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The Laplace Transform by Richard Bellman, Robert S. Roth
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About this book :-
The Laplace Transform written by
Richard Bellman, Robert Roth .
Book Detail :-
Title: The Laplace Transform
Edition:
Author(s): Richard Bellman, Robert S. Roth
Publisher:
Series:
Year: 1984
Pages: 81 (Some Pages)
Type: Read Online
Language: English
ISBN:
Country:
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Book Contents :-
The Laplace Transform written by
Richard Bellman, Robert Roth
cover the following topics.
1. THE LAPLACE TRANSFORM
1.1 Introduction
1.2 Functions of a Bounded Variation
1.3 The Stieltjes Integral
1.4 Improper Stieltjes Integral
1.5 The Laplace Transform
1.6 Existence and Convergence
1.7 Properties of the Laplace Transform
1.8 The Inversion of the Laplace Transform
1.9 The Convolution Theorem
1.10 Instability of the Inverse of the Laplace Transform
1.11 The Laplace Transform and Differential Equations
1.12 Transient Solutions
1.13 Generating Functions; Problems
2. ORDINARY DIFFERENTIAL EQUATIONS
2.1 Introduction.
2.2 Linear Differential Equations With Constant Coefficients
2.3 The Laplace Transform Solution
2.4 Systems of Linear Differential Equations
2.5 Mismatched Solutions
2.6 Behavior Of The Higher Derivatives
2.7 An Example; Problems
3. DIFFERENTIAL-DIFFERENCE EQUATIONS
3.1 Introduction
3.2 Examples
3.3 Types of Differential-Difference Equations
3.4 Existence and Uniqueness
3.5 Exponential Solutions
3.6 Laplace-Transform Solutions
3.7 Order Of Growth Of Solutions
3.8 The Characteristic Roots
3.9 Asymptotic Behavior of the Solution
3.10 The Shift Theorem
3.11 Equations of the Neutral and Advanced Types
3.12 Linear Systems Of Differential-Difference Equations
3.13 A Limiting Case For Differential-Difference Equations; Problems
4. PARTIAL DIFFERENTIAL EQUATIONS
4.1 Introduction
4.2 The Hyperbolic Partial Differential Equation
4.3 The Parabolic Partial Differential Equation
4.4 The Elliptic Partial Differential Equation
5. THE RENEWAL EQUATION
5.1 Introduction
5.2 The Formal Laplace Transform Solution
5.3 Exponential Bounds on u(t)
5.4 A Convolution Theorem
5.5 Use of the Contour Integral Representatio.
5.6 Some Important Results
5.7 Systems of Renewal Equations
5.8 Branching Processes; Problems Chapter
6. NUMERICAL INVERSION OF THE LAPLACE TRANSFORM
6.1 Introduction
6.2 The Complex Laplace Transform
6.3 Numerical Quadrature
6.4 The Legendre Polynomials
6.5 Numerical Inversion of the Laplace Transform
6.6 Explicit Inversion Formula
6.7 Instability of the Inverse of the Laplace Transform
6.8 Tychonov Regularization
6.9 Obtaining the Initial Approximation
6.10 Change of the Time Scale
Problems; SUBJECT INDEX.
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