|
Showing 1 - 19 of
19 matches in All Departments
This book is intended for students of computational systems biology
with only a limited background in mathematics. Typical books on
systems biology merely mention algorithmic approaches, but without
offering a deeper understanding. On the other hand, mathematical
books are typically unreadable for computational biologists. The
authors of the present book have worked hard to fill this gap. The
result is not a book on systems biology, but on computational
methods in systems biology. This book originated from courses
taught by the authors at Freie Universität Berlin. The guiding
idea of the courses was to convey those mathematical insights that
are indispensable for systems biology, teaching the necessary
mathematical prerequisites by means of many illustrative examples
and without any theorems. The three chapters cover the mathematical
modelling of biochemical and physiological processes, numerical
simulation of the dynamics of biological networks and
identification of model parameters by means of comparisons with
real data. Throughout the text, the strengths and weaknesses of
numerical algorithms with respect to various systems biological
issues are discussed. Web addresses for downloading the
corresponding software are also included.
In this book, the new and rapidly expanding field of scientific
computing is understood in a double sense: as computing for
scientific and engineering problems and as the science of doing
such computations. Thus scientific computing touches at one side
mathematical modelling (in the various fields of applications) and
at the other side computer science. As soon as the mathematical
models de scribe the features of real life processes in sufficient
detail, the associated computations tend to be large scale. As a
consequence, interest more and more focusses on such numerical
methods that can be expected to cope with large scale computational
problems. Moreover, given the algorithms which are known to be
efficient on a tradi tional computer, the question of
implementation on modern supercomputers may get crucial. The
present book is the proceedings of a meeting on "Large Scale
Scientific Computing," that was held a t the Oberwolfach
Mathematical Institute (July 14-19, 1985) under the auspices of the
Sonderforschungsbereich 123 of the University of Heidelberg.
Participants included applied scientists with computational
interests, numerical analysts, and experts on modern parallel
computers. 'l'he purpose of the meeting was to establish a common
under standing of recent issues in scientific computing, especially
in view of large scale problems. Fields of applications, which have
been covered, included semi-conductor design, chemical combustion,
flow through porous media, climatology, seismology, fluid dynami.
cs, tomography, rheology, hydro power plant optimization, subwil. y
control, space technology."
For rather a long time numerical results in chemical kinetics could
only be obtained for very simple chemical reactions, most of which
were of minor practi ca 1 importance. The avail abil ity of fast
computers has provi ded new opportunities for developments in
chemical kinetics. Chemical systems of practical interest are
usually very complicated. They consi st of a great number of
different el ementary chemi cal reacti ons, mostly with rate
constants differi ng by many orders of magni tude, frequently with
surface reacti on steps and often wi th transport processes. The
deri vati on of a 'true' chemical mechani sm can be extremely
cumbersome. Mostly this work is done by setting up 'reaction
models' which are im- proved step by step in comparison with
precise experimental data. At this early stage mathematics is
involved, which may al ready be rather complicated. Mathematical
methods such as pertubation theory, graph theory, sensitivity
analysis or numerical integration are necessary for the derivation
and application of optimal chemical reaction models. Most
theoretical work aimed at improving the mathematical methods was
done on chemical reactions which mostly were of little practical
im- portance. Chemi cal engi neers, who evi dently k now well how
important the chemical model s and their dynamics are for reactor
desi gn, have al so to be convinced not only on the theoretical
work but also on its practical applic- abil ity.
This book deals with the efficient numerical solution of
challenging nonlinear problems in science and engineering, both in
finite dimension (algebraic systems) and in infinite dimension
(ordinary and partial differential equations). Its focus is on
local and global Newton methods for direct problems or Gauss-Newton
methods for inverse problems. The term 'affine invariance' means
that the presented algorithms and their convergence analysis are
invariant under one out of four subclasses of affine
transformations of the problem to be solved. Compared to
traditional textbooks, the distinguishing affine invariance
approach leads to shorter theorems and proofs and permits the
construction of fully adaptive algorithms. Lots of numerical
illustrations, comparison tables, and exercises make the text
useful in computational mathematics classes. At the same time, the
book opens many directions for possible future research.
