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IPython Interactive Computing and Visualization Cookbook

IPython Interactive Computing and Visualization Cookbook

By : Cyrille Rossant
4.4 (7)
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IPython Interactive Computing and Visualization Cookbook

IPython Interactive Computing and Visualization Cookbook

4.4 (7)
By: Cyrille Rossant

Overview of this book

Python is one of the leading open source platforms for data science and numerical computing. IPython and the associated Jupyter Notebook offer efficient interfaces to Python for data analysis and interactive visualization, and they constitute an ideal gateway to the platform. IPython Interactive Computing and Visualization Cookbook, Second Edition contains many ready-to-use, focused recipes for high-performance scientific computing and data analysis, from the latest IPython/Jupyter features to the most advanced tricks, to help you write better and faster code. You will apply these state-of-the-art methods to various real-world examples, illustrating topics in applied mathematics, scientific modeling, and machine learning. The first part of the book covers programming techniques: code quality and reproducibility, code optimization, high-performance computing through just-in-time compilation, parallel computing, and graphics card programming. The second part tackles data science, statistics, machine learning, signal and image processing, dynamical systems, and pure and applied mathematics.
Table of Contents (17 chapters)
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16
Index

Simulating an ordinary differential equation with SciPy

Ordinary Differential Equations (ODEs) describe the evolution of a system subject to internal and external dynamics. Specifically, an ODE links a quantity depending on a single independent variable (time, for example) to its derivatives. In addition, the system can be under the influence of external factors. A first-order ODE can typically be written as:

Simulating an ordinary differential equation with SciPy

More generally, an Simulating an ordinary differential equation with SciPy-th order ODE involves successive derivatives of Simulating an ordinary differential equation with SciPy until the order Simulating an ordinary differential equation with SciPy. The ODE is said to be linear or nonlinear depending on whether Simulating an ordinary differential equation with SciPy is linear in Simulating an ordinary differential equation with SciPy or not.

ODEs naturally appear when the rate of change of a quantity depends on its value. Therefore, ODEs are found in many scientific disciplines such as mechanics (evolution of a body subject to dynamic forces), chemistry (concentration of reacting products), biology (spread of an epidemic), ecology (growth of a population), economics, and finance, among others.

Whereas simple ODEs can be solved analytically, many ODEs...

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