables; Functions of four variables: World line in the theory of relativity; General properties of functions y=f(x); Exotic functions; The limiting process for obtaining the differential quotient; Derivatives and differential equations; Phase space diagrams; Antiderivatives; Definition of the antiderivative via its differential equation; Definite integral and initial value; Integral as limit of a sum; The definition of the Riemann integral; Lebesgue integral. Rules for the analytical integrationNumerical integration methods; Error estimates for numerical integration; Series expansion (2): the Fourier series; Taylor series and Fourier series; Determination of the Fourier coefficients; Visualizing the calculation of coefficients and spectrum; Examples of Fourier expansions; Complex Fourier series; Numerical solution of equations and iterative methods; Visualization of functions in the space of real numbers; Standard functions y=f(x); Some functions y=f(x) that are important in physics; Standard functions of two variables z=f(x, y); Waves in space. Mathematics Study and teaching Simulation methods. Physics Study and teaching Simulation methods. Mathematics Textbooks. Physics Textbooks. Mathématiques Étude et enseignement Méthodes de simulation. Physique Étude et enseignement Méthodes de simulation. MATHEMATICS Study & Teaching. bisacsh Mathematics fast Mathematics Study and teaching Simulation methods fast Physics fast Textbooks fast has work: Learning and teaching mathematics using simulations (Text) https://id.oclc.org/worldcat/entity/E39PCGqMKFcQYvK9DpBHcjQ3w3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Röss, Dieter. Learning and Teaching Mathematics using Simulations : Plus 2000 Examples from Physics. Berlin : Walter de Gruyter, ©2011 9783110250053 De Gruyter textbook. http://id.loc.gov/authorities/names/n94049545 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=420528 Volltext |
| spellingShingle | Röss, Dieter, 1932- Learning and teaching mathematics using simulations : plus 2000 examples from physics / De Gruyter textbook. Introduction; Goal and structure of the digital book; Directories; Usage and technical conventions; Example of a simulation: The Möbius band; Physics and mathematics; Mathematics as the ``Language of physics''; Physics and calculus; Numbers; Natural numbers; Whole numbers; Rational numbers; Irrational numbers; Algebraic numbers; Transcendental numbers; and the quadrature of the circle, according to Archimedes; Real numbers; Complex numbers; Representation as a pair of real numbers; Normal representation with the ``imaginary unit i''; Complex plane; Representation in polar coordinates. Simulation of complex addition and subtractionSimulation of complex multiplication and division; Extension of arithmetic; Sequences of numbers and series; Sequences and series; Sequence and series of the natural numbers; Geometric series; Limits; Fibonacci sequence; Complex sequences and series; Complex geometric sequence and series; Complex exponential sequence and exponential series; Influence of limited accuracy of measurements and nonlinearity; Numbers in mathematics and physics; Real sequence with nonlinear creation law: Logistic sequence. Complex sequence with nonlinear creation law: FractalsFunctions and their infinitesimal properties; Definition of functions; Difference quotient and differential quotient; Derivatives of a few fundamental functions; Powers and polynomials; Exponential function; Trigonometric functions; Rules for the differentiation of combined functions; Derivatives of further fundamental functions; Series expansion: the Taylor series; Coefficients of the Taylor series; Approximation formulas for simple functions; Derivation of formulas and errors bounds for numericaldifferentiation. Interactive visualization of Taylor expansionsGraphical presentation of functions; Functions of one to three variables; Functions of four variables: World line in the theory of relativity; General properties of functions y=f(x); Exotic functions; The limiting process for obtaining the differential quotient; Derivatives and differential equations; Phase space diagrams; Antiderivatives; Definition of the antiderivative via its differential equation; Definite integral and initial value; Integral as limit of a sum; The definition of the Riemann integral; Lebesgue integral. Rules for the analytical integrationNumerical integration methods; Error estimates for numerical integration; Series expansion (2): the Fourier series; Taylor series and Fourier series; Determination of the Fourier coefficients; Visualizing the calculation of coefficients and spectrum; Examples of Fourier expansions; Complex Fourier series; Numerical solution of equations and iterative methods; Visualization of functions in the space of real numbers; Standard functions y=f(x); Some functions y=f(x) that are important in physics; Standard functions of two variables z=f(x, y); Waves in space. Mathematics Study and teaching Simulation methods. Physics Study and teaching Simulation methods. Mathematics Textbooks. Physics Textbooks. Mathématiques Étude et enseignement Méthodes de simulation. Physique Étude et enseignement Méthodes de simulation. MATHEMATICS Study & Teaching. bisacsh Mathematics fast Mathematics Study and teaching Simulation methods fast Physics fast |
| title | Learning and teaching mathematics using simulations : plus 2000 examples from physics / |
| title_alt | Mathematik mit Simulationen lehren und lernen. |
| title_auth | Learning and teaching mathematics using simulations : plus 2000 examples from physics / |
| title_exact_search | Learning and teaching mathematics using simulations : plus 2000 examples from physics / |
| title_full | Learning and teaching mathematics using simulations : plus 2000 examples from physics / Dieter Röss. |
| title_fullStr | Learning and teaching mathematics using simulations : plus 2000 examples from physics / Dieter Röss. |
| title_full_unstemmed | Learning and teaching mathematics using simulations : plus 2000 examples from physics / Dieter Röss. |
| title_short | Learning and teaching mathematics using simulations : |
| title_sort | learning and teaching mathematics using simulations plus 2000 examples from physics |
| title_sub | plus 2000 examples from physics / |
| topic | Mathematics Study and teaching Simulation methods. Physics Study and teaching Simulation methods. Mathematics Textbooks. Physics Textbooks. Mathématiques Étude et enseignement Méthodes de simulation. Physique Étude et enseignement Méthodes de simulation. MATHEMATICS Study & Teaching. bisacsh Mathematics fast Mathematics Study and teaching Simulation methods fast Physics fast |
| topic_facet | Mathematics Study and teaching Simulation methods. Physics Study and teaching Simulation methods. Mathematics Textbooks. Physics Textbooks. Mathématiques Étude et enseignement Méthodes de simulation. Physique Étude et enseignement Méthodes de simulation. MATHEMATICS Study & Teaching. Mathematics Mathematics Study and teaching Simulation methods Physics Textbooks |
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