Well-known authors; Includes topics and results that have
previously not been covered in a book; Uses many interesting
examples from science and engineering; Contains numerous homework
exercises; Scientific computing is a hot and topical area
This book introduces the main topics of modern numerical
analysis: sequence of linear equations, error analysis, least
squares, nonlinear systems, symmetric eigenvalue problems,
three-term recursions, interpolation and approximation, large
systems and numerical integrations. The presentation draws on
geometrical intuition wherever appropriate and is supported by a
large number of illustrations, exercises, and examples.
This book deals with the efficient numerical solution of
challenging nonlinear problems in science and engineering, both in
finite and in infinite dimension. Its focus is on local and global
Newton methods for direct problems or Gauss-Newton methods for
inverse problems. Lots of numerical illustrations, comparison
tables, and exercises make the text useful in computational
mathematics classes. At the same time, the book opens many
directions for possible future research.
This introductory book directs the reader to a selection of useful elementary numerical algorithms on a reasonably sound theoretical basis, built up within the text. The primary aim is to develop algorithmic thinking -- emphasizing long living computational concepts over fast changing software issues. The guiding principle is to explain modern numerical analysis concepts applicable in complex scientific computing at much simpler model problems. For example, the two adaptive techniques in numerical quadrature elaborated here carry the germs for either extrapolation methods or multigrid methods in differential equations, which are not treated here. The presentation draws on geometrical intuition wherever appropriate, supported by a large number of illustrations. Numerous exercises are included for further practice and improved understanding. This text will appeal to undergraduate and graduate students as well as researchers in mathematics, computer science, science, and engineering. At the same time it is addressed to practical computational scientists who, via self-study, wish to become acquainted with modern concepts of numerical analysis and scientific computing on an elementary level. Sole prerequisite is undergraduate knowledge in Linear Algebra and Calculus.
This text provides an introduction to the numerical solution of initial and boundary value problems in ordinary differential equations on a firm theoretical basis. The book strictly presents numerical analysis as part of the more general field of scientific computing. Important algorithmic concepts are explained down to questions of software implementation. For initial value problems a dynamical systems approach is used to develop Runge-Kutta, extrapolation, and multistep methods. For boundary value problems including optimal control problems both multiple shooting and collocation methods are worked out in detail. Graduate students and researchers in mathematics, computer science, and engineering will find this book useful. Chapter summaries, detailed illustrations, and exercises are contained throughout the book with many interesting applications taken from a rich variety of areas.Peter Deuflhard is founder and president of the Zuse Institute Berlin (ZIB) and full professor of scientific computing at the Free University of Berlin, department of mathematics and computer science.Folkmar Bornemann is full professor of scientific computing at the Center of Mathematical Sciences, Technical University of Munich.
These lecture notes by very authoritative scientists survey recent
advances of mathematics driven by industrial application showing
not only how mathematics is applied to industry but also how
mathematics has drawn benefit from interaction with real-word
problems.
The famous David Report underlines that innovative high technology
depends crucially for its development on innovation in mathematics.
The speakers include three recent presidents of ECMI, one of
ECCOMAS (in Europe) and the president of SIAM.
