Partial Differential Equations for Scientists and Engineers (Dover Books on Mathematics) by Stanley J. Farlow (PDF)

Description

Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading.

User’s Reviews

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

⭐I love APPLIED MATH and this is applied math in spades ! I have on occasion felt sorry for engineering graduates. Most of them don’t get nearly enough math in their coursework. So, oftentimes, I would be called on to help them out with some math. This book will definitely develop your math skills and broaden the range of problems that you can understand and solve. And, I will be able to spend more time on my own work. hehe This is a great book.

⭐I bought the book about 2 years ago. I have to say this is by far the best book on the topic that can accompany with any other “text book”.The topics are well explained and can be understood by people from decent backgrounds. I have had friends who had never taken ODE before and said they understood the topic very well from this book. Another big point is that the books lays a good amount of foundation and uses a build up procedure to come to showing you various methods.I have used this and Colton for primarily learning the subject and used Strauss more as an “Excercise Book”.The main issue I have is that it lack problems. To learn mathematics, you have to do mathematics. So where are practice problems? This is the only concern.The coverage on Numerical method is very shallow. But this is expected due the vastness of this topic. It is normal to look at books specialized in that topic

⭐Structured into lessons very much like Khan Academy. Very undemanding since prerequisites are provided on the fly. I had not previously studied the calculus of variations. The introductory chapter on this managed to get my interest for the first time. The presentation is as untechnical and plain as it can possibly be. Maybe someone could complain that it is not totally rigorous? However, any possible lack of rigour is amply compensated for by an elegantly simple and straight forward presentation. If like me you like to read elementary math for fun you’ll love this book. Also the size and weight makes it feasible to read this on the couch and go to sleep with it over your face and still wake up alive (as opposed to Kreyzig, then you wake up dead).

⭐The best book that I have on this topic. Without much mathematical detail, this book explains various topics in visual and intuitive fashion. If you prefer mathematical rigor with theorems and proofs, this book is not for you.

⭐Do you need to know more about pde’s and their solutions? This book will help you.Emphasis is on the heat equation and gaining a physical understanding of the solutions but the techniques are broadly applicable.

⭐It is still a hard subject I wouldn’t want to tackle without an instructor, however this book was very helpful when COVID moved my class online. One of the best text books I own.

⭐I have only began reading this book and find it to be a clear and concise review of multi-variate differentials suitable for practicing engineers and those engineers whose knowledge has tarnished with time. This book also includes how to apply the knowledge as well. I consider a math level that includes ordinary differentials to be an absolute prerequisite before attempting partials. This book is eye candy for engineers.

⭐I was recommended this book as supplemental material for differential equations 2 and found it to be much more helpful than the required text. For some reason the thought process was easier for me to follow.

⭐A very intuitive text on a potentially difficult topic! The author presents each topic in the form of a “lesson” and it’s a breath of fresh air. The oldies are definitely the goodies!

⭐Initial facts [updated MARCH ’14]This ‘Dover’ book is a unabridged, corrected book originally published by ‘Wiley & Sons’ (1982). The Dover brand often reprints great books otherwise would be out – of – print. The book has a font of a size that’s easy to read, and has b&w text, graphs, drawings.Impressions of the bookThe first topics covered in this glorious book covers what is known a the ‘Seebeck Effect’. This is where my previous studies ended! The actual mechanic’s are assumed and you follow the methods written in a formal math shorthand, as are many books of this type. If you require a bit of foundation work on the properties of P.D.E’s I would recommend the two Stroud’s for ‘Mathematical Methods’ coverage. The whole book explains problems which include ‘Hyperbolic’, ‘Parabolic’ and ‘Elliptic types of equation’s . The manner in which it explains is if the dense proofs are removed from the front parts of the book, and suspended until later. What is left is a very broad spread of information. The methods in which the equations are solved uses the most straight forward manner, such as ‘Separation of Variables’. The coverage of several types of ‘Transforms’ is really brilliantly and simply built-up, but the ‘donkey – work’ is assumed you know what these entail in terms of the fine print in details. Say ‘Laplace transforms’, these cannot be learnt form this book, as the details are not present, but this is expanded in the knowledge you know these details already and just build upon these.The book covers a nice introduction to Fourier methods. This breaks it down into chunks and is nicely done.By readily applying these understandable facts they become foundations for subsequent information. Then brilliantly, and helpfully, exploring these issues by choosing problems a physics / engineering student would feel some physical familiarity. This is the way this book is differing from other P. D. E. pure maths books. These types are also great as well, but reading both types is a boon.Conclusions & summaryBut each of the remaining explanations still invoke wonder at the beauty of it. When you plough through the book the depth of the complexity increases over time. But the whole aggregation of explanations make learning these topics eventually very satisfying. I am again going through this book and grasping these topics again and again. This book carries a smoothly done introduction into Fourier topics that is really is a great piece of work, if you have done the previous P.D.E’s ‘Mathematical Methods’ foundation work on, say, the two Stroud’s.

⭐Book arrived in new condition. Great aid for my own research and teaching.

⭐An excellent reference for anybody developing and solving PDE models for scientific or engineering purposes. I found this text to be great as a reference but not something I would read cover to cover. A relatively advanced text that should cover the needs of most users.

⭐Does what it says on the tin. Not too complex either, so it’s well accessible.

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