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Scientific Computing with Python

You're reading from   Scientific Computing with Python High-performance scientific computing with NumPy, SciPy, and pandas

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Product type Paperback
Published in Jul 2021
Publisher Packt
ISBN-13 9781838822323
Length 392 pages
Edition 2nd Edition
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Authors (4):
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Olivier Verdier Olivier Verdier
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Olivier Verdier
Jan Erik Solem Jan Erik Solem
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Jan Erik Solem
Claus Führer Claus Führer
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Claus Führer
Claus Fuhrer Claus Fuhrer
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Claus Fuhrer
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Table of Contents (23) Chapters Close

Preface 1. Getting Started 2. Variables and Basic Types FREE CHAPTER 3. Container Types 4. Linear Algebra - Arrays 5. Advanced Array Concepts 6. Plotting 7. Functions 8. Classes 9. Iterating 10. Series and Dataframes - Working with Pandas 11. Communication by a Graphical User Interface 12. Error and Exception Handling 13. Namespaces, Scopes, and Modules 14. Input and Output 15. Testing 16. Symbolic Computations - SymPy 17. Interacting with the Operating System 18. Python for Parallel Computing 19. Comprehensive Examples 20. About Packt 21. Other Books You May Enjoy 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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