|
Computational Molecular Dynamics: Challenges, Methods, Ideas - Proceeding of the 2nd International Symposium on Algorithms for Macromolecular Modelling, Berlin, May 21-24, 1997 (Paperback, Softcover reprint of the original 1st ed. 1999)
Peter Deuflhard, Jan Hermans, Benedict Leimkuhler, Alane Mark, Sebastian Reich, …
|
R3,027
Discovery Miles 30 270
|
Ships in 10 - 15 working days
|
On May 21-24, 1997 the Second International Symposium on Algorithms for Macromolecular Modelling was held at the Konrad Zuse Zentrum in Berlin. The event brought together computational scientists in fields like biochemistry, biophysics, physical chemistry, or statistical physics and numerical analysts as well as computer scientists working on the advancement of algorithms, for a total of over 120 participants from 19 countries. In the course of the symposium, the speakers agreed to produce a representative volume that combines survey articles and original papers (all refereed) to give an impression of the present state of the art of Molecular Dynamics.The 29 articles of the book reflect the main topics of the Berlin meeting which were i) Conformational Dynamics, ii) Thermodynamic Modelling, iii) Advanced Time-Stepping Algorithms, iv) Quantum-Classical Simulations and Fast Force Field and v) Fast Force Field Evaluation.
In many scientific or engineering applications, where ordinary
differen tial equation (OOE), partial differential equation (POE),
or integral equation (IE) models are involved, numerical simulation
is in common use for prediction, monitoring, or control purposes.
In many cases, however, successful simulation of a process must be
preceded by the solution of the so-called inverse problem, which is
usually more complex: given meas ured data and an associated
theoretical model, determine unknown para meters in that model (or
unknown functions to be parametrized) in such a way that some
measure of the "discrepancy" between data and model is minimal. The
present volume deals with the numerical treatment of such inverse
probelms in fields of application like chemistry (Chap. 2,3,4,
7,9), molecular biology (Chap. 22), physics (Chap. 8,11,20),
geophysics (Chap. 10,19), astronomy (Chap. 5), reservoir simulation
(Chap. 15,16), elctrocardiology (Chap. 14), computer tomography
(Chap. 21), and control system design (Chap. 12,13). In the actual
computational solution of inverse problems in these fields, the
following typical difficulties arise: (1) The evaluation of the sen
sitivity coefficients for the model. may be rather time and storage
con suming. Nevertheless these coefficients are needed (a) to
ensure (local) uniqueness of the solution, (b) to estimate the
accuracy of the obtained approximation of the solution, (c) to
speed up the iterative solution of nonlinear problems. (2) Often
the inverse problems are ill-posed. To cope with this fact in the
presence of noisy or incomplete data or inev itable discretization
errors, regularization techniques are necessary."
This book is intended for students of computational systems biology
with only a limited background in mathematics. Typical books on
systems biology merely mention algorithmic approaches, but without
offering a deeper understanding. On the other hand, mathematical
books are typically unreadable for computational biologists. The
authors of the present book have worked hard to fill this gap. The
result is not a book on systems biology, but on computational
methods in systems biology. This book originated from courses
taught by the authors at Freie Universitat Berlin. The guiding idea
of the courses was to convey those mathematical insights that are
indispensable for systems biology, teaching the necessary
mathematical prerequisites by means of many illustrative examples
and without any theorems. The three chapters cover the mathematical
modelling of biochemical and physiological processes, numerical
simulation of the dynamics of biological networks and
identification of model parameters by means of comparisons with
real data. Throughout the text, the strengths and weaknesses of
numerical algorithms with respect to various systems biological
issues are discussed. Web addresses for downloading the
corresponding software are also included.
This textbook deals with the numerical solution of initial and
boundary value problems for ordinary differential equations. It
takes the reader directly to the practically proven methods - from
their theoretical foundation via their analysis to questions of
implementation. The textbook contains a wealth of exercises
together with numerous application examples. Sections of this third
edition have been revised and it has been supplemented with MATLAB
codes.
