Download e-book for iPad: Handbook of Linear Partial Differential Equations for by Andrei D. Polyanin

By Andrei D. Polyanin

ISBN-10: 146658145X

ISBN-13: 9781466581456

  • Includes approximately 4,000 linear partial differential equations (PDEs) with solutions
  • Presents ideas of diverse difficulties proper to warmth and mass move, wave conception, hydrodynamics, aerodynamics, elasticity, acoustics, electrodynamics, diffraction thought, quantum mechanics, chemical engineering sciences, electric engineering, and different fields
  • Outlines easy tools for fixing a variety of difficulties in technological know-how and engineering
  • Contains even more linear equations, difficulties, and options than the other e-book presently available
  • Provides a database of try difficulties for numerical and approximate analytical tools for fixing linear PDEs and platforms of coupled PDEs

New to the second one Edition

  • More than seven hundred pages with 1,500+ new first-, second-, third-, fourth-, and higher-order linear equations with solutions
  • Systems of coupled PDEs with solutions
  • Some analytical equipment, together with decomposition equipment and their applications
  • Symbolic and numerical equipment for fixing linear PDEs with Maple, Mathematica, and MATLAB®
  • Many new difficulties, illustrative examples, tables, and figures

To accommodate varied mathematical backgrounds, the authors stay away from at any place attainable using particular terminology, define many of the equipment in a schematic, simplified demeanour, and organize the fabric in expanding order of complexity.

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Extra resources for Handbook of Linear Partial Differential Equations for Engineers and Scientists

Example text

1 a + eλx . n y − bx − c λ 2 ∂w ∂y 2 + y 2 + 2aλxeλx − a2 e2λx = 0. Principal integral: Ξ= 36. ∂w ∂x E 2 + y − aeλx 2 + ae−λx y 2 + λxy + ab2 ∂w ∂x 38. ∂w ∂x ∂w ∂y 2 + axn y 2 + λxy + ab2 xn eλx = 0. − ab ∂w ∂y y exp − 12 λx2 b Principal integral: Ξ = arctan 2 eλx dx . E = exp 2a 1 y exp − 12 λx2 b Principal integral: Ξ = arctan 37. E dx, exp − 12 λx2 dx. = 0. − ab + (ae2λx y 3 + beλx y 2 + cy + de−λx ) ∂w ∂y xn exp 2 1 2 λx dx. = 0. Principal integral: Ξ= 39. ∂w ∂x av 3 + bv 2 dv − x, + (c + λ)v + d v = eλx y.

Zaitsev’s Handbook of Exact Solutions for Ordinary Differential Equations (CRC Press, 1995 and 2003); A. D. Polyanin and A. V. Manzhirov’s Handbook of Integral Equations (CRC Press, 1998 and 2008); A. D. Polyanin’s Handbook of Linear Partial Differential Equations for Engineers and Scientists (Chapman & Hall/CRC Press, 2002); A. D. Polyanin, V. F. Zaitsev, and A. Moussiaux’s Handbook of First Order Partial Differential Equations (Taylor & Francis, 2002); A. D. Polyanin and V. F. Zaitsev’s Handbook of Nonlinear Partial Differential Equations (Chapman & Hall/CRC Press, 2004 and 2012); A.

Bv − c − a(m + 3)xy 2 + b(m + 2)y − cxm ∂w ∂y Principal integral: Ξ = cxm+2 cxm − 2(m + 1)y(axy + b) . 89. x2 (2axy + b) ∂w ∂x − (4ax2 y 2 + 3bxy − cx2 − k) ∂w ∂y Principal integral: Ξ = (cx2 + k)2 − 4cx3 y(axy + b). 90. axm ∂w ∂x + by n ∂w ∂y = 0. 1◦ . Principal integral for m = 1 and n = 1: Ξ = b(n − 1)x1−m − a(m − 1)y 1−n . 2◦ . Principal integral for m = 1 and n = 1: Ξ = b ln |x| + a y 1−n . n−1 3◦ . Principal integral for m = 1 and n = 1: Ξ= b x1−m + a ln |y|. m−1 4◦ . Principal integral for m = n = 1: Ξ = b ln |x| − a ln |y|.

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Handbook of Linear Partial Differential Equations for Engineers and Scientists by Andrei D. Polyanin

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