Introduction to Computational Models with Python

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 Python Programs Introduction Programming with the Python Programming Language Data Definitions Structure of a Python Program Instructions Simple Functions A Simple Python Program A Simple Problem: Temperature Conversion Modular Decomposition in Python Introduction: Functions, Classes, and Modules Modular Decomposition Defining Functions Calling Functions Defining and using Python modules Numerical Types Built-in Mathematical Functions Algorithms and Python Programs Introduction Problem Solving Algorithms Algorithm Description Python Design Structures Implementing Algorithms Computing Area and Circumference 5. Selection Introduction Selection Structure with Python A Computational Model with Selection Multi-Level Selection Complex Conditions Repetition Introduction Repetition with the While Loop in Python Repeat-Until Loop For Loop Structure Python Lists Introduction Operations on Lists Using Python lists as arrays A Simple Application with Arrays Arithmetic Operations with Vectors Multi-Dimensional Arrays Applications Using Arrays Linked Lists Introduction basic data structures in Python Nodes and Linked List Linked List with Two Ends Double-Linked Lists Higher-Level Data Structures Strings or Text Data Introduction Python Strings String Input and Output String Operations Using the String Functions Python for Scientific Computing Introduction to NumPy, SciPy, and matplotlib libraries for numerical computing used in science and engineering Implementing Computational Models in Python More Concepts of Computational Models Introduction to Errors in Computing Using NumPy arrays and functions Average and Instantaneous Rate of Change The Free-Falling Object Simulation: Basic Concepts Using Numpy and matplotlib Introduction to Errors in Computing Average and Instantaneous Rate of Change The Free-Falling Object Simulation: Basic Concepts Computational Models with Arithmetic Growth Introduction Mathematical Modeling Models with Arithmetic Growth Using the Python Programming Language with NumPy and matplotlib Producing the plots for visualization of data in 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 Using the polynomial module in NumPy Evaluation of Polynomial Functions Solving Polynomial Equations Models with Interpolation and Curve Fitting Using the Polynomial Module in NumPy Interpolation Curve Fitting Using Vectors with the Python NumPY Module Introduction Vectors and Operations Vector Properties and Characteristics Implementation of Vectors in Python Simple Vector Operations Matrices and Sets of Linear Equations Matrices with the NumPy and Scipy modules Simple Matrix Operations Solving Systems of Linear Equations Introduction to Dynamical Systems Introduction to the NumPy and Scipy Modules 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 to the Python PyGLPK (Python Gnu Linear Programming Kit) Formulation of Problems Solving Linear Optimization Problems General Form Foundations of the Algorithm The Simplex Algorithm Using PyGLPK Sensitivity Analysis and Duality Sensitivity Analysis Duality Transportation Models Model of a Transportation Problem Transportation Case Studies Transshipment Models Assignment Problems Network Models 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: Scipy, Numpy, and matplotlib Python Libraries Appendix B: Introduction to Linux Appendix C: Installing Python and Libraries on Linux Ubuntu Appendix D: Installing Python and Libraries on Windows