(EBOOK PDF)Functional methods in differential equations 1st Edition by Veli Matti Hokkanen 1584882832 9781584882831 full chapters

Functional methods in differential equations 1st Edition by Veli Matti Hokkanen – Ebook PDF Instant Download/Delivery: 1584882832, 9781584882831

Full download Functional methods in differential equations 1st Edition after payment

Product details:

• ISBN 10:1584882832 

• ISBN 13:9781584882831

• Author:Veli Matti Hokkanen 

 In recent years, functional methods have become central to the study of theoretical and applied mathematical problems. As demonstrated in this Research Note, functional methods can not only provide more generality, but they can also unify results and techniques and lead to better results than those obtained by classical methods.

Presenting entirely original results, the authors use functional methods to explore a broad range of elliptic, parabolic, and hyperbolic boundary value problems and various classes of abstract differential and integral equations. They show that while it is crucial to choose an appropriate functional framework, this approach can lead to mathematical models that better describe concrete physical phenomena. In particular, they reach a concordance between the physical sense and the mathematical sense for the solutions of some special models. Beyond its importance as a survey of the primary techniques used in the area, the results illuminated in this volume will prove valuable in a wealth of interesting applications

Readership: This volume will be of interest to pure and applied mathematicians, engineers, and physicists.

Functional methods in differential equations 1st Table of contents:

Contents
1 First-Order Differential Equations
1.1 Dynamical Systems: Modeling 
1.2 Solutions and Direction Fields: Qualitative Analysis 
1.3 Separation of Variables: Quantitative Analysis 
1.4 Approximation Methods: Numerical Analysis 
1.5 Picard¿s Theorem: Theoretical Analysis 
2 Linearity and Nonlinearity
2.1 Linear Equations: The Nature of Their Solutions 
2.2 Solving the First-Order Linear Differential Equation 
2.3 Growth and Decay Phenomena 
2.4 Linear Models: Mixing and Coolin
2.5 Nonlinear Models: Logistic Equation 
2.6 Systems of Differential Equations: A First Look 
3 Linear Algebra
3.1 Matrices: Sums and Products 
3.2 Systems of Linear Equations 
3.3 The Inverse of a Matrix 
3.4 Determinants and Cramer¿s Rule 
3.5 Vector Spaces and Subspaces 
3.6 Basis and Dimension 
4 Higher-Order Linear Differential Equations
4.1 The Harmonic Oscillator 
4.2 Real Characteristic Roots 
4.3 Complex Characteristic Roots 
4.4 Undetermined Coefficients 
4.5 Variation of Parameters 
4.6 Forced Oscillations 
4.7 Conservation and Conversion 
5 Linear Transformations
5.1 Linear Transformations 
5.2 Properties of Linear Transformations 
5.3 Eigenvalues and Eigenvectors 
5.4 Coordinates and Diagonalization 
6 Linear Systems of Differential Equations
6.1 Theory of Linear DE Systems 
6.2 Linear Systems with Real Eigenvalues 
6.3 Linear Systems with Nonreal Eigenvalues 
6.4 Stability and Linear Classification 
6.5 Decoupling a Linear DE System 
6.6 Matrix Exponential 
6.7 Nonhomogeneous Linear Systems 
7 Nonlinear Systems of Differential Equations
7.1 Nonlinear Systems 
7.2 Linearization 
7.3 Numerical Solutions 
7.4 Chaos, Strange Attractors, and Period Doubling 
7.5 Chaos in Forced Nonlinear Systems 
8 Laplace Transforms
8.1 The Laplace Transform and Its Inverse 
8.2 Solving DEs and IVPs with Laplace Transforms 
8.3 The Step Function and the Delta Function 
8.4 The Convolution Integral and the Transfer Function 
8.5 Laplace Transform Solution of Linear Systems 
9 Discrete Dynamical Systems
9.1 Iterative Equations 
9.2 Linear Iterative Systems 
9.3 Nonlinear Iterative Equations: Chaos Again 
10 Control Theory
10.1 Feedback Controls 
10.2 Introduction to Optimal Control 
10.3 Pontryagin Maximum Principle 
Library of Congress Subject Headings for this publication:

Differential equations.
Algebras, Linear.

People also search for Functional methods in differential equations 1st:

 
functional methods in differential
 
differential methods
 
functional differential
 
functional differential equations
 
differential functional importance

Tags:

Functional methods,differential equation,Veli Matti Hokkanen