The text covers the standard topics on ordinary differential equations with a wealth of applications drawn from engineering and sciences.PedagogicaI ApproachThis bookintended as a friendly introduction to dif-ferential equations within the context of science and engineering. It dwells more on intuition rather than rigor， The emphasis is kept on the conceptual ar-guments in order to develop an intuitive understanding of the subject matter.The text strives to be simple and understandable， and encourages creative thinking. The authors believe that legal documents such as a rental lease agreements intended for plain people should be written in plain English instead of being written in a precise legal language that is beyond most peo-ple''s grasp and requires a lawyer to translate， Likewise， a differential equa-tions textbook should be written for the student to read and understand.Instructors do not need textbooks， students do. It is common experience that students flip through the pages of a mathematics textbook only when they are trying to find an example similar to the problem assigned. It is often stated that mathematical concepts must be explained in plain language to have a lasting impression.
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Differential equations have long been an essential part of core curricula in most branches of physical sciences and engineering all over the world.Scientists and engineers often study systems that undergo changes， and differential equations enable the scientists and engineers to study the changes in key variables in a system and to gain a deeper understanding of the under-lying physical phenomena. This book is intended to serve as a textbook for a first course on differential equations taken primarily by science and engineer-ing students. It is the outcome of the lecture notes developed by the first author over the years in teaching differential equations to engineering students at the University of Nevada， Reno， and by computer assignments and engineering examples developed by the second author while teaching at the University of Rhode Island. The text covers the standard topics on ordinary differential equations with a wealth of applications drawn from engineering and sciences.PedagogicaIApproachThis bookintended as a friendly introduction to dif-ferential equations within the context of science and engineering. It dwells more on intuition rather than rigor， The emphasis is kept on the conceptual ar-guments in order to develop an intuitive understanding of the subject matter.The text strives to be simple and understandable， and encourages creative thinking. The authors believe that legal documents such as a rental lease agreements intended for plain people should be written in plain English instead of being written in a precise legal language that is beyond most peo-ple''s grasp and requires a lawyer to translate， Likewise， a differential equa-tions textbook should be written for the student to read and understand.Instructors do not need textbooks， students do. It is common experience that students flip through the pages of a mathematics textbook only when they are trying to find an example similar to the problem assigned. It is often stated that mathematical concepts must be explained in plain language to have a lasting impression. We should be able -to tell our students that solving a differential equation is basically integration， and integration is basically summation， in-stead of using some abstract language for the sake of precision and rigor.
The material in the text is introduced at a level that an average student can follow comfortably. It speaks to the students， not over them. In fact， it is self-instructive. This frees the instructor to use class time more productively. The topics are ordered such that they flow well in a logical order， and each topic provides motivation for the subsequent topic. Every attempt is made to make tlus a "readable" mathematics text and to enhance learning and understanding.The goal throughout this project has been to offer an introductory differential equations textbook that is read by the students with interest and enthusiasm in-stead of one which is used as a reference guide to solve problems.
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