Introduction to Differential Equations Deterministic Modeling, Methods and Analysis

ISBN-10: 9814368903
ISBN-13: 9789814368902
Edition: 2012
List price: $85.00
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Description: This title is proactive in preparing for the modelling of dynamic processes in various disciplines. It introduces an innovative and unifed method of solving nonlinear scalar differential equations, known as the energy/lyapunov function method.

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Book details

List price: $85.00
Copyright year: 2012
Publisher: World Scientific Publishing Co Pte Ltd
Publication date: 5/31/2012
Binding: Paperback
Pages: 544
Size: 6.75" wide x 9.75" long x 1.25" tall
Weight: 1.980
Language: English

This title is proactive in preparing for the modelling of dynamic processes in various disciplines. It introduces an innovative and unifed method of solving nonlinear scalar differential equations, known as the energy/lyapunov function method.

Preface
Elements of Matrices, Determinants, and Calculus
Introduction
Problem-Solving Process
Problem analysis
Solutions (proof) strategies
Algebra of Matrices
Determinants
Matrix Calculus
Notes and Comments
First-Order Differential Equations
Introduction
Mathematical Modeling
Integrable Equations
General problem
Procedure for finding a general solution
Initial value problem
Procedure for solving the IVP
Linear Homogeneous Equations
General problem
Procedure for finding a general solution
Initial value problem
Procedure for solving the IVP
Linear Nonhomogeneous Equations
General problem
Procedure for finding a general solution
Initial value problem
Procedure for solving the IVP
Fundamental Conceptual Algorithms and Analysis
Notes and Comments
First-Order Nonlinear Differential Equations
Introduction
Mathematical Modeling
Energy Function Method
General problem
Procedure for finding a general solution representation
Integrable Reduced Equations
General problem
Procedure for finding a general solution representation
Linear Nonhomogeneous Reduced Equations
General problem
Procedures for finding a general solution representation
Variable Separable Equations
General problem
Procedure for finding a general solution
Homogeneous Equations
General problem
Procedure for finding a general solution
Bernoulli Equations
General problem
Procedure for finding a general solution
Essentially Time-Invariant Equations
General problem
Procedure for finding a general solution
Notes and Comments
First-Order Systems of Linear Differential Equations
Introduction
Mathematical Modeling
Linear Homogeneous Systems
General problem
Procedure for finding a general solution
Initial value problem
Procedure for the solving IVP
Procedure for Finding the Fundamental Matrix Solution
General Linear Homogeneous Systems
General problem
Procedure for finding a general solution
Initial value problem
Procedure for solving the IVP
Linear Nonhomogeneous Systems
General problem
Procedure for finding a general solution
Initial value problem
Procedure for solving the IVP
Fundamental Conceptual Algorithm Analysis
Notes and Comments
Higher-Order Linear Differential Equations
Introduction
Mathematical Modeling
Linear Homogeneous Equations
General problem
Procedure for finding a general solution
Initial value problem
Procedure for solving the IVP
Companion System
Higher-Order Linear Nonhomogeneous Equations
The Laplace Transform
Applications of the Laplace Transform
Notes and Comments
Topics in Differential Equations
Introduction
Fundamental Conceptual Algorithms and Analysis
Method of Variation of Parameters
Generalized Method of Variation of Parameters
Differential Inequalities and Comparison Theorems
Energy/Lyapunov Function and Comparison Theorems
Variational Comparison Method
Linear Hybrid Systems
General problem
Linear Hereditary Systems
General problem
Qualitative Properties of the Solution Process
Linear Stochastic Systems
Notes and Comments
Bibliography
Index

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