Schaum's Mathematical Handbook of Formulas and Tables

Book Description

Students and research workers in mathematics, physics, engineering and other sciences will find this compilation of more than 2000 mathematical formulas and tables invaluable. They will see quickly why half a million copies were sold of the first edition! All the information included is practical -- rarely used results are excluded. Topics range from elementary to advanced-from algebra, trigonometry and calculus to vector analysis, Bessel functions, Legendre polynomials and elliptic integrals. Great care has been taken to present all results concisely and clearly. Excellent to keep as a handy reference!

Customer Reviews:

Mathematical Handbook of Formulas and Tables.......2007-09-25

A very useful book that gathers all the mathmatical formals 'as the title states. As an Engineering Student it is very helpful to have everything in one text instead of getting your old books and digging through them to find them.

Handbook of formulas and Tables.......2007-01-04

It is a good quick reference to getting formulas for math problems.

great reference.......2007-01-04

tables are concise with out missing any important integrals. the table is my constant companion for undergrad physics and mathematics.

one of the best.......2006-11-10

one of the best books i've ever got....
it has every thing i need

Very useful in a pinch.......2006-11-10

As a tabular summary of many useful mathematical relations, the book is very job-specific; however, it contains most of the functions and functional relations that a scientist or engineer might need. The layout is clean and very well organized. It's a useful reference, but does not actually derive anything, so if one is looking for derivations, then try looking at applied mathematics textbooks.

Mathematical Methods of Physics and Engineering

Average customer rating:

Just one comment, this is a great book.
There are much better options.

Mathematical Methods of Physics and Engineering
K. F. Riley , M. P. Hobson , and S. J. Bence
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521890675

Book Description

The new edition of this highly acclaimed textbook contains several major additions, including more than four hundred new exercises (with hints and answers). To match the mathematical preparation of current senior college and university entrants, the authors have included a preliminary chapter covering areas such as polynomial equations, trigonometric identities, coordinate geometry, partial fractions, binomial expansions, induction, and the proof of necessary and sufficient conditions. Elsewhere, matrix decompositions, nearly-singular matrices and non-square sets of linear equations are treated in detail. The presentation of probability has been reorganized and greatly extended, and includes all physically important distributions. New topics covered in a separate statistics chapter include estimator efficiency, distributions of samples, t- and F- tests for comparing means and variances, applications of the chi-squared distribution, and maximum likelihood and least-squares fitting. In other chapters the following topics have been added: linear recurrence relations, curvature, envelopes, curve-sketching, and more refined numerical methods.

Customer Reviews:

Just one comment, this is a great book........2007-05-30

This is one of the best mathematical methods book, very readable.
It has very clear explainations, in each topic it's developing from basic intuitions until it reaches the genralized equations, several detailed examples help a reader checks his understanding and follows the authors.

The contents are very well-organized and self-contained, one can looks directly at the topic he wants to know. It's lucid and normally answer and teach a reader what he wants to do. All definitions make sense and a reader can accepts easily it's a smart thing to do math that way.

It also serves as a one-stop, if you feel confused when you're reading because your background knowledge is not strong enough, just search for the previous related topics, all brilliant explainations are waiting for you to grasp them, make you ready for what you need.

Any undergrads and beginning grad students in Physics will find this book is great. This is an excellent example how to write an approachable math methods book. Eventhough it has a thick over than 1,300 pages, but it never turns a reader away becuase of its thickness at all. Once one starts reading it, he'll enjoy and come back looking for another explaination.

One more great point is, this book contains a lot of real physical examples besides the math formulations, make a reader understands the topic deeply and sees a practical use.

Besides the book, I totally don't agree with a previous comment from a chemical physicist who gave this book just one star.

There are much better options........2007-04-24

This book is only good for someone who is very experienced in these areas of mathematics it discusses. It is not whatsoever for a student who wants to learn these things for the first time. It should be avoided at all costs to someone who does not already know how to do these mathematical operations. If you want to learn techniques of math for science, read Mary Boas's book (excellent) or Glen Fletcher.

If you are looking for an in depth analysis of these subjects after a course in mathematical methods and comfort in mathematics of physics undergraduate, then this book is comprehensive and good reference book. I still, however, find the book very lacking and regret buying it overall.

Nonlinear Interactions: Analytical, Computational, and Experimental Methods

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Nonlinear Interactions: Analytical, Computational, and Experimental Methods
Ali H. Nayfeh
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471175919

Book Description

Nonlinear Interactions provides a coherent and unified treatment of analytical, computational, and experimental methods and concepts of modal interactions. This book is an obvious extension of Ali Nayfeh's well-known book Applied Nonlinear Dynamics (with Bala Balachandran). These methods are used to explore and unfold in a unified manner the fascinating complexities in nonlinear dynamical systems. The systems discussed are drawn from fluid mechanics and structural dynamics.

