Introduction to elementary computational modeling

With an emphasis on problem solving, this book introduces the basic principles and fundamental concepts of computational modeling. It emphasizes reasoning and conceptualizing problems, the elementary mathematical modeling, and the implementation using computing concepts and principles. Examples are included that demonstrate the computation and visualization of the implemented models.

The author provides case studies, along with an overview of computational models and their development. The first part of the text presents the basic concepts of models and techniques for designing and implementing problem solutions. It applies standard pseudo-code constructs and flowcharts for designing models. The second part covers model implementation with basic programming constructs using MATLAB^®, Octave, and FreeMat.

Aimed at beginning students in computer science, mathematics, statistics, and engineering, Introduction to Elementary Computational Modeling: Essential Concepts, Principles, and Problem Solving focuses on fundamentals, helping the next generation of scientists and engineers hone their problem solving skills.

Each chapter includes a Summary, Key Terms, and Exercises

Understanding Problem Solving
Understanding Word Problems
Introduction
Nouns and Verbs
Problem Decomposition
The Language of Computational Problems
Objects
Problems with Many Numbers

Problem Solving and Computing
Introduction
Programs
Data Definitions
Programming Languages
Interpretation of Commands with MATLABR and Octave
Computer Problem Solving

MATLAB R and Octave Programming
Introduction
The MATLAB and Octave Prompt
Variables and Constants
Assignment statements
Simple Mathematical Expressions
Scientific Notation
Built-in Mathematical Functions
Internal Documentation

Computational Models
Introduction To Computational Models
Introduction
Preliminary Concepts
A Simple Problem: Temperature Conversion
Using MATLAB and Octave

Computational Models and Simulation
Introduction
Categories of Computational Models
Development of Computational Models
Simulation: Basic Concepts
Modular Decomposition
Average and Instantaneous Rate of Change
Area under a Curve
The Free-Falling Object

Algorithms and Design Structures
Introduction
Problem Solving
Algorithms
Describing Data
Notations for Describing Algorithms
Algorithmic Structures
Implementation of Algorithms
Computing Area and Circumference

Selection
Introduction
Selection Structure
Complex Numbers with MATLAB and Octave
A Computational Model with Selection
Multilevel Selection
Complex Conditions

Repetition
Introduction
Repetition with While Construct
Repeat-Until Construct
For Loop Structure

Data Lists
Introduction
Creating An Array
Operations on Arrays
Multidimensional Arrays
Applications Using Arrays
Average and Instantaneous Rate of Change
Area Under a Curve

Modules
Introduction
Modular Design
MATLAB and Octave Script Files
Functions
Documenting MATLAB and Octave Functions

Mathematical Models: Basic Concepts
Introduction
From the Real-World to the Abstract World
Discrete and Continuous Models
Difference Equations and Data Lists
Functional Equations
Validating a Model
Models with Arithmetic Growth
Using MATLAB and Octave to Implement the Model
Producing the Charts of the Model

Models with Quadratic Growth
Introduction
Quadratic Growth
Differences of the Data
Difference Equations
Functional Equations
Models with Quadratic Growth
Solution and Graphs of Quadratic Equations

Models with Polynomial Functions
Introduction
General Forms of Polynomial Functions
Evaluation and Graphs of Polynomial Functions
Solution to Polynomial Equations

Data Estimation and Empirical Modeling
Introduction
Interpolation
Curve Fitting

Models with Geometric Growth
Introduction
Basic Concepts of Geometric Growth
Functional Equations in Geometric Growth
Properties of Exponential Functions

Vectors and Matrices
Introduction
Vectors
Simple Vector Operations
Matrices
Array Indexing
Plotting Vectors

Text Data
Introduction
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