Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers (Oxford Texts in Applied and Engineering Mathematics, 10) 4th Edition by Dominic Jordan (PDF)

Description

This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinic bifurcation and Liapunov exponents. Over 500 end-of-chapter problems are also included and as an additional resource fully-worked solutions to these are provided in the accompanying text Nonlinear Ordinary Differential Equations: Problems and Solutions, (OUP, 2007). Both texts cover a wide variety of applications while keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences.

User’s Reviews

Editorial Reviews: Review UNEDITED UK REVIEW: “Review from previous edition “…classic book…The book succeeds as an exceptionally well written test fot its intended audience…No doubt one of its strongest features is over 500 problems…throughout the entire book only important physical processes are described… The new edition is greatly enhanced…I strongly recommend that you take a look. The presentation is exquisitely straightforward with numerous physically interesting examples, and it is carefully and well written””–SIAM”The book should be recommended to scientists and engineers.”–Mathematical Reviews About the Author Prior to his retirement, Dominic Jordan was a professor in the Mathematics Department at Keele University. His research interests include applications of applied mathematics to elasticity, asymptotic theory, wave and diffusion problems, as well as research on the development of applied mathematics in its close association with late 19th century engineering technologies. Peter Smith is a professor in the Mathematics Department of Keele University. He has taught courses in mathematical methods, applied analysis, dynamics, stochastic processes, and nonlinear differential equations, and his research interests include fluid dynamics and applied analysis.

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

⭐Jordan and Smith have done an excellent job in describing and providing techniques to solve non-linear differential equations. Non-linear ordinary differential equations are stiff and can be solved numerically, but numerical solutions do not provide physical parametric insight. Consequently, it is often necessary to find a closed analytical solution. When faced with this challenge in my personal research, I looked around for books that would help me solve the non-linear forced differential equation that science had presented to me. Even in a good research university library, I could not find any that beat Jordan and Smith’s work. I did find summary presentations in the specialized literature of physics, but those works referenced Jordan and Smith for futher details. Together, Jordan and Smith’s textbook and sourcbook provide a wealth of practical information for solving non-linear equations along with lots of good examples. I feel fortunate that I found their work and have successfully solved my equations following their advice. Their work even helped me to visualize and interpret my results. I heartily recommend the two books to anyone faced with the need to solve nonlinear ordinary differential equations using techniques (for example, averaging methods, perturbation methods, Fourier expansion methods, liapunov methods, chaos, etc.# that lie beyond those studied in college for solving linear differential equations.

⭐This is something like the ninth or tenth textbook I’ve bought from Book Depository since 2014. The fact that I keep going back to them should tell you all you need to know.

⭐Seller was great – just don’t love the actual book

⭐I used this very intensively when studying for a graduate qualifying exam in ODES. This was not the text used in the course I took but I found it extremely helpful. It is a great book that I will keep around.

⭐I used the 2nd edition of this book for both a master’s course in Ordinary Differential Equations (ODEs) and for my master’s exam in ODEs. It is an excellent book for an intermediate course in ODEs at the beginning graduate level or to use for self-study. It contains over 500 problems ranging from understanding the basic concepts to generalization of theory. I still have the original copy I used back then in my library.The topics covered in the book include: phase plane analysis of first order systems and 2nd order ODEs, geometrical and computational aspects of the phase diagram, averaging methods; limit cycles, perturbation, stability, Liapunov and Poincare methods for determining stability, existence of periodic solutions, bifurcation, and an introduction to chaos. Plus it contains many practical applications of ODEs to science and real world problems.The prerequisites for this book are courses in linear algebra and differential equation. Also, some acquaintance with advanced calculus is useful in understanding the theoretical aspect of ODEs and proving some of the theorems on Liapunov and Poincare stability.

