Ebook Download Finite Difference Equations (Dover Books on Mathematics), by H. Levy, F. Lessman, Mathematics
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Finite Difference Equations (Dover Books on Mathematics), by H. Levy, F. Lessman, Mathematics
Ebook Download Finite Difference Equations (Dover Books on Mathematics), by H. Levy, F. Lessman, Mathematics
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The calculus of finite differences is an area of mathematics important to a broad range of professions, from physical science and engineering to social sciences and statistics. This comprehensive study, directed to advanced undergraduate-level students, graduate students, and professionals, concentrates primarily on how the calculus of finite differences may be used as an approximation method for solving troublesome differential equations.
Stressing problem solving rather than pure mathematics, the authors begin with elementary difference operations, treat interpolation and extrapolation, the derivation of difference equations, solution of linear difference equations with variable and constant coefficients, and the properties of the general difference equations. Chapter 5 develops the various modes of expansion of the solutions of nonlinear equations and the conditions under which these are valid. In addition, in Chapter 6, there is the estimation of the eigenvalues that arise in connection with linear difference equations, and the investigation of the properties of the corresponding orthogonal functions in the form of factorial series. The final two chapters treat applications of difference equations, and the investigation of the properties of the corresponding orthogonal functions in the form of factorial series. The final two chapters treat applications of difference equations and difference equations associated with functions of two variables. Included are a number of exercises with answers.
- Sales Rank: #1638686 in Books
- Published on: 2011-11-17
- Released on: 2011-10-27
- Original language: English
- Number of items: 1
- Dimensions: 8.50" h x .64" w x 5.51" l, .70 pounds
- Binding: Paperback
- 304 pages
Most helpful customer reviews
13 of 13 people found the following review helpful.
Clear introduction and very useful exercises
By Juan Pablo Pira
As offered on the back cover, stress is on problem solving and not on pure mathematics. However, this does not mean that the treatment is informal. The language is precise and the concepts are clearly defined. The exercises are useful and range from very easy to somewhat challenging. Preliminaries have been kept to a minimum and people who have taken their Calculus and Linear Algebra should have no problems working their way through this book.
8 of 8 people found the following review helpful.
Very good introduction
By Bruno Vanbever
The best and most accessible introduction to FDE's I have seen , compared with other
books about the same subject like :
-P Cull , M Flahive and R Robson (Springer)
-Saber N Elaydi (Springer)
-Murray R Spiegel (Schaum)
-Walter G Kelley and Allan C Peterson (Harcourt Academic Press)
-Ravi P Agarwal (Marcel Dekker Inc) [graduate level !]
-G Boole
which are , in my opinion , for more advanced students.
The Schaum book is good for it's real world problems but sometimes confusing
because it often do not use the unit step.
This book (from Levy & Lessman) starts with a relative extensive study about the difference
calculus (a good preparation to solve FDE's) which is not the case in most other books about finite difference
equations (FDE's) except the book of Murray R Spiegel (Schaum).
It also contains an interesting chapter about the use of FDE's to solve real world problems.Maybe difficult
for students in pure mathematics to understand this chapter completely.
The explanations are logical , with sufficient intermediate steps and several examples.
Do not buy this book to approximate ordinary differential equations as mentioned
at the back cover because the explanation of this subject is poor , although it is
relative easy to adapt FDE's to solve (troublesome) ordinary differential equations numericaly when you have
read the book!
It is very good on how to solve linear ordinary difference equations (and systems of FDE's)
with constant coefficients (also some pseudo nonlinear FDE's),only some partial finite difference equations
with constant coefficients (because it reaches quickly the frontiers of math at the time the book was written)
and to do some interpolation and extrapolation in difference tables.
Chapter 5 deals with the general analytical approximative partial solutions of nonlinear (only first order of type Y(n+1)=f[Y(n)]) FDE's
with the help of "web plots".
Regrettable that "generating functions" and Z-transforms are not used in this book to solve linear FDE's with variable coefficients.
The book contains some mistakes (not only typos!) like:
page 27 5 Show that ...
page 33 exercise XIX 1
page 35 exercise xx 4
page 35 miscellaneous exercises 3 (i) and (ii)
page 47 expression at the bottom
page 78 continuation of example 2
page 85 example 2
page 136 continuation of example 2
page 149 Hence v(x)=-2.A.(-2)^x-7.B.3^x+2.C.5^x
page 153 example 2 at the end
...
page 271 answer to exercise (xx) 5
page 272 answer to exercise chapter4:6
In spite of this mistakes I recommend the book very much because of it's clearness!
It is suitable for home study and inexpensive.
2 of 19 people found the following review helpful.
Interesting
By A Customer
Very good book on how to use finite difference equations.
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