Book Image

Scientific Computing with Python 3

By : Claus Führer, Jan Erik Solem, Olivier Verdier
Book Image

Scientific Computing with Python 3

By: Claus Führer, Jan Erik Solem, Olivier Verdier

Overview of this book

Python can be used for more than just general-purpose programming. It is a free, open source language and environment that has tremendous potential for use within the domain of scientific computing. This book presents Python in tight connection with mathematical applications and demonstrates how to use various concepts in Python for computing purposes, including examples with the latest version of Python 3. Python is an effective tool to use when coupling scientific computing and mathematics and this book will teach you how to use it for linear algebra, arrays, plotting, iterating, functions, polynomials, and much more.
Table of Contents (23 chapters)
Scientific Computing with Python 3
Credits
About the Authors
About the Reviewer
www.PacktPub.com
Acknowledgement
Preface
References

Exercises


Ex. 1 → Compute the value of the sum:

Ex. 2 → Create a generator that computes the sequence defined by the relation:

Ex. 3 → Generate all the even numbers.

Ex. 4 → Let . In calculus, it is shown that . Determine experimentally the smallest number n such that . Use a generator for this task.

Ex. 5 → Generate all prime numbers less than a given integer. Use the algorithm called Sieve of Eratosthenes.

Ex. 6 → Solving the differential equation  by applying the explicit Euler method results in the recursion:

Write a generator that computes the solution values un for a given initial value u0 and for a given value of the time step h.

Ex. 7 → Compute π using the formula:

The integral can be approximated using the composite trapezoidal rule, that is, by this formula:

where .

Program a generator for the values yi = f(xi) and evaluate the formula by summing one term after the other. Compare your results with the quad function of SciPy.

Ex. 8 → Let x = [1, 2, 3] and y = [-1, -2, -3...