Publication is planned for April 2003 | Paperback
| 430 pages
100 line diagrams 3 colour plates | ISBN:
0-521-00794-1
Publication is planned for April 2003 | Hardback
(| 430 pages 100
line diagrams 3 colour plates | ISBN: 0-521-81026-4
Numerical analysis provides the theoretical
foundation for the
numerical algorithms we rely on to solve
a multitude of
computational problems in science. Based
on a successful course
at Oxford University, this book covers a
wide range of such
problems ranging from the approximation of
functions and
integrals to the approximate solution of
algebraic,
transcendental, differential and integral
equations. Throughout
the book, particular attention is paid to
the essential qualities
of a numerical algorithm - stability, accuracy,
reliability and
efficiency. The authors go further than simply
providing recipes
for solving computational problems. They
carefully analyse the
reasons why methods might fail to give accurate
answers, or why
one method might return an answer in seconds
while another would
take billions of years. This book is ideal
as a text for students
in the second year of a university mathematics
course. It
combines practicality regarding applications
with consistently
high standards of rigour.
Contents
1. Solution of equations by iteration; 2.
Solution of systems of
linear equations; 3. Special matrices; 4.
Simultaneous nonlinear
equations; 5. Eigenvalues and eigenvectors
of a symmetric matrix;
6. Polynomial interpolation; 7. Numerical
integration - I; 8.
Polynomial approximation in the ?-norm; 9.
Approximation in the 2-norm;
10. Numerical integration - II; 11. Piecewise
polynomial
approximation; 12. Initial Value Problems
for ODEs; 13. Boundary
Value Problems for ODEs; 14. The Finite Element
Method; Appendix
1. An overview of results from real analysis;
Appendix 2. WWW-resources.
March 2003 | Paperback (Mixed Media) | 528
pages | ISBN: 0-521-01718-1
March 2003 | Hardback (Mixed Media) | 528
pages | ISBN: 0-521-81589-4
This book provides a rigorous course in the
calculus of functions
of a real variable. Its gentle approach,
particularly in its
early chapters, makes it especially suitable
for students who are
not headed for graduate school but, for those
who are, this book
also provides the opportunity to engage in
a penetrating study of
real analysis. The companion onscreen version
of this text
contains hundreds of links to alternative
approaches, more
complete explanations and solutions to exercises;
links that make
it more friendly than any printed book could
be. In addition,
there are links to a wealth of optional material
that an
instructor can select for a more advanced
course, and that
students can use as a reference long after
their first course has
ended. The onscreen version also provides
exercises that can be
worked interactively with the help of the
computer algebra
systems that are bundled with Scientific
Notebook.
Contents
1. The emergence of rigorous calculus; 2.
Mathematical grammar; 3.
Strategies for writing proofs; 4. Elements
of set theory; 5. The
real number system; 6. Elementary topology
of the real line; 7.
Limits of sequences; 8. Limits and continuity
of functions; 9.
Differentiation; 10. The exponential and
logarithmic functions;
11. The Riemann integral; 12. Infinite series;
13. Improper
integrals; 14. Sequences and series of functions;
15. Calculus of
a complex variable; 16. Integration of functions
of two
variables; 17. Sets of measure zero; 18.
Calculus of several
variables.
Publication is planned for March 2003 | Paperback
| 404 pages
55 line diagrams | ISBN: 0-521-52344-3
Now available in the Cambridge Mathematical
Library, the classic
work from Luis Santalo. Integral geometry
originated with
problems on geometrical probability and convex
bodies. Its later
developments, however, have proved to be
useful in several fields
ranging from pure mathematics (measure theory,
continuous groups)
to technical and applied disciplines (pattern
recognition,
stereology). The book is a systematic exposition
of the theory
and a compilation of the main results in
the field. The volume
can be used to complement courses on differential
geometry, Lie
groups or probability or differential geometry.
It is ideal both
as a reference and for those wishing to enter
the field.
Contents
Part I. Integral Geometry in the Plane: 1.
Convex sets in the
plane; 2. Sets of points and Poisson processes
in the plane; 3.
Sets of lines in the plane; 4. Pairs of points
and pairs of
lines; 5. Sets of strips in the plane; 6.
The group of motions in
the plane: kinematic density; 7. Fundamental
formulas of Poincare
and Blaschke; 8. Lattices of figures; Part
II. General Integral
Geometry: 9. Differential forms and Lie groups;
10. Density and
measure in homogenous spaces; 11. The affine
groups; 12. The
group of motions in En; Part III. Integral
Geometry in En: 13.
Convex sets in En; 14. Linear subspaces,
convex sets and compact
manifolds; 15. The kinematic density in En;
16. Geometric and
statistical applications: stereology; Part
IV. Integral Geometry
in Spaces of Constant Curvature: 17. Noneuclidean
integral
geometry; 18. Crofton’s formulas and the
kinematic fundamental
formula in noneuclidean spaces; 19. Integral
geometry and
foliated spaces: trends in integral geometry.
Publication is planned for March 2003 | Paperback
| 176 pages
22 line diagrams 141 exercises | ISBN: 0-521-52903-4
Publication is planned for March 2003 | Hardback
| 176 pages 22
line diagrams 141 exercises | ISBN: 0-521-82151-7
The aim of this book is to provide in depth
coverage of selected
areas of graph theory, and throughout the
focus is mainly on
symmetry properties of graphs. Standard topics
on graph
automorphisms are presented early on, while
in later chapters,
more specialised topics are tackled, such
as graphical regular
representations and pseudosimilarity. The
four final chapters are
devoted to the reconstruction problem, and
here greater emphasis
is given to those results that involve the
symmetry of graphs. As
much as possible, the authors have tried
to present results and
proofs which are not often to be found in
textbooks. Any student
who has mastered the contents of this book
will be well prepared
for current research in many aspects of the
theory of graph
automorphisms and the reconstruction problem.
Contents
1. Graphs and groups: preliminaries; 2. Various
types of graph
symmetry; 3. Cayley graphs; 4. Orbital graphs
and strongly
regular graphs; 5. Graphical regular representations
and
pseudosimilarity; 6. Products of graphs;
7. Special cases of
vertex-transitive graphs and digraphs; 8.
The reconstruction
conjectures; 9. Reconstructuring from subdecks;
10. Counting
arguments in vertex-reconstruction; 11. Counting
arguments in
edge-reconstruction; Bibliography; List of
notation; Index of
terms and definitions