This textbook provides a brief and lucid introduction to the theory of linear partial differential equations. It clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions. The solution operators associated to non-homogeneous equations are used to make transition to the theory of nonlinear PDEs. Organized on three parts, this material is suitable for three one-semester courses, a beginning one in the frame of classical analysis, a more advanced course in modern...
This textbook provides a brief and lucid introduction to the theory of linear partial differential equations. It clearly explains the transition fr...
Precup's introduction into Ordinary Differential Equations combines models arising in physics and biology for motivation with rigorous reasoning in describing the theory of ODEs and applications and computer simulations with Maple.
While offering a concise course of the theory of ODEs it enables the reader to enter thie field of computer simulations. Thus, it is a valuable read for students of mathematics as well as physics and engineering.
Precup's introduction into Ordinary Differential Equations combines models arising in physics and biology for motivation with rigorous reasoning in...
This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis. In particular, fixed point theory is established for many classes of maps, such as contractive, non-expansive, accretive, and compact maps, to name but a few. This book also presents coincidence and multiplicity results. Many applications of current interest in the theory of nonlinear differential equations are presented to complement the theory. The text is essentially self-contained, so it may also be used as an introduction to topological methods in nonlinear analysis....
This volume presents a systematic and unified treatment of Leray-Schauder continuation theorems in nonlinear analysis. In particular, fixed point theo...
