Introduction to Elementary Computational Modeling

List of Figures -- List of Tables -- Preface -- About the Author -- I Understanding Problem Solving -- 1 Understanding Word Problems -- 1.1 Introduction -- 1.2 Nouns and Verbs -- 1.3 Problem Decomposition -- 1.4 The Language of Computational Problems -- 1.4.1 Terms for Computed Values -- 1.4.2 Implied Phrases -- 1.4.3 Units of Measure -- 1.4.4 Conditions -- 1.4.5 Repetition -- 1.5 Objects -- 1.6 Problems with Many Numbers -- 1.6.1 Working with Patterns -- 1.7 Summary -- Key Terms -- Exercises -- 2 Problem Solving and Computing -- 2.1 Introduction -- 2.2 Programs -- 2.3 Data Definitions -- 2.3.1 Name of Data Items -- 2.3.2 Data Types -- 2.3.3 Data Declarations -- 2.4 Programming Languages -- 2.4.1 High-Level Programming Languages -- 2.4.2 Interpreters -- 2.4.3 Compilers -- 2.4.4 Compiling and Execution of Java Programs -- 2.4.5 Compiling and Executing C++ Programs -- 2.5 Interpretation of Commands with MATLAB and Octave . -- 2.6 Computer Problem Solving -- 2.7 Summary -- Key Terms -- Exercises -- 3 MATLAB and Octave Programming -- 3.1 Introduction -- 3.2 The MATLAB and Octave Prompt -- 3.3 Variables and Constants -- 3.4 Assignment Statements -- 3.5 Simple Mathematical Expressions -- 3.6 Scientific Notation -- 3.7 Built-In Mathematical Functions -- 3.8 Internal Documentation -- 3.9 Summary -- Key Terms -- Exercises -- II Computational Models -- 4 Introduction to Computational Models -- 4.1 Introduction -- 4.2 Preliminary Concepts -- 4.3 A Simple Problem: Temperature Conversion -- 4.3.1 Initial Problem Statement -- 4.3.2 Analysis and Conceptual Model -- 4.3.3 The Mathematical Model -- 4.4 Using MATLAB and Octave -- 4.4.1 Basic MATLAB and Octave Commands -- 4.4.2 The Computational Model -- 4.4.3 Using Data Lists with MATLAB and Octave -- 4.4.4 Implementation of Model with Data Lists -- 4.5 Summary -- Key Terms -- Exercises -- 5 Computational Models and Simulation -- 5.1 Introduction -- 5.2 Categories of Computational Models -- 5.3 Development of Computational Models -- 5.4 Simulation: Basic Concepts -- 5.4.1 Simulation Models -- 5.4.2 Simulation Results -- 5.5 Modular Decomposition -- 5.6 Average and Instantaneous Rate of Change -- 5.7 Area under a Curve -- 5.8 The Free-Falling Object -- 5.8.1 Initial Problem Statement -- 5.8.2 Analysis and Conceptual Model -- 5.8.2.1 Assumptions -- 5.8.2.2 Basic Definitions -- 5.8.3 The Mathematical Model -- 5.8.4 The Computational Model -- 5.8.4.1 Simple Implementation -- 5.8.4.2 Implementation with Arrays -- 5.8.4.3 Computing the Rates of Change -- 5.9 Summary -- Key Terms -- Exercises -- 6 Algorithms and Design Structures -- 6.1 Introduction -- 6.2 Problem Solving -- 6.3 Algorithms -- 6.4 Describing Data -- 6.5 Notations for Describing Algorithms -- 6.5.1 Flowcharts -- 6.5.2 Pseudo-Code -- 6.6 Algorithmic Structures -- 6.6.1 Sequence -- 6.6.2 Selection -- 6.6.3 Repetition -- 6.7 Implementation of Algorithms -- 6.7.1 Programming Languages -- 6.7.2 Assignment and Arithmetic Expressions -- 6.7.3 Simple Numeric Computations -- 6.7.4 Simple Input /Output -- 6.8 Computing Area and Circumference -- 6.8.1 Specification -- 6.8.2 Algorithm with the Mathematical Model -- 6.9 Summary -- Key Terms -- Exercises -- 7 Selection -- 7.1 Introduction -- 7.2 Selection Structure -- 7.2.1 General Concepts of the Selection Structure -- 7.2.2 Selection with Pseudo-Code -- 7.2.3 Selection with MATLAB and Octave -- 7.2.4 Conditional Expressions -- 7.2.5 Example with Selection -- 7.3 Complex Numbers with MATLAB and Octave -- 7.4 A Computational Model with Selection -- 7.4.1 Analysis and Mathematical Model -- 7.4.2 Algorithm for General Solution -- 7.4.3 Detailed Algorithm -- 7.5 Multilevel Selection -- 7.5.1 General Multipath Selection -- 7.5.2 The Case Structure -- 7.6 Complex Conditions -- 7.7 Summary -- Key Terms -- Exercises -- 8 Repetition -- 8.1 Introduction -- 8.2 Repetition with While Construct -- 8.2.1 While-Loop Flowchart -- 8.2.2 The While Structure in Pseudo-Code -- 8.2.3 While-Loop with MATLAB and Octave -- 8.2.4 Loop Counter -- 8.2.5 Accumulator Variables -- 8.2.6 Summation of Input Numbers -- 8.3 Repeat-Until Construct -- 8.4 For Loop Structure -- 8.4.1 The Summation Problem with a For Loop -- 8.4.2 The Factorial Problem -- 8.4.2.1 Mathematical Specification of Factorial . -- 8.4.2.2 Computing Factorial -- 8.5 Summary -- Key Terms -- Exercises -- 9 Data Lists -- 9.1 Introduction -- 9.2 Creating an Array -- 9.2.1 Creating Arrays in Pseudo-Code -- 9.2.2 Creating Arrays in MATLAB and Octave -- 9.3 Operations on Arrays -- 9.3.1 Array Elements in Pseudo-Code -- 9.3.2 Using Array Elements with MATLAB and Octave -- 9.3.3 Arithmetic Operations on Vectors -- 9.4 Multidimensional Arrays -- 9.4.1 Multidimensional Arrays with Pseudo-Code -- 9.4.2 Multidimensional Arrays with MATLAB and Octave -- 9.5 Applications Using Arrays -- 9.5.1 Problems with Simple Array Manipulation -- 9.5.1.1 The Average Value in an Array -- 9.5.1.2 Maximum Value in an Array -- 9.5.2 Searching -- 9.5.2.1 Linear Search -- 9.5.2.2 Binary Search -- 9.6 Average and Instantaneous Rate of Change -- 9.6.1 Average Rate of Change -- 9.6.2 Instantaneous Rate of Change -- 9.6.3 Computing the Rates of Change -- 9.7 Area under a Curve -- 9.8 Summary -- Key Terms -- Exercises -- 10 Modules -- 10.1 Introduction -- 10.2 Modular Design -- 10.3 MATLAB and Octave Script Files -- 10.4 Functions -- 10.4.1 Function Definition -- 10.4.2 Function Definition in MATLAB and Octave -- 10.4.3 Simple Function Calls -- 10.4.4 Functions with Parameters -- 10.4.5 Function Calls with Data -- 10.4.6 Functions with Return Data -- 10.5 Documenting MATLAB and Octave Functions -- 10.6 Summary -- Key Terms -- Exercises -- 11 Mathematical Models: Basic Concepts -- 11.1 Introduction -- 11.2 From the Real-World to the Abstract World -- 11.3 Discrete and Continuous Models -- 11.4 Difference Equations and Data Lists -- 11.5 Functional Equations -- 11.6 Validating a Model -- 11.7 Models with Arithmetic Growth -- 11.8 Using MATLAB and Octave to Implement the Model . . . -- 11.8.1 MATLAB and Octave Implementation -- 11.8.2 Producing the Charts of the Model -- 11.9 Summary -- Key Terms -- Exercises -- 12 Models with Quadratic Growth -- 12.1 Introduction -- 12.2 Quadratic Growth -- 12.3 Differences of the Data -- 12.4 Difference Equations -- 12.5 Functional Equations -- 12.6 Models with Quadratic Growth -- 12.6.1 Simple Quadratic Growth Models -- 12.6.2 Models