⭐* Target Audience, H.N.D, Undergraduate, Post Graduate, Masters?It aimed for Mathematical, Engineering, and sciences third-year degree. And Masters in the same too.* Topics Covered1 Second-Order differential equations in the phase plane, 2 Plane Autonomous systems and linearization, 3 Geometric aspects of autonomous systems, 4 Periodic solutions, averaging methods, 5 Perturbation methods, 6 Singular Pertabation methods, 7 Forced oscillations: harmonic and subharmonic response, stability and entrainment, 8 Stability, 9 Stability by solution perturbation: Mathieu’s equation, 10 Liapunov methods for determining the stability of the zero solution, 11 the existence of periodic solutions, 12 Bifurcations and manifolds, 13 Poncare sequences, homoclinic bifurcation and chaos.* What’s the best bits?The book starts with the idea that if you are reading engineering, scientific and mathematics areas of degrees, as you are reading this book level, you have probably seen some calculation of differential equations and linear algebra? Maybe you have experience with second-order versions? It shares that these are only a couple of per cent of differential equations in the real world! This we have learned is just foot-in-the-door mathematics! To tackle these new types of equations, those qualitative methods reveal phenomena of non-linear equations, that features of stability, periodicity and chaotic behaviour can be applied without solving the equations directly, and without needing to solve exactly. Generally, exact numerical solutions of nonlinear equations are rarely obtainable but can use standard numerical techniques one at a time. It’s better to solve numerical equations with software such as Mathematica, Maple.The book covers phase diagrams starting using the non-linear pendulum equations to introduce Conservative energy systems with potential and kinetic systems and equilibrium points. The major parts are applied using the linearised Maclaurin series and Taylor series to get around and generate fresh series getting around the inability to use the standard series of sin(x), cos(x), exp(x) and so on. In i.m.h.o. recommended Stroud’ Further engineering Mathematics’ for these ordinary differential equations. I also enjoyed the partial diff between animal groups, otherwise known as Predator-Prey equations. Fourier Series is also used in fresh ways, but again I learned this from ‘Fourier Series’ (Tolstov.)These two methods are used are explained well in how they are used. But I liked how to learn it from these two books. Using the construction of phase diagrams with equilibrium points helped how to get around the requirement of applying numerical solutions. I liked the Greens Theorum exploration too. Some methods used ways to turn features of an equation off and see how they affect the equation resounds helps too. Some equations are used with substitutions to solve the equation, and it gets pretty deep at times. Stability is a big feature of the solution to non-linear equations, and are used to describe the behaviour in two or three dimensions, which is great fun. Later on, the usage of Greek Symbolic Mathematical Language is more and more to the front of the methods, with matrices used heavily so you need to be on the ball here.* SummaryThis book I started reading in mid-April 2021, I have taken chapters 1-5, 8 – 10 – 11 with a few more in the later chapters. This rate is as suggested by the authors, and to be explored over a semester. I am making progress and it has a light touch even if it is final year math level. I have bought the companion book of non-linear equations explained and explored and will try it sometime in the future.As an update, and in my case reading it daily, it took at least six months to get a hold of the topics.

⭐I have to concur with other reviewers — although this book contains interesting material which is not found in other texts, it is stuffed full of errors. On the first page of chapter one, for example, “representation” is spelled “representaion”, with only one ‘t’. This does not inspire confidence, and the pace of errata hardly decreases thereafter.How is it possible that a textbook can get to its fourth editing and still be so defective? I guess the answer is that there really isn’t much else on the market. If you want an inclusive text that deals with all aspects of handling non-linear DEs, it’s this or nothing.There are other problems, it seems to me, than the mistakes.First, many concepts are used without being explained. Sometimes the explanation turns up later in the chapter, sometimes later in the book, and sometimes not at all. Chapter one deals with essentially the same physical system in two different formulations, and it isn’t clear why this approach is taken.Second, the book assumes a certain knowledge of mechanical systems. In fact, physico-mechanical jargon is used from start to finish. Probably a person studying non-linear ODEs will have an interest in these areas, but I don’t think that should be assumed.Third, I’m not sure it makes sense to introduce systems of first-order ODEs be decomposing them out of higher-order ODEs. This is always possible, of course, but wouldn’t it be better to introduce naturally first-order systems first? It seems that the author has sort out ways to make a fabulously complex subject even more complex.In a one-horse race, this book certainly comes in second. The only conceivable reason to buy it is that there isn’t any alternative. Which there isn’t.

⭐This a very good book, in that it covers a vast number of examples, techniques and methods of solving non-Linear Ordinary Differential Equations. My problem with it is there are two many typographical errors. For students this can be confusing and disconcerting as the examples are difficult in any case. So seeing correct solutions, techniques and methods where the algebra can be followed and correct is very important in my view. Given its the 4th edition, someone should have taken the responsibility to correct these issues.

⭐I purchased this at the same time that i purchased Steven Strogatz’s Nonlinear Dynamics and Chaos. In comparison, I found that whilst they dont cover exactly the same material, where they do overlap, Strogatz’s book was better structured, had clearer explanations and fewer errors. if you have the options or you can only afford one, my recommendation would be to go with Strogatz’s book.

⭐Normally I would have said this is a good book. However the (very) large numbers of typographical errors really spoil it. You can deal with errors in sentences but when you get errors in mathematical equations, this can make following mathematical arguments hard to understand because you’re never quite sure if you’ve got it wrong (as the subject matter is quite advanced) or the book has. This can be a big time waster.There isn’t even a web page for readers to look up and post errata (at least I haven’t found one). (If I’m wrong on this, please let me know).I don’t really know if this is the fault of authors editors or the publishers. Maybe all. Either way, it ruins what could have been a good book on a maths subject for which there are not that many texts at this level.

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