Programming for Computations Python : A Gentle Introduction to Numerical Simulations with Python

This work presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. It outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write s...

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Bibliographic Details
Main Authors: Linge, Svein, Langtangen, Hans Petter
Format: eBook Book
Language:English
Published: Cham Springer Nature 2016
Springer Open
Springer International Publishing AG
Springer
Edition:1
Series:Texts in Computational Science and Engineering
Subjects:
Business & Economics
Computers & Information Technology
Data processing Computer science
Economics, Finance, Business and Management
Industries
Industry and industrial studies
Information technology industries
Media, entertainment, information and communication industries
Numerical simulations
programming
Python
Python (Computer program language)
Textbook
ISBN:3319324284, 9783319324289, 9783319324272, 3319324276
Online Access:Get full text
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Table of Contents:
  • Intro -- Preface -- Contents -- List of Exercises -- 1 The First Few Steps -- 1.1 What Is a Program? And What Is Programming? -- 1.2 A Python Program with Variables -- 1.3 A Python Program with a Library Function -- 1.4 A Python Program with Vectorization and Plotting -- 1.5 More Basic Concepts -- 1.6 Exercises -- 2 Basic Constructions -- 2.1 If Tests, Colon and Indentation -- 2.2 Functions -- 2.3 For Loops -- 2.4 While Loops -- 2.5 Lists and Tuples - Alternatives to Arrays -- 2.6 Reading from and Writing to Files -- 2.7 Exercises -- 3 Computing Integrals -- 3.1 Basic Ideas of Numerical Integration -- 3.2 The Composite Trapezoidal Rule -- 3.3 The Composite Midpoint Method -- 3.4 Testing -- 3.5 Vectorization -- 3.6 Measuring Computational Speed -- 3.7 Double and Triple Integrals -- 3.8 Exercises -- 4 Solving Ordinary Differential Equations -- 4.1 Population Growth -- 4.2 Spreading of Diseases -- 4.3 Oscillating One-Dimensional Systems -- 4.4 Exercises -- 5 Solving Partial Differential Equations -- 5.1 Finite Difference Methods -- 5.2 Exercises -- 6 Solving Nonlinear Algebraic Equations -- 6.1 Brute Force Methods -- 6.2 Newton's Method -- 6.3 The Secant Method -- 6.4 The Bisection Method -- 6.5 Rate of Convergence -- 6.6 Solving Multiple Nonlinear Algebraic Equations -- 6.7 Exercises -- A Getting Access to Python -- A.1 Required Software -- A.2 Anaconda and Spyder -- A.3 How to Write and Run a Python Program -- A.4 The SageMathCloud and Wakari Web Services -- A.5 Writing IPython Notebooks -- References -- Index