(Hardback)
ISBN-10: 0-19-921525-1
ISBN-13: 978-0-19-921525-6
Estimated publication date: July 2007
624 pages, 234x156 mm
Series: Oxford Graduate Texts in Mathematics number 14
Description
Applications to many fields of mathematical modelling
Clear, logical exposition
Numerous examples, detailed proofs, and cross-referencing aid
understanding
Companion website provides further examples and problems
This graduate level text covers the theory of stochastic
integration, an important area of Mathematics that has a wide
range of applications, including financial mathematics and signal
processing. Aimed at graduate students in Mathematics,
Statistics, Probability, Mathematical Finance, and Economics, the
book not only covers the theory of the stochastic integral in
great depth but also presents the associated theory (martingales,
Levy processes) and important examples (Brownian motion, Poisson
process).
Readership: Graduates and researchers in Mathematics, Statistics,
Probability, Mathematical Finance, and Economics
Contents
1. Stochastic processes
2. Stochastic integration with locally square-integrable
martingales
3. The structure of local martingales
4. General theory of stochastic integration
5. Some other theorems
6. Ito's formula
7. Processes with independent increments
Appendices
A. Results from measure theory
B. Wiener processes
C. Poisson processes
(paper)
ISBN-10: 0-19-921203-1
ISBN-13: 978-0-19-921203-3
Estimated publication date: August 2007
450 pages, 272 illus., 246x171 mm
Description
Over 500 exercises and fully worked solutions
Can be easily adapted for coursework or self-study
An excellent accompaniment to the 4th edition of Nonlinear
Ordinary Differential Equations (Jordan and Smith, OUP, 2007)
Over 250 figures
Ideal for lecturers and students in science and engineering
An ideal companion to the new 4th Edition of Nonlinear Ordinary
Differential Equations by Jordan and Smith (OUP, 2007), this text
contains over 500 problems and fully-worked solutions in
nonlinear differential equations. With 272 figures and diagrams,
subjects covered include phase diagrams in the plane,
classification of equilibrium points, geometry of the phase
plane, perturbation methods, forced oscillations, stability,
Mathieu's equation, Liapunov methods, bifurcations and manifolds,
homoclinic bifurcation, and Melnikov's method.
The problems are of variable difficulty; some are routine
questions, others are longer and expand on concepts discussed in
Nonlinear Ordinary Differential Equations 4th Edition, and in
most cases can be adapted for coursework or self-study.
Both texts cover a wide variety of applications whilst keeping
mathematical prequisites to a minimum making these an ideal
resource for students and lecturers in engineering, mathematics
and the sciences.
Readership: An ideal resource for students and lecturers in
engineering, mathematics and the sciences.
(hardback)
ISBN-10: 0-19-920824-7
ISBN-13: 978-0-19-920824-1
(paperback)
ISBN-10: 0-19-920825-5
Estimated publication date: August 2007
560 pages, line illus. throughout, 246x171 mm
Series: Oxford Texts in Applied and Engineering Mathematics
number 10
Description
Emphasizes the practical and application side of the subject
Ideal for lecturers and students in science and engineering
Highly illustrated
Worked examples and exercises are included throughout the text,
with answers to the exercises included at the end of the book
Over 500 end-of-chapter problems are provided
Fully worked solutions to the end-of-chapter problems may be
found in a companion volume, Nonlinear Ordinary Differential
Equations: Problems and Solutions (OUP, 2007)
New to this edition
Extended sections on Mathieu's equation
New section on Liapunov exponents added
Exercises added throughout the text
Appendices extended to include trigonometric identities
This is a thoroughly updated and expanded 4th edition of the
classic text Nonlinear Ordinary Differential Equations by Dominic
Jordan and Peter Smith. Including numerous worked examples and
diagrams, further exercises have been incorporated into the text
and answers are provided at the back of the book. Topics include
phase plane analysis, nonlinear damping, small parameter
expansions and singular perturbations, stability, Liapunov
methods, Poincare sequences, homoclinic bifurcation and Liapunov
exponents.
Over 500 end-of-chapter problems are also included and as an
additional resource fully-worked solutions to these are provided
in the accompanying text Nonlinear Ordinary Differential
Equations: Problems and Solutions, (OUP, 2007).
Both texts cover a wide variety of applications whilst keeping
mathematical prequisites to a minimum making these an ideal
resource for students and lecturers in engineering, mathematics
and the sciences.
Readership: An ideal resource for students and lecturers in
engineering, mathematics and the sciences.