Nonlinear interactions between high-frequency and low-frequency modes are of great practical importance. Through the mechanisms discussed in this book, energy from high-frequency sources can be transferred to the low-frequency modes of supporting structures and foundations, and the result can be harmful large-amplitude oscillations that decrease their fatigue lives. On the other hand, these mechanisms can be exploited to transfer the energy from a system to a sacrificial subsystem and hence decrease considerably the vibrations of the main system and increase its fatigue life.

Computational Methods for Fluid Dynamics

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Only great for complete novices
Excellent teaching book
One of the best books for CFD code developers
I give it 5 stars
A lot of excellent detail

Computational Methods for Fluid Dynamics
Joel H. Ferziger , and Milovan Peric
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540420746

Book Description

In its 3rd revised and extended edition the book offers an overview of the techniques used to solve problems in fluid mechanics on computers and describes in detail those most often used in practice. Included are advanced methods in computational fluid dynamics, like direct and large-eddy simulation of turbulence, multigrid methods, parallel computing, moving grids, structured, block-structured and unstructured boundary-fitted grids, free surface flows. The 3rd edition contains a new section dealing with grid quality and an extended description of discretization methods. The book shows common roots and basic principles for many different methods. The book also contains a great deal of practical advice for code developers and users; it is designed to be equally useful to beginners and experts.The issues of numerical accuracy, estimation and reduction of numerical errors are dealt with in detail, with many examples.

Customer Reviews:

Only great for complete novices.......2002-01-29

Peric's PhD thesis is one of my most precious possessions. I consider Ferziger to be one of THE greats in Large Eddy Simulation. So I had great hopes for this book. I was warned before I saw it that it contained nothing that I wouldn't already know, but even so it was a big disappointment. I could have written a better book myself and I don't have half the brain of either of the authors. I've looked at it three times and each time turned away in disgust.

This book will point a novice in the correct direction, unlike Roach's book, and unlike Patankar's in a post Rhie-Chow age, but it avoids like the plague any subject with even the slightest whiff of controversy. As any new technique is always controversial, the book was some 5 to 10 years out of date even before it hit the press. Further, it discusses each subject in a very superficial way. More depth is needed.

I want a book that will tell me what the advantages are and how to program the conjugate gradient method, algebraic multigrid, superbee, wall reflection terms for Reynolds Stress, multiphase flow, viscoelasticity, coalescence, the axis in cylindrical coordinates, grid generation, surface tension, adaptive grids, spectral elements etc. This book is no help with any of these.

I frequently get asked "What's a good book for Computational Fluid Dynamics?". I have to admit that there isn't one. The best that I know are the user manuals for the various commercial CFD packages.

To summarise, if programming CFD is a 100 step journey then this book will only take you the first 3 steps, but at least they're 3 steps in the right direction. After you've been programming CFD for a year you can probably toss the book out without any great loss.

Excellent teaching book.......2001-07-10

I found this book an excellent support in teaching and invaluable as an occasional reference in my practical work in industry. It is particularly gratifying to see that free surface flows are covered well. Best book I have seen so far in the field.

One of the best books for CFD code developers.......2001-05-24

This is the best book on CFD I' ve read. It is more useful to those who want to develop their own codes rather than CFD users: It mostly describes in deep detail (although in a concise manner) a single method used by the authors and developed by themselves and their colleagues. It is not intended to be a list of the vast number of CFD techniques developed so far.

Their method is state-of-the-art and they provide plenty of results to support it's quality. It is mostly directed towards incompressible flows. They provide a chapter that extends their method to compressible flows but they do not describe any special convection schemes for flows with shock waves. It can be applied to both structured and arbitrarily unstructured grids, although their approach to the discretization of the convection and diffusion terms is particularly useful in the case of arbitrarily unstrucured grids. State of the art subjects such as multigrid and error-driven grid refinement are also covered and integrated into their method.

I agree with a previous reviewer that they provide a very good coverage of solution methods for linear equation systems which arise in CFD. Most other books on CFD (all the ones that I have read) have a poor coverage of the subject and describe only old and inneficient methods. However even this book does not sufficiently describe conjugate-gradient type methods or Krylov subspace methods in general, but references are provided.

In conclusion, this book is not for beginners but for code developers who have some basic knowlwdge of CFD and a relatively good mathematical background.

I give it 5 stars.......2001-03-16

I agree with the reviewer that said this book is complimentary to an intro text such as Patankar. This is not a cook book for a first time coder. But it is a really great reference for the Finite Volume dilettante.

