Differential Equations: Linear, Nonlinear, Ordinary, Partial 1st Edition by A. C. King (PDF)

Description

Finding and interpreting the solutions of differential equations is a central and essential part of applied mathematics. This book aims to enable the reader to develop the required skills needed for a thorough understanding of the subject. The authors focus on the business of constructing solutions analytically, and interpreting their meaning, using rigorous analysis where needed. MATLAB is used extensively to illustrate the material. There are many worked examples based on interesting and unusual real world problems. A large selection of exercises is provided, including several lengthier projects, some of which involve the use of MATLAB. The coverage is broad, ranging from basic second-order ODEs and PDEs, through to techniques for nonlinear differential equations, chaos, asymptotics and control theory. This broad coverage, the authors’ clear presentation and the fact that the book has been thoroughly class-tested will increase its attraction to undergraduates at each stage of their studies.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The author skips alot of details which can cause some confusion.

⭐Background of bookThe authors note this book falls between graduate-level books emphasizing abstract mathematical results with fully rigor, and some other undergraduate books that using algorithmic techniques. Most of the material has been tested with undergraduates in ‘University of Birmingham’ and its been designed to help students with what they find difficult.DescriptionThis challenging book is printed on high quality & heavy grade paper, has been on my shelf for a long time, but until recently I have lacked the skills to read it properly. As noted, many real-world problems do not have analytical answers. The introductory topics require at a minimum required skills with ‘Frobenius’ methods to solve differential equations to fully engage with the early chapters with a wider background with constant -coefficient, ordinary differential equations.The beauty of this approach is i.m.h.o the increasingly in-depth and detailed exposure of the reader to topics such as Frobenius -based solution techniques to solve differing forms of Bessel based equations, which are used with FM broadcasting for example. And also really interesting is the unsuspected application of Fourier-based methods and other methods such as Bessel and Laplace- based problems. It would help if the reader could build upon some experience with vector calculus. Although it could be said some of this is formalizing summaries, it’s really beautifully linked and clearly written. (i.m.h.o)SummaryThe book does not shy away from progressive exposure of involved topics such as finding solutions to non-linear ordinary differential equations via orthonormal eigenfunctions based methods (up to 3 by 3) including airflows. Then ends with much discussion with Time-Optimal Control and simple chaotic systems.This is a truly beautiful, carefully written book for any undergraduate with Math/science-based topics involving differential equations.* UpdateI have returned to this book – October 2021 – to try the later chapters of greater depth. It’s a stronger explanations and its warrants deeper analysis. I read one page of proofs (page 284) for a few hours to understand this. Say what you see can help. I have made real progress. It’s satisfying when I can assimilate this higher level of math!

⭐I have found this book very useful over the past couple of years. Great as a reference text as well as to work through. Clear and instructive examples. Would probably be suited more for courses on differential equations in the later years of a undergraduate degree or start of a graduate course.

⭐Excellent textbook if a bit heavy in parts

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