Therearemanyexcellenttextsonelementarydi?erentialequationsdesignedfor the standard sophomore course. However, in spite of the fact that most courses are one semester in length, the texts have evolved into calculus-like pres- tations that include a large collection of methods and applications, packaged with student manuals, and Web-based notes, projects, and supplements. All of this comes in several hundred pages of text with busy formats. Most students do not have the time or desire to read voluminous texts and explore internet supplements. The format of this di?erential equations book is di?erent; it is a one-semester, brief treatment of the basic ideas, models, and solution methods. Itslimitedcoverageplacesitsomewherebetweenanoutlineandadetailedte- book. I have tried to write concisely, to the point, and in plain language. Many worked examples and exercises are included. A student who works through this primer will have the tools to go to the next level in applying di?erential eq- tions to problems in engineering, science, and applied mathematics. It can give some instructors, who want more concise coverage, an alternative to existing texts.

Emphasizing a practical approach for engineers and scientists, A First Course in Differential Equations, Modeling, and Simulation avoids overly theoretical explanations and shows readers how differential equations arise from applying basic physical principles and experimental observations to engineering systems. It also covers classical methods for

A First course in Ordinary Differential Equations provides a detailed introduction to the subject focusing on analytical methods to solve ODEs and theoretical aspects of analyzing them when it is difficult/not possible to find their solutions explicitly. This two-fold treatment of the subject is quite handy not only for undergraduate students in mathematics but also for physicists, engineers who are interested in understanding how various methods to solve ODEs work. More than 300 end-of-chapter problems with varying difficulty are provided so that the reader can self examine their understanding of the topics covered in the text. Most of the definitions and results used from subjects like real analysis, linear algebra are stated clearly in the book. This enables the book to be accessible to physics and engineering students also. Moreover, sufficient number of worked out examples are presented to illustrate every new technique introduced in this book. Moreover, the author elucidates the importance of various hypotheses in the results by providing counter examples. Features Offers comprehensive coverage of all essential topics required for an introductory course in ODE. Emphasizes on both computation of solutions to ODEs as well as the theoretical concepts like well-posedness, comparison results, stability etc. Systematic presentation of insights of the nature of the solutions to linear/non-linear ODEs. Special attention on the study of asymptotic behavior of solutions to autonomous ODEs (both for scalar case and 2✕2 systems). Sufficient number of examples are provided wherever a notion is introduced. Contains a rich collection of problems. This book serves as a text book for undergraduate students and a reference book for scientists and engineers. Broad coverage and clear presentation of the material indeed appeals to the readers. Dr. Suman K. Tumuluri has been working in University of Hyderabad, India, for 11 years and at present he is an associate professor. His research interests include applications of partial differential equations in population dynamics and fluid dynamics.

lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.

First-rate introduction for undergraduates examines first order equations, complex-valued solutions, linear differential operators, the Laplace transform, Picard's existence theorem, and much more. Includes problems and solutions.

This book provides a complete analysis of those subjects that are of fundamental importance to the qualitative theory of differential equations and related to current research-including details that other books in the field tend to overlook. Chapters 1-7 cover the basic qualitative properties concerning existence and uniqueness, structures of solutions, phase portraits, stability, bifurcation and chaos. Chapters 8-12 cover stability, dynamical systems, and bounded and periodic solutions. A good reference book for teachers, researchers, and other professionals.