The Resource Learning and teaching mathematics using simulations : plus 2000 examples from physics, Dieter Röss, (electronic resource)
Learning and teaching mathematics using simulations : plus 2000 examples from physics, Dieter Röss, (electronic resource)
Resource Information
The item Learning and teaching mathematics using simulations : plus 2000 examples from physics, Dieter Röss, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Massey University Library, University of New Zealand.This item is available to borrow from 1 library branch.
Resource Information
The item Learning and teaching mathematics using simulations : plus 2000 examples from physics, Dieter Röss, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Massey University Library, University of New Zealand.
This item is available to borrow from 1 library branch.
 Language

 eng
 ger
 eng
 Extent
 1 online resource (238 pages)
 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
 Isbn
 9783110250077
 Label
 Learning and teaching mathematics using simulations : plus 2000 examples from physics
 Title
 Learning and teaching mathematics using simulations
 Title remainder
 plus 2000 examples from physics
 Statement of responsibility
 Dieter Röss
 Language

 eng
 ger
 eng
 Cataloging source
 DLC
 http://library.link/vocab/creatorDate
 1932
 http://library.link/vocab/creatorName
 Röss, Dieter
 Illustrations
 illustrations
 Index
 no index present
 Literary form
 non fiction
 Series statement
 De Gruyter textbook
 http://library.link/vocab/subjectName

 Mathematics
 Physics
 Mathematics
 Physics
 Label
 Learning and teaching mathematics using simulations : plus 2000 examples from physics, Dieter Röss, (electronic resource)
 Antecedent source
 unknown
 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
 Control code
 ocn775864413
 Dimensions
 unknown
 Extent
 1 online resource (238 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783110250077
 Level of compression
 unknown
 Note
 eBooks on EBSCOhost
 Quality assurance targets
 unknown
 Reformatting quality
 unknown
 Specific material designation
 remote
 System control number
 (OCoLC)775864413
 Label
 Learning and teaching mathematics using simulations : plus 2000 examples from physics, Dieter Röss, (electronic resource)
 Antecedent source
 unknown
 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
 Control code
 ocn775864413
 Dimensions
 unknown
 Extent
 1 online resource (238 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783110250077
 Level of compression
 unknown
 Note
 eBooks on EBSCOhost
 Quality assurance targets
 unknown
 Reformatting quality
 unknown
 Specific material designation
 remote
 System control number
 (OCoLC)775864413
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