Garrido Introduction to Computational Models with Python

1. Auflage 2015
ISBN: 978-1-4987-1204-0
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 496 Seiten

Reihe: Chapman & Hall/CRC Computational Science

Introduction to Computational Models with Python explains how to implement computational models using the flexible and easy-to-use Python programming language. The book uses the Python programming language interpreter and several packages from the huge Python Library that improve the performance of numerical computing, such as the Numpy and Scipy modules. The Python source code and data files are available on the author’s website.

The book’s five sections present:

- An overview of problem solving and simple Python programs, introducing the basic models and techniques for designing and implementing problem solutions, independent of software and hardware tools

- Programming principles with the Python programming language, covering basic programming concepts, data definitions, programming structures with flowcharts and pseudo-code, solving problems, and algorithms

- Python lists, arrays, basic data structures, object orientation, linked lists, recursion, and running programs under Linux

- Implementation of computational models with Python using Numpy, with examples and case studies

- The modeling of linear optimization problems, from problem formulation to implementation of computational models

This book introduces the principles of computational modeling as well as the approaches of multi- and interdisciplinary computing to beginners in the field. It provides the foundation for more advanced studies in scientific computing, including parallel computing using MPI, grid computing, and other methods and techniques used in high-performance computing.

Autoren/Hrsg.

Garrido, Jose M.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik EDV | Informatik EDV & Informatik Allgemein

Inhaltsverzeichnis

Problem Solving
Problem Solving and Computing
INTRODUCTION
COMPUTER PROBLEM SOLVING
ELEMENTARY CONCEPTS
DEVELOPING COMPUTATIONAL MODELS
TEMPERATURE CONVERSION
AREA AND PERIMETER OF A CIRCLE
CATEGORIES OF COMPUTATIONAL MODELS
GENERAL PROCESS OF SOFTWARE DEVELOPMENT
MODULAR DESIGN
PROGRAMMING LANGUAGES
PRECISION, ACCURACY, AND ERRORS

Simple Python Programs
INTRODUCTION
COMPUTING WITH PYTHON
PROGRAMS
DATA DEFINITIONS
SIMPLE PYTHON PROGRAMS
A SIMPLE PROBLEM: TEMPERATURE CONVERSION
DISTANCE BETWEEN TWO POINTS
GENERAL STRUCTURE OF A PYTHON PROGRAM
SIMPLE FUNCTIONS

Basic Programming Principles with Python
Modules and Functions
INTRODUCTION
MODULAR DECOMPOSITION
FUNCTIONS
CATEGORIES OF FUNCTIONS
BUILT-IN MATHEMATICAL FUNCTIONS

Program Structures
INTRODUCTION
ALGORITHMS
IMPLEMENTING ALGORITHMS
ALGORITHM DESCRIPTION
DESIGN STRUCTURES
COMPUTING AREA AND CIRCUMFERENCE

The Selection Program Structure
INTRODUCTION
CONDITIONAL EXPRESSIONS
THE SELECTION STRUCTURE
A COMPUTATIONAL MODEL WITH SELECTION
MULTI-LEVEL SELECTION

The Repetition Program Structure
INTRODUCTION
REPETITION WITH THE WHILE-LOOP
REPEAT-UNTIL LOOP
FOR-LOOP STRUCTURE

Data Structures, Object Orientation, and Recursion
Python Lists, Strings, and Other Data Sequences
INTRODUCTION
LISTS
TEMPERATURE CONVERSION PROBLEM
LIST COMPREHENSIONS
LISTS OF LISTS
TUPLES
DICTIONARIES
STRINGS
SIMPLE NUMERICAL APPLICATIONS USING LISTS

Object Orientation
INTRODUCTION
OBJECTS IN THE PROBLEM DOMAIN
DEFINING CLASSES
DESCRIBING OBJECTS
INTERACTION BETWEEN TWO OBJECTS
DESIGN WITH CLASSES

Object-Oriented Programs
INTRODUCTION
PROGRAMS
DEFINITION OF CLASSES
CLASS DEFINITIONS IN PYTHON
CREATING AND MANIPULATING OBJECTS
COMPLETE PROGRAM WITH A CLASS
SCOPE OF VARIABLES
CLASS HIERARCHY WITH INHERITANCE
DEFINING CLASSES WITH INHERITANCE
OVERLOADING AND OVERRIDING METHODS

Linked Lists
INTRODUCTION
NODES AND LINKED LISTS
LINKED LISTS WITH TWO ENDS
DOUBLE-LINKED LISTS
STACKS AND QUEUES DATA STRUCTURES