with Sums of Arithmetic Growth -- 12.7 Solution and Graphs of Quadratic Equations -- 12.8 Summary -- Key Terms -- Exercises -- 13 Models with Polynomial Functions -- 13.1 Introduction -- 13.2 General Forms of Polynomial Functions -- 13.3 Evaluation and Graphs of Polynomial Functions -- 13.3.1 Evaluating Polynomial Functions -- 13.3.2 Generating Graphs of Polynomial Functions -- 13.4 Solution to Polynomial Equations -- 13.5 Summary -- Key Terms -- Exercises -- 14 Data Estimation and Empirical Modeling -- 14.1 Introduction -- 14.2 Interpolation -- 14.2.1 Linear Interpolation -- 14.2.2 Nonlinear Interpolation -- 14.3 Curve Fitting -- 14.4 Summary -- Key Terms -- Exercises -- 15 Models with Geometric Growth -- 15.1 Introduction -- 15.2 Basic Concepts of Geometric Growth -- 15.2.1 Geometric Growth with Increasing Data -- 15.2.2 Geometric Growth with Decreasing Data -- 15.2.3 Geometric Growth: Case Study 1 -- 15.2.4 Geometric Growth: Case Study 2 -- 15.3 Functional Equations in Geometric Growth -- 15.4 Properties of Exponential Functions -- 15.4.1 Exponentiation -- 15.4.2 Logarithms -- 15.5 Summary -- Key Terms -- Exercises -- 16 Vectors and Matrices -- 16.1 Introduction -- 16.2 Vectors -- 16.3 Simple Vector Operations -- 16.3.1 Arithmetic Operations -- 16.3.2 Applying Vector Functions -- 16.4 Matrices -- 16.4.1 Arithmetic Operations -- 16.4.2 Function Application -- 16.5 Array Indexing -- 16.6 Plotting Vectors -- 16.7 Summary -- Key Terms -- Exercises -- 17 Text Data -- 17.1 Introduction -- 17.2 String Vectors -- 17.2.1 String Operations -- 17.2.2 String Functions -- 17.3 String Matrices -- 17.4 Summary -- Key Terms -- Exercises -- 18 Advanced Data Structures -- 18.1 Introduction -- 18.2 Cell Arrays -- 18.3 Structures -- 18.4 Summary -- Key Terms -- Exercises -- Appendix A MATLAB and GNU Octave Software -- A.l Introduction -- A.2 The MATLAB Components -- A.3 The Desktop -- A.4 Starting MATLAB -- A.5 Exiting MATLAB -- A.6 The Command Window -- A.7 Current User Folder -- A.8 The Startup Folder -- A.9 Using Command Files (Scripts) -- A. 10 MATLAB Functions -- A. 11 GNU Octave -- Appendix B Computer Systems -- B.l Introduction -- B.2 Computer Systems -- B.2.1 Hardware Components -- B.2.1.1 Processors -- B.2.1.2 Main Memory -- B.2.1.3 Storage Devices -- B.2.1.4 Input Devices -- B.2.1.5 Output Devices -- B.2.1.6 Bus -- B.2.2 Computer Networks -- B.2.3 Software Components -- B.3 Operating Systems -- B.3.1 Operating System User Interfaces -- B.3.2 Contemporary Operating Systems -- B.3.2.1 Unix -- B.3.2.2 Microsoft Windows -- B.4 Summary -- Key Terms -- Bibliography -- Index.

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Mathematical Expression;Command Prompt;Understanding Problem Solving;NUM;Computational Models;Simple Mathematical Techniques;Advanced Data Structures;General Functional Equation;Data Estimation and Empirical Modeling;Script File;Algorithms and Design Structures;Cartesian Plane;Function Polyval;Command File;Computational Thinking;Functional Equations;Point P1;Quadratic Equation;Difference Equation;Polynomial Function;Arithmetic Growth;Selection Structure;Repetition Structure;Data Item;Enter Array;Row Vector;Basic MATLAB;Type Float;Intermediate Data Points;Follow