What are Partial Differential Equations?.- Linear and Nonlinear Waves.- Fourier Series.- Separation of Variables.- Finite Differences.- Generalized Functions and Green's Functions.- Complex Analysis and Conformal Mapping.- Fourier Transforms.- Linear and Nonlinear Evolution Equations.- A General Framework for Linear Partial Differential Equations.- Finite Elements and Weak Solutions.- Dynamics of Planar Media.- Partial Differential Equations in Space .
Peter J. Olver is professor of mathematics at the University of Minnesota. His wide-ranging research interests are centered on the development of symmetry-based methods for differential equations and their manifold applications. He is the author of over 130 papers published in major scientific research journals as well as 4 other books, including the definitive Springer graduate text, Applications of Lie Groups to Differential Equations, and another undergraduate text, Applied Linear Algebra.
"This textbook furnishes the basis for a 1-year introductory course in partial differential equations for advanced undergraduates. ... The book is written with great care and great attention to detail throughout. At the end of every chapter there are well-chosen exercises that genuinely add depth to the concepts treated in the text. ... this book can be wholeheartedly recommended." (M. Kunzinger, Monatshefte fur Mathematik, Vol. 181, 2016)"This book easily covers all the material one might want in a course aimed at first-time students of PDEs. ... I recommend this one highly: It provides the best first-course introduction to a vast and ever-more relevant and active area. Students, and perhaps instructors too, will learn much from it. If they wish to go beyond the material taught in a first course, this text will prepare them better than any other I know." (SIAM Review, Vol. 56 (3), September, 2014)"Introduction to Partial Differential Equations is a complete, well-written textbook for upper-level undergraduates and graduate students. Olver ... thoroughly covers the topic in a readable format and includes plenty of examples and exercises, ranging from the typical to independent projects and computer projects. ... Instructors teaching an introduction to partial differential equations course will want to consider this textbook as a viable option for their students. Summing Up: Highly Recommended. Upper-division undergraduates, graduate students, and faculty." (S. L. Sullivan, Choice, Vol. 51 (11), July, 2014)"This introduction to partial differential equations is addressed to advanced undergraduates or graduate students ... . an imposing book that includes plenty of material for two semesters even at the graduate level. ... The author succeeds at maintaining a good balance between solution methods, mathematical rigor, and applications. With appropriate selection of topics this could serve for a one semester introductory course for undergraduates or a full year course for graduate students. ... the author has clearly taken pains to make it readable and accessible." (William J. Satzer, MAA Reviews, January, 2014)