Recursion
INTRODUCTION
RECURSIVE APPROACH TO PROBLEM SOLVING
RECURSIVE DEFINITION OF FUNCTIONS
ANALYZING RECURSION

Fundamental Computational Models with Python
Computational Models with Arithmetic Growth
INTRODUCTION
MATHEMATICAL MODELING
MODELS WITH ARITHMETIC GROWTH
USING THE PYTHON LANGUAGE AND NUMPY
PRODUCING THE CHARTS OF THE MODEL
VALIDATION OF A MODEL
FILE I/O

Computational Models with Quadratic Growth
INTRODUCTION
DIFFERENCES OF THE DATA
DIFFERENCE EQUATIONS
FUNCTIONAL EQUATIONS
EXAMPLES OF QUADRATIC MODELS

Models with Geometric Growth
INTRODUCTION
BASIC CONCEPTS
FUNCTIONAL EQUATIONS IN GEOMETRIC GROWTH

Computational Models with Polynomial Growth
INTRODUCTION
GENERAL FORMS OF POLYNOMIAL FUNCTIONS
THE polynomial MODULE OF THE numpy PACKAGE
EVALUATION OF POLYNOMIAL FUNCTIONS
SOLVING POLYNOMIAL FUNCTIONS

Empirical Models with Interpolation and Curve Fitting
INTRODUCTION
INTERPOLATION
CURVE FITTING
MODELING THE HEAT CAPACITY OF CARBON DIOXIDE

Using Arrays with Numpy
INTRODUCTION
VECTORS AND OPERATIONS
VECTOR PROPERTIES AND CHARACTERISTICS
USING ARRAYS IN PYTHON WITH NUMPY
SIMPLE VECTOR OPERATIONS

Models with Matrices and Linear Equations
INTRODUCTION
MATRICES
MATRIX MANIPULATION WITH NUMPY
SOLVING SYSTEMS OF LINEAR EQUATIONS
INDUSTRIAL MIXTURES IN MANUFACTURING

Introduction to Models of Dynamical Systems
INTRODUCTION
AVERAGE AND INSTANTANEOUS RATE OF CHANGE
THE FREE-FALLING OBJECT
DERIVATIVE OF A FUNCTION
NUMERICAL INTEGRATION
WORK PRODUCED IN A PISTON WITH AN IDEAL GAS
DIFFERENTIAL EQUATIONS
MODELS OF DYNAMICAL SYSTEMS
FORMULATING SIMPLE EXAMPLES
SOLUTION OF DIFFERENTIAL EQUATIONS

Linear Optimization Models
Linear Optimization Modeling
INTRODUCTION
GENERAL FORM OF A LINEAR OPTIMIZATION MODEL
THE SIMPLEX ALGORITHM
DESCRIPTION OF THE SIMPLEX ALGORITHM
FORMULATION OF LINEAR OPTIMIZATION MODELS
EXAMPLE PROBLEMS

Solving Linear Optimization Models
INTRODUCTION
LINEAR OPTIMIZATION MODELS WITH PYTHON
MODELING WITH PYOMO
MODELING WITH PULP
SOFTWARE LINEAR OPTIMIZATION SOLVERS
SHORT LIST OF OPTIMIZATION SOLVERS

Sensitivity Analysis and Duality
INTRODUCTION
SENSITIVITY ANALYSIS
DUALITY

Transportation Models
INTRODUCTION
MODEL OF A TRANSPORTATION PROBLEM
TRANSPORTATION CASE STUDY 1
UNBALANCED PROBLEM: CASE STUDY 2
UNBALANCED PROBLEM: CASE STUDY 3
TRANSSHIPMENT MODELS
TRANSSHIPMENT PROBLEM: CASE STUDY 4
ASSIGNMENT PROBLEMS 7
ASSIGNMENT PROBLEM: CASE STUDY 5

Network Models
INTRODUCTION
GRAPHS
SHORTEST PATH PROBLEM
SHORTEST PATH: CASE STUDY 1
MAXIMUM FLOW PROBLEMS
CRITICAL PATH METHOD
REDUCING THE TIME TO COMPLETE A PROJECT

Integer Linear Optimization Models
INTRODUCTION
MODELING WITH INTEGER VARIABLES
APPLICATIONS OF INTEGER LINEAR OPTIMIZATION
INTEGER LINEAR OPTIMIZATION: CASE STUDY 1
INTEGER LINEAR OPTIMIZATION: CASE STUDY 2

A Summary and Exercises appear at the end of each chapter.

Über Autor(innen)

José M. Garrido is a professor in the Department of Computer Science at Kennesaw State University. Dr. Garrido is the author of several books and numerous research papers. His research interests include software development, operating systems, computational modeling, object-oriented simulation, and system formal specification.