I really appreciate that all numerical results presented are thoroughly documented. That counts.

Really, really nice chapter on iterative solvers....

Good overall description on many other topics such as multi-grid methods, turbulence, grid geometry and PV coupling.

This book really helped me speed up my homegrown quite a bit.

They also have all kinds of stuff available by ftp....

A lot of excellent detail.......1998-12-22

This is a very good book for learning the details of implementing the Finite Volume method in Computational Fluid Dynamics. I view it as very complimentary to S. V. Patankar's book, which is more general in nature. Both books are geared toward people who want to write computer programs to solve fluid transport problems (heat transfer, Navier-Stokes, etc.) Both tend to focus on numerical issues (as opposed to the physics of transport phenomena). But while Pantankar's book provides a very easy, approachable introduction that is thin on the details, Ferziger & Peric have written a book rich in details. For instance, they devote an entire chapter to solving linear systems of equations. They compare all of the commonly used methods and contrast their rates of convergence for various test cases. This level of detail is great if you already understand the big picture. I think it may be somewhat difficult for someone new to CFD to really understand the finite volume method from this book alone. I would recommend Patankar's book for a good intro and this book for the implementation details.

Advanced Topics in Finite Element Analysis of Structures: With Mathematica and MATLAB Computations

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Advanced Topics in Finite Element Analysis of Structures: With Mathematica and MATLAB Computations
M. Asghar Bhatti
Manufacturer: Wiley
ProductGroup: Book
Binding: Hardcover

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ASIN: 0471648078

Book Description

Starting from governing differential equations, a unique and consistently weighted residual approach is used to present advanced topics in finite element analysis of structures, such as mixed and hybrid formulations, material and geometric nonlinearities, and contact problems. This book features a hands-on approach to understanding advanced concepts of the finite element method (FEM) through integrated Mathematica and MATLAB® exercises.

Smooth Particle Applied Mechanics: The State of the Art (Advanced Series in Nonlinear Dynamics) (Advanced Series in Nonlinear Dynamics)

Average customer rating:

SPAM and sph, a superior route to continuum solutions

Smooth Particle Applied Mechanics: The State of the Art (Advanced Series in Nonlinear Dynamics) (Advanced Series in Nonlinear Dynamics)
William G. Hoover
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover

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ASIN: 9812700021

Customer Reviews:

SPAM and sph, a superior route to continuum solutions.......2007-01-15

This excellent monograph, prepared by Professor Hoover with the help of his wife Carol, contains all that a reader needs to understand, develop, and use smooth-particle techniques for computer simulations of continua. Applications to solid deformation and to fluid flow display a variety of useful techniques for avoiding the usual pitfalls with standard sph.

An Introduction to the Mathematical Theory of Waves (Student Mathematical Library, V. 3)

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An Introduction to the Mathematical Theory of Waves (Student Mathematical Library, V. 3)
Roger Knobel
Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Paperback

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ASIN: 0821820397

Book Description

This book is based on an undergraduate course taught at the IAS/Park City Mathematics Institute (Utah) on linear and nonlinear waves. The first part of the text overviews the concept of a wave, describes one-dimensional waves using functions of two variables, provides an introduction to partial differential equations, and discusses computer-aided visualization techniques.

The second part of the book discusses traveling waves, leading to a description of solitary waves and soliton solutions of the Klein-Gordon and Korteweg-deVries equations. The wave equation is derived to model the small vibrations of a taut string, and solutions are constructed via d'Alembert's formula and Fourier series.

Book Description

This book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory and explains how to use these methods to obtain approximate analytical solutions to differential and difference equations. These methods allow one to analyze physics and engineering problems that may not be solvable in closed form and for which brute-force numerical methods may not converge to useful solutions. The objective of this book is to teaching the insights and problem-solving skills that are most useful in solving mathematical problems arising in the course of modern research. Intended for graduate students and advanced undergraduates, the book assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations; develops local asymptotic methods for differential and difference equations; explains perturbation and summation theory; and concludes with a an exposition of global asymptotic methods, including boundary-layer theory, WKB theory, and multiple-scale analysis. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach the reader how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions; over 600 problems, of varying levels of difficulty; and an appendix summarizing the properties of special functions.

Customer Reviews:

Deeply insightful and utterly fascinating.......2006-12-20

I had the privilege to explore this guide to the universe of asymptotics under Prof. Bender. I used to think, and still do (about 2 decades on), that this book is like the Rosetta Stone, and enables us to solve anything in applied mathematics.

A must have for anyone looking to understand the incredible universe we find ourselves in!

