LEADER 04349nam 2200649Ia 450 001 9910815621203321 005 20240313125146.0 010 $a1-283-97137-2 010 $a981-4415-15-4 035 $a(CKB)2670000000328633 035 $a(EBL)1113157 035 $a(OCoLC)827210219 035 $a(SSID)ssj0000850985 035 $a(PQKBManifestationID)12402937 035 $a(PQKBTitleCode)TC0000850985 035 $a(PQKBWorkID)10838690 035 $a(PQKB)10228546 035 $a(WSP)00000107 035 $a(Au-PeEL)EBL1113157 035 $a(CaPaEBR)ebr10648641 035 $a(CaONFJC)MIL428387 035 $a(MiAaPQ)EBC1113157 035 $a(EXLCZ)992670000000328633 100 $a19850424d1984 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Laplace transform /$fRichard E. Bellman, Robert S. Roth 205 $a1st ed. 210 $aSingapore $cWorld Scientific$dc1984 215 $a1 online resource (175 p.) 225 0$aSeries in modern applied mathematics ;$vv. 3 300 $aIncludes index. 311 $a9971-966-73-5 327 $aPREFACE; CONTENTS; Chapter 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; Chapter 2 ORDINARY DIFFERENTIAL EQUATIONS; 2.1 Introduction 327 $a2.2 Linear Differential Equations With Constant Coefficients2.3 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; Chapter 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 327 $a3.11 Equations of the Neutral and Advanced Types3.12 Linear Systems Of Differential-Difference Equations; 3.13 A Limiting Case For Differential-Difference Equations; Problems; Chapter 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; Chapter 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 Representation 327 $a5.6 Some Important Results5.7 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 330 $aThe classical theory of the Laplace Transform can open many new avenues when viewed from a modern, semi-classical point of view. In this book, the author re-examines the Laplace Transform and presents a study of many of the applications to differential equations, differential-difference equations and the renewal equation. 410 0$aModern Applied Mathematics S. 606 $aLaplace transformation 606 $aTransformations (Mathematics) 615 0$aLaplace transformation. 615 0$aTransformations (Mathematics) 676 $a515.723 676 $a515/.723 700 $aBellman$b Richard$f1920-1984.$0121312 701 $aRoth$b Robert$f1930-$01668192 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910815621203321 996 $aThe Laplace transform$94028617 997 $aUNINA