Coverart for item
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)

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
Creator
Subject
Genre
Language
  • eng
  • ger
  • eng
Member of
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)
Instantiates
Publication
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)
Publication
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

Library Locations

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