The Classic Text on Asymptotics.......2005-12-09

I am a mathematics professor, and asymptotic methods is my area of expertise. Bender and Orszag was the standard text on this topic in the early 1980s, and it remains by far the most thorough book on the subject. I had two courses from it in graduate school and have taught from it 3 times now. I have never found a mistake. The book is very well written; its only weakness is that its graphics reflect the technology of the 1970s. Nevertheless, I am teaching from it again next year, because it is in a class by itself.

There is one thing that individual readers and faculty users should be aware of. Some of the exercises, including a few marked as "intermediate," are incredibly difficult. My instructor made the mistake of assigning exercises without working them first. I am careful not to assign any exercises until after I have worked them.

A Classic Resource.......2005-10-07

I'll echo the sentiments of the other reviewers here. I have a well-worn and well-used copy of the first (1978) edition. Believe it or not, I actually had a chance to use these methods as recently as last month (September 2005). I would recommend, though, if you want to get the most out of this book, pick up a symbolic calculation program or calculator capable of doing symbolic math. I use the open-source programs Maxima and Axiom for this, but if you want to actually spend money, Amazon has some calculators that will handle this sort of thing.

Extremely useful.......2003-12-13

Great for anyone taking Partial differential equations, mathematical physics, and the related courses. Carl Bender is a master of the field as well as a great book writer, as well as Orszag. The only complaint is the type setting--a bit too small. But not a big problem

Excellent.......2003-10-19

This is an essential textbook for all applied mathematicians, physicists and research oriented engineers. It is very well written, and explains an enormous lot. It explains it all very well too. I've used chapter 3 and 6 in class, and they were full of insights and information that you cannot find in any other textbook.

Advanced Design Problems in Aerospace Engineering: Volume 1: Advanced Aerospace Systems (Mathematical Concepts and Methods in Science and Engineering)

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Advanced Design Problems in Aerospace Engineering: Volume 1: Advanced Aerospace Systems (Mathematical Concepts and Methods in Science and Engineering)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0306484633

Book Description

Advanced Design Problems in Aerospace Engineering, Volume 1: Advanced Aerospace Systems presents six authoritative lectures on the use of mathematics in the conceptual design of various types of aircraft and spacecraft. It covers the following topics: design of rocket-powered orbital spacecraft (Miele/Mancuso), design of Moon missions (Miele/Mancuso), design of Mars missions (Miele/Wang), design of an experimental guidance system with a perspective flight path display (Sachs), neighboring vehicle design for a two-stage launch vehicle (Well), and controller design for a flexible aircraft (Hanel/Well). This is a reference book of interest to engineers and scientists working in aerospace engineering and related topics.

MultiBody System SIMulation: Numerical Methods, Algorithms, and Software (Lecture Notes in Computational Science and Engineering)

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Not Quite What One Would Expect

MultiBody System SIMulation: Numerical Methods, Algorithms, and Software (Lecture Notes in Computational Science and Engineering)
Reinhold von Schwerin
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 3540656626

Book Description

The book presents innovative methods for the solution of multibody descriptor models. It emphasizes the interdependence of modeling and numerical solution of the arising system of differential-algebraic equations (DAE). Here, it is shown that modifications of non-stiff ODE-solvers are very effective for a large class of multibody systems. In particular, implicit methods are found to dovetail optimally with the linearly implicit structure of the model equations, allowing an inverse dynamics approach for their solution. Furthermore, the book stresses the importance of software development in scientific computing and thus presents a complete example of an interdisciplinary problem solution for an important field of application from technical mechanics.

Customer Reviews:

Not Quite What One Would Expect.......2002-02-07

While the book contained an enormous amount of useful information and is elagantly written, it missed the mark on providing useful, "here's how you do it..", numerical methods and algorithms for MBS as the title implies. Since the book originated from lecture notes, it was assumed there would be a few simple examples of MBS which would be solved, in detail, using different methods to illustrate various techniques and formulations. The Chapter on software engineering, I feel, is completely out of place. Again, a useful view but not necessary within the topic of MBS and in the context of this book. To the extent software engineering is discussed, it's best left to a book explicitily on software engineering. It's between too much and not enough. In my opinion, this book would be most useful as a reference to individuals who already have an intimate knowledge of MBS and numerical methods and not to individuals with knowledge in mechanics and software seeking to learn practical formulations and numerical methods for MBS. For the price of the book, I was quite dissapointed amount of useful, "hands on" material. On a positive note, the book does cover many topics in numerical methods (e.g. integrators, contraints..) with great detail. The book is very well written, easy to read, and it apparent that great deal of effort was made to provide elegant formulas and consise notation.

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