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Contents:

  • Quick start
  • Installation guide
  • Documentation
  • Theory
    • The algebra of truncated polynomials
    • Elementary functions
    • Inverse functions
    • Practical Examples (to be done by hand)
    • Taylor models

Basic Python Tutorials:

  • The very basics
  • Understanding gduals and floats
  • Using vectorized doubles

Advanced Python Tutorials:

  • Differential Intelligence
  • Training Artificial Neural Networks
  • High Order Taylor Maps I
  • High Order Taylor Maps II
  • Map (series) inversion

Taylor Model Tutorials:

  • Taylor models of univariate functions
  • Taylor models of multivariate functions
  • Exploration of Volterra ODE system
  • Exploration of Kepler dynamics with a Neural network
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  • Theory
  • View page source

Theory

Contents:

  • The algebra of truncated polynomials
    • Formal definition
  • Elementary functions
    • Exponential
    • Logarithm
    • Sine and cosine
    • Exponentiation
  • Inverse functions
    • Inverse hyperbolic tangent
    • Inverse tangent
    • The other inverse functions
  • Practical Examples (to be done by hand)
    • Example 1 - A multiplication
    • Example 2 - A division
    • Example 3 - An exponential
  • Taylor models
    • Taylor’s theorem
    • Formal definition
    • Arithmetic
    • References
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© Copyright 2018, Dario Izzo and Francesco Biscani.

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