Books that demystify
algebra, statistics, calculus,
and partial
differential equations
(Gunnar.Backstrom@physics.umu.se )
PDEs by FEA Learn
Math by MATLAB
Böcker på svenska
Do your students have difficulties
with
partial differential equations?
Partial differential
equations (PDEs) predict how fields vary in space and time, and they are hence
of critical importance in physics and engineering. In spite of this
central role, PDEs have not yet received the attention they deserve in college
curricula. This is because very few exact solutions exist and numerical
solutions are cumbersome, to the extent that the latter are taught within
separate academic disciplines, such as Applied Mathematics, Numerical Analysis, or Computation. These
disciplines focus on numerical methods rather than actual solutions and are
accordingly of little practical value to scientists and engineers.
The last decade brought software for solving PDEs with various
boundary conditions. One such program may now be downloaded for free on the web,
and the user only needs superficial knowledge of how solutions are generated
internally. This program is exploited in the following self-instructional books.
Samples from these books are free on the web.
A program available on
the web solves PDEs in seconds on a simple PC. FlexPDE® is a finite-element program, written in C language for Windows 98 and
later versions. The Student Version is free
on the web. This
program is simple to use and has a built-in editor. It constitutes a powerful tool for teaching classical
fields, which are notoriously difficult parts of the physics curriculum.
Electro- and magnetostatics are examples of fields that are now easily
accessible to numerical analysis. Heat transfer, electromagnetic waves, wave
mechanics, elastic deformation and vibration, and liquid flow are other
examples.
The Student Version of FlexPDE 5 is FREE!
The recent FlexPDE version 5 offers some enhancements, in particular more direct 1D operation.
NEW:
Simple Fields
of Physics by Finite Element Analysis
Paperback
edition (311 pages, $43.00
/ £22.00)
Applications to Electricity,
Magnetism, Heat Transport, Electromagnetic Waves, Wave Mechanics, and Viscous Flow in 2D
and 3D.
Entirely
based
on the FREE
Student Version of FlexPDE®
Comprises 125
examples, illustrated by plots. End-of-chapter exercises are included.
This textbook is based on version 5 of FlexPDE, which offers more convenient
scripts for one-dimensional problems.
A "must" for
physics and engineering libraries
ISBN: 9197555304
CONTENTS
Available at major bookstores.
Order: from
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in the UK
Scandinavians can also order it through www.bokus.com
Have you
ever solved a partial differential equation ?
The laws of physics may be transformed
mathematically into second-order partial differential equations (PDEs). The
simplest one of this type is
known as the Laplace equation. This governs the distribution of gravitation in
free space. Other PDEs, for the electric and magnetic fields etc., are
similar but somewhat more complicated.
Few of these equations have exact solutions, which explains why they do not receive the attention they deserve in the academic curriculum. Only in recent years has it become possible to solve PDEs numerically on an ordinary PC by finite element analysis.
The present book is unique in its approach. It is not another volume on conceivable algorithms of FEA. Its main purpose is to exploit a free web program for dealing with PDEs occurring in physics. This program solves a typical example in seconds and promptly presents the results graphically by a variety of plots.
The first 8 chapters of the above book are for
FREE NEW:
Simple
Deformation and Vibration
by Finite Element Analysis
Paperback
edition (226 pages, $43.00
/ £22.00)
Problems in 2D and 3D solved by
the FREE
Student Version of FlexPDE®
Comprises 95
examples, illustrated by plots.
End-of-chapter exercises are included.
A "must" for
mechanics libraries
ISBN: 9197555320
CONTENTS
Available at major bookstores.
Order : from
Amazon.com - Amazon.co.uk
- Amazon.de,
- Amazon.fr - Amazon.co.jp.
Booksellers: Please order from
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in the US
www.gardners.com/,
www.bertrams.com/BertWeb/public/search.do
in the UK
Scandinavians can also order it through www.bokus.com
The first
6 chapters of the above book are
for FREE
FreeDownload
Note:
A university library that has purchased a copy of any of the following
e-books
may make it available inside the university by the local network.
This e-book (311 pages) sells on
the web for $19
NEW:
Simple
Fields by Finite Element
Analysis
Applications to Electricity,
Magnetism, Heat Transport, Electromagnetic Waves, Wave Mechanics, and Viscous Flow in 2D
and 3D
Exclusively exploits the FREE
Student Version of FlexPDE®
v.5
CONTENTS is
the
same as in the above paperback
This work comprises elementary examples of fields from Electricity,
Magnetism, Heat Transport, Electromagnetic Waves, Wave Mechanics, and Viscous Flow
. The problems treated are in (x), (x,y),
and (x,y,z). The
free software program
required may be obtained from www.pdesolutions.com.
Order (Note the option "Location: Outside the U.S.?" just above the VISA card details.)
The first
8 chapters of the above book are
for FREE
FreeDownload
Includes table of contents.
To read an e-book is simple:
Download the free Adobe® Acrobat®
Reader from
www.adobe.com/products/acrobat/
Double-click on the icon for the book file *.pdf to start Acrobat Reader 5 (or later version).
View the list of contents by
pushing the F5 keyboard button (or click for
Bookmarks).
Toggle by
F5 to view the text
only.
After downloading you may annotate and print the PDF file for your personal use.
This e-book (226 pages) sells on
the web for $19
NEW:
Simple
Deformation and Vibration
by Finite Element
Analysis
Problems in 2D and 3D solved by
the FREE
Student Version of FlexPDE®
Comprises 95
examples, illustrated by plots.
End-of-chapter exercises are included.
CONTENTS is the same as in the corresponding paperback
This book on elasticity is an independent treatise, which assumes no previous knowledge about finite element methods. It may be used as a teaching tool in undergraduate courses. The text deals with displacement, strain, and stress in solids.
The problems are in the form of text files that can be run by the Student Version of the FlexPDE program (v.5), distributed for free at www.pdesolutions.com under Download.
This book begins by explaining the plotting facilities of FlexPDE by
simple examples. After an introduction to Laplace and Poisson equations it shows
how the definitions of strain, Hooke's law, and the relations of force balance
lead to 2nd-order partial differential equations, which may be solved
conveniently by the numerical software.
The first applications are elementary, but the following
chapter on beams involves an analysis of principal axes and the corresponding
stresses. Forces, bending moments and energy are also obtained without effort on
the part of the user.
Hooks, rings and tubes are first treated in 2D,
after which there is an analysis in 3D. The static analysis
in (x,y) includes a discussion of torsion, warping, and thermoelastic deformation.
The dynamic analysis follows the same general pattern as
the static counterpart, with the difference that the equations of equilibrium
are replaced