zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A first course in integral equations. (English) Zbl 0924.45001
Singapore: World Scientific. xi, 208 p. £ 23.00 (1997).
This book is an elementary introduction to integral equations and the author is mainly interested in solving such equations explicitly or approximately; it contains a lot of examples. It is not concerned with the theory of integral equations, questions of existence and uniqueness of solutions, even questions of convergence of approximate solutions to a solution are not touched. In Chapter 1 the usual classification of integral equations is given. Further the question of converting integral equations and initial and boundary value problems of ordinary differential equations into each other is discussed and illustrated by examples. The further Chapters 2 to 6 are dedicated to solving explicitly Fredholm and Volterra integral equations, integro-differential equations and nonlinear integral equations by several methods which are: Decomposition method, which was developed by {\it G. Adomian} [Solving frontier problems of physics: the decomposition method (1994: Zbl 0802.65122)], the solution is given by a series $u(x)=\sum^\infty_{n=0}u_n(x)$; direct computation method for special kernels; successive approximation; successive substitution; series expansion; converting of integral equations into initial or boundary value problems for ordinary differential equations. The methods are not discussed in general but illustrated by many examples, and the different methods are compared. This book should be useful for engineers who are only interested in solving integral equations.

45-01Textbooks (integral equations)
65R20Integral equations (numerical methods)
00A06Mathematics for non-mathematicians