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Scientific Computing with Python

Scientific Computing with Python

By : Führer, Claus Fuhrer, Solem, Verdier
4.5 (15)
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Scientific Computing with Python

Scientific Computing with Python

4.5 (15)
By: Führer, Claus Fuhrer, Solem, Verdier

Overview of this book

Python has tremendous potential within the scientific computing domain. This updated edition of Scientific Computing with Python features new chapters on graphical user interfaces, efficient data processing, and parallel computing to help you perform mathematical and scientific computing efficiently using Python. This book will help you to explore new Python syntax features and create different models using scientific computing principles. The book presents Python alongside mathematical applications and demonstrates how to apply Python concepts in computing with the help of examples involving Python 3.8. You'll use pandas for basic data analysis to understand the modern needs of scientific computing, and cover data module improvements and built-in features. You'll also explore numerical computation modules such as NumPy and SciPy, which enable fast access to highly efficient numerical algorithms. By learning to use the plotting module Matplotlib, you will be able to represent your computational results in talks and publications. A special chapter is devoted to SymPy, a tool for bridging symbolic and numerical computations. By the end of this Python book, you'll have gained a solid understanding of task automation and how to implement and test mathematical algorithms within the realm of scientific computing.
Table of Contents (23 chapters)
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About Packt
22
References

7.1 Functions in mathematics and functions in Python

In mathematics, a function is written as a map that uniquely assigns to every element from the domain a corresponding element from the range .

This is expressed by .

Alternatively, when considering particular elements and , you write .

Here, is called the name of the function and is its value when applied to . Here, is sometimes called the argument of . Let's first look at an example before considering functions in Python.

For example, and . This function maps two real numbers to their difference.

In mathematics, functions can have numbers, vectors, matrices, and even other functions as arguments. Here is an example of a function with mixed arguments:

In this case, a real number is returned. When working with functions, we have to distinguish between two different steps:

  • The definition of the function
  • The evaluation of the function, that is, the computation of for a given value of

The first step is done once, while...

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