Sale!

Difference Equations Theory Applications and Advanced Topics 3rd Edition by Ronald E Mickens ISBN 148223078X 9781482230789

Original price was: $50.00.Current price is: $35.00.

Difference Equations Theory Applications and Advanced Topics 3rd Edition Ronald E. Mickens Digital Instant Download

Author(s): Ronald E. Mickens
ISBN(s): 9781482230789, 148223078X
Edition: 3
File Details: PDF, 2.72 MB
Year: 2015
Language: english
SKU: EB-5066498 Category: Tag:

Difference Equations Theory Applications and Advanced Topics 3rd Edition by Ronald E Mickens – Ebook PDF Instant Download/Delivery: 148223078X, 9781482230789
Full download Difference Equations Theory Applications and Advanced Topics 3rd Edition after payment

Product details:

ISBN 10: 148223078X 
ISBN 13: 9781482230789
Author: Ronald E Mickens

Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of difference equations. Along with adding several advanced topics, this edition continues to cover general, linear, first-, second-, and n-th order difference equations; nonlinear equations that may be reduced to linear equations; and partial difference equations.

New to the Third Edition

  • New chapter on special topics, including discrete Cauchy–Euler equations; gamma, beta, and digamma functions; Lambert W-function; Euler polynomials; functional equations; and exact discretizations of differential equations
  • New chapter on the application of difference equations to complex problems arising in the mathematical modeling of phenomena in engineering and the natural and social sciences
  • Additional problems in all chapters
  • Expanded bibliography to include recently published texts related to the subject of difference equations

Suitable for self-study or as the main text for courses on difference equations, this book helps readers understand the fundamental concepts and procedures of difference equations. It uses an informal presentation style, avoiding the minutia of detailed proofs and formal explanations.

Difference Equations Theory Applications and Advanced Topics 3rd Table of contents:

  • Introduction to Difference Equations

    • 1.1 Definition and Basic Concepts

    • 1.2 Types of Difference Equations

    • 1.3 The Role of Difference Equations in Mathematical Modeling

    • 1.4 Historical Development and Applications

    • 1.5 How to Use This Book

  • Basic Theory of Linear Difference Equations

    • 2.1 First-Order Linear Difference Equations

    • 2.2 Second-Order Linear Difference Equations

    • 2.3 Higher-Order Linear Difference Equations

    • 2.4 Homogeneous vs Non-Homogeneous Equations

    • 2.5 Solution Techniques: Iteration, Generating Functions, and Series

    • 2.6 Initial Conditions and Existence Theorems

  • Methods of Solving Difference Equations

    • 3.1 Separation of Variables

    • 3.2 The Z-Transform and Its Applications

    • 3.3 The Characteristic Equation Method

    • 3.4 Solving Non-Homogeneous Difference Equations

    • 3.5 Matrix Methods and Eigenvalue Solutions

    • 3.6 Numerical Solutions and Computational Methods

  • Stability Analysis of Difference Equations

    • 4.1 Stability and Convergence in Difference Equations

    • 4.2 Linear Stability Theory

    • 4.3 Lyapunov’s Direct Method for Stability

    • 4.4 Global vs Local Stability

    • 4.5 Asymptotic Behavior and Bounded Solutions

    • 4.6 Stability Criteria for Nonlinear Systems

  • Nonlinear Difference Equations

    • 5.1 Introduction to Nonlinear Difference Equations

    • 5.2 Methods for Analyzing Nonlinear Equations

    • 5.3 Fixed Points and Their Stability

    • 5.4 Bifurcations and Chaos in Nonlinear Systems

    • 5.5 Numerical Methods for Nonlinear Difference Equations

    • 5.6 Applications in Population Dynamics and Epidemiology

  • Applications of Difference Equations in Discrete Dynamical Systems

    • 6.1 Discrete Dynamical Systems and Their Properties

    • 6.2 Periodicity, Fixed Points, and Cycles

    • 6.3 The Logistic Equation and Population Growth Models

    • 6.4 Modeling Predator-Prey Dynamics with Difference Equations

    • 6.5 Epidemic Modeling and the Spread of Infectious Diseases

    • 6.6 Applications in Economics and Finance

  • Difference Equations in Control Theory

    • 7.1 Introduction to Control Theory

    • 7.2 Discrete-Time Control Systems

    • 7.3 Stability Analysis in Discrete-Time Control Systems

    • 7.4 State-Space Representation of Discrete Systems

    • 7.5 Optimal Control and Dynamic Programming

    • 7.6 Applications in Robotics and Process Control

  • Advanced Topics in Difference Equations

    • 8.1 Difference Equations with Delays (Functional Differential Equations)

    • 8.2 Nonlinear Difference Equations and Chaos Theory

    • 8.3 Fractional Difference Equations

    • 8.4 Boundedness and Asymptotic Behavior of Solutions

    • 8.5 Difference Equations on Networks and Graphs

    • 8.6 Stochastic Difference Equations and Random Walks

  • Computational Techniques and Algorithms

    • 9.1 Numerical Solution Methods for Difference Equations

    • 9.2 Fixed-Point Iteration and Convergence

    • 9.3 The Runge-Kutta Method for Discrete Equations

    • 9.4 Discrete Fourier Transform and Its Applications

    • 9.5 Software Tools and Programming for Difference Equations

    • 9.6 Computational Challenges in High-Dimensional Systems

  • Applications in Engineering and Science

    • 10.1 Difference Equations in Signal Processing

    • 10.2 Modeling Electrical Circuits and Networks

    • 10.3 Applications in Mechanical Systems and Vibrations

    • 10.4 Heat Transfer and Fluid Dynamics in Discrete Systems

    • 10.5 Applications in Environmental Systems Modeling

    • 10.6 Difference Equations in Neuroscience and Biology

  • Theoretical Developments and Recent Advances

    • 11.1 Theoretical Results in Linear Difference Equations

    • 11.2 Advances in Nonlinear Difference Equation Theory

    • 11.3 Functional Equations and Their Connections to Difference Equations

    • 11.4 Recent Developments in Stability and Chaos Theory

    • 11.5 Emerging Trends in Research and Applications

  • Case Studies and Practical Examples

    • 12.1 Case Study: Modeling Epidemics with Difference Equations

    • 12.2 Case Study: Financial Modeling Using Discrete Time Models

    • 12.3 Case Study: Discrete Models in Ecology and Conservation

    • 12.4 Case Study: Engineering Applications in Systems and Controls

    • 12.5 Case Study: Using Difference Equations in Machine Learning Models

People also search for Difference Equations Theory Applications and Advanced Topics 3rd:

difference equations theory applications and advanced topics pdf

difference equations theory applications and advanced topics

applications of advanced mathematics

applied mathematics for advanced level

advanced studies in theoretical and applied econometrics

Tags: Ronald E Mickens, Difference Equations, Advanced Topics