Problem Solving and Computing
Introduction
Computer Problem Solving
Elementary Concepts
Developing Computational Models
A Simple Problem: Temperature Conversion
Categories of Computational Models
Computing the Area and Circumference of a Circle
General Process of Software Development
Programming Languages
Programs
Introduction
Programs
Data Definitions
Structure of a C Program
Instructions
Simple Functions
A Simple C Program
A Simple Problem: Temperature Conversion
Modular Decomposition: Functions
Introduction
Modular Decomposition
Defining Functions
Calling Functions
Classification of Functions
Numerical Types
Built-in Mathematical Functions
More Concepts of Computational Models
Introduction
Introduction to Errors in Computing
Average and Instantaneous Rate of Change
The Free-Falling Object
Simulation: Basic Concepts
Algorithms and Programs
Introduction
Problem Solving
Algorithms
Algorithm Description
Design Structures
Implementing Algorithms
Computing Area and Circumference
Selection
Introduction
Selection Structure
A Computational Model with Selection
Multi-Level Selection
Complex Conditions
Repetition
Introduction
Repetition with the While Loop
Repeat-Until Loop
For Loop Structure
Arrays
Introduction
Declaring an Array
Operations on Arrays
Arrays as Arguments
A Simple Application with Arrays
Arithmetic Operations with Vectors
Multi-Dimensional Arrays
Applications Using Arrays
Pointers
Introduction
Pointer Fundamentals
Pointers with C
Dereferencing
Converting Pointer Types
Reference Parameters
Pointers with Value NULL
Arrays as Pointers
Complex Data Structures
Defining Type Names
Enumerated Types
Linked Lists
Introduction
Nodes and Linked List
Linked List with Two Ends
Double-Linked Lists
Higher-Level Data Structures
Text Data
Introduction
C Strings
String Input and Output
String Operations
Using the String Functions
Computational Models with Arithmetic Growth
Introduction
Mathematical Modeling
Models with Arithmetic Growth
Using the C Programming Language
Producing the Charts of the Model
Validation of a Model
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
Computational Models with Polynomials
Introduction
General Forms of Polynomial Functions
GNU Scientific Library
Evaluation of Polynomial Functions
Solving Polynomial Equations
Models with Interpolation and Curve Fitting
Introduction
Interpolation
Curve Fitting
Using Vectors with the GSL
Introduction
Vectors and Operations
Vector Properties and Characteristics
Implementation of Vectors in C and the GSL
Simple Vector Operations
Matrices and Sets of Linear Equations
Introduction
Matrices
Simple Matrix Operations
Solving Systems of Linear Equations
Introduction to Dynamical Systems
Introduction
Continuous and Discrete Models
Derivative of a Function
Numerical Integration
Differential Equations
Dynamical Systems and Models
Formulating Simple Examples
Solution of Differential Equations
Linear Optimization Modeling
Introduction
Formulation of Problems
Solving Linear Optimization Problems
Introduction
General Form
Foundations of the Algorithm
The Simplex Algorithm
Software Implementations
Sensitivity Analysis and Duality
Introduction
Sensitivity Analysis
Duality
Transportation Models
Introduction
Model of a Transportation Problem
Transportation Case Studies
Transshipment Models
Assignment Problems
Network Models
Introduction
Graphs
Shortest Path Problem
Shortest Path Problem: Case Study 1
Maximum Flow Problems
Critical Path Method
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
Appendix A: GNU C Compiler Tool
Appendix B: Introduction to Linux
A Summary and Exercises appear at the end of each chapter.
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