|
Atlas der Weltbilder (German, Hardcover)
Christoph Markschies, Ingeborg Reichle, Jochen Bruning, Peter Deuflhard; Contributions by Steffen Siegel, …
|
R5,939
R5,093
Discovery Miles 50 930
Save R846 (14%)
|
Ships in 10 - 15 working days
|
Praktiken visueller Welterzeugung in Form von Weltbildern lassen
sich bereits in der Antike beobachten und haben sich bis heute als
Mittel zur Konstruktion von Ordnungsvorstellungen bewahrt. Seit
jeher steht der begrifflichen Ordnung der Welt eine modellhaft
anschauliche Ordnung gegenuber. Die grundlegende Bedeutung, die
Anschaulichkeit fur unser Verstandnis von der Welt spielt und die
die vielfaltigsten Weltbilder hervorgebracht hat, ist jedoch mehr
als eine blosse Wiederholung des Sehens. Die Bildwelten der
Weltbilder geben uns nicht nur ein anschauliches Bild von der Welt
und vom Kosmos. Sie sind zugleich wirkungsmachtige Instrumente zum
praktischen und theoretischen Handeln in der Welt und formen auf
unterschiedlichste Weise unsere Vorstellungen von der Welt und
unsere Weltanschauung. Die grundlegenden Fragen, die dabei gestellt
werden, haben sich durch die Jahrhunderte nicht wirklich geandert.
Sie betreffen die den Menschen umfassende Ordnung und seine
Stellung innerhalb dieser Ordnung: Welche Gestalt hat die Welt?
Welche Krafte und Ideen wirken in ihr? Woraus besteht sie? Wie ist
sie entstanden? Wie sieht ihre Zukunft aus? Bereits die fruhen
Beispiele von Weltbildern machen deutlich, dass die sowohl in
Bildern als auch in Erzahlungen zur Erscheinung gebrachte
Wirklichkeit immer eine vom Menschen hervorgebrachte ist und daher
stets interpretierte Wirklichkeit und symbolische Konstruktion
bedeutet. Die gesammelten Beispiele reprasentieren zugleich
unterschiedliche visuelle Medien, die im Dienst der Konstruktion
der Welt als Bild stehen. Damit ist die Geschichte der Weltbilder
nicht nur eine Geschichte wechselnder Weltvorstellungen, sondern
zugleich auch eine Geschichte wechselnder Darstellungsmethoden und
unterschiedlicher Tragermedien. Der Atlas der Weltbilder behandelt
ein breites Spektrum von Artefakten und schreitet einen grossen
zeitlichen Bogen ab, der mit altorientalischen und altagyptischen
Weltkonzeptionen beginnt und mit aktuellen Simulationen der
Astrophysik endet. Der Atlas der Weltbilder dokumentiert somit
Aspekte der Kulturgeschichte visueller Welterzeugung in Form von
Weltbildern aus den zuruckliegenden zweieinhalb Jahrtausenden.
Paradigmatische Analysen der Prinzipien und Funktionen sowie der
Geschichte und Bedeutung von Weltbildern geben erstmals umfassenden
Aufschluss uber dieses umfangreiche Themengebiet."
Hat Europa die Zentralperspektive erfunden? Oder existieren nicht
auch Alternativen, den optischen Sprung aus zwei in drei
Dimensionen zu realisieren, aus dem Bild in den Raum? Diesen Fragen
widmet sich das vorliegende Buch aus den Blickwinkeln von
Kunstgeschichte, Bildwissenschaft, Mathematik, Informatik,
Psychologie, Museumspädagogik und Philosophie. Historisch gesehen
ist die mathematisch konstruierbare "Perspektive" ein Produkt der
frühen italienischen Renaissance. Seit ihrer Erfindung wurden
jedoch immer wieder Zweifel an ihrer ästhetischen Substanz laut,
die sich in den nächsten Jahrhunderten insbesondere im
ostasiatischen Raum ausbreiteten. Neben der europäischen
Bilderwelt werden deshalb auch zahlreiche Beispiele aus der
chinesischen, der japanischen und der melanesischen Kultur zum
Vergleich dargestellt. Darüber hinaus unterlagen 'Bilder' auch
einem epochalen Wandel: Heute verstehen wir darunter nicht nur
analoge Medien, etwa Tafelmalereien oder Druckgraphiken, Diagramme,
Karten oder Modelle, sondern auch Resultate digitaler Verfahren in
Naturwissenschaft und Medizin.
|
You may like...
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
|