02707nam a2200301 i 4500 CSPC 20251216135620.0 251211s2019 sz b 000 0 eng d 2018940344 9783319906461 CSPC eng CSPC rda QA374 .M36 2019 23 620.00151 M338e Marin, Marin, author. Essentials of partial differential equations : with applications / Marin Marin and Andreas Öchsner. Cham, Switzerland : Springer, 2019. xi, 380 pages ; 24 cm. rdacontent text rdamedia unmediated rdacarrier volume Includes bibliographical references. Part I. Classical solutions -- Quasilinear equations -- Differential operators of second order -- The theory of potential -- Boundary value problems for elliptic operators -- Operational Calculus -- Parabolic equations -- Hyperbolic equations -- Part II. Solutions in distributions -- Elements of distributions -- Integral formulas -- Partial differential equations of the first order -- Linear partial differential equations of second order -- Harmonic functions -- Weak solutions of classical problems -- Regularity of the solutions -- Weak solutions of parabolic equations -- Weak solutions for hyperbolic equations. "This book offers engineering students an introduction to the theory of partial differential equations and then guiding then through the modern problems in this subject. Divided into two parts, in the first part readers already well-acquainted with problems from the theory of differential and integral equations gain insights into the classical notions and problems, including differential operators, characteristics surfaces, Levi functions, Green's functions, and Green's formulas. Readers are also instructed in the extended potential theory in its three forms: the volume potential, the surface single-layer potential and the surface double-layer potential. Furthermore, the book presents the main initial boundary value problems associated with elliptic, parabolic and hyperbolic equations. The second part of the book, which is addressed first and foremost to those who are already acquainted with the notions and the results from the first part, introduces readers to modern aspects of the theory of partial differential equations." -- Back cover Differential equations, partial. Öchsner, Andreas, author. ddc 0 BK 23 620.00151 M338e CIR 2019 0 0 ddc 0 0 CSPC CSPC CIR 2025-12-11 0 CIR 620.00151 M338e 2019 031025 2025-12-11 16:04:36 1-1 2025-12-11 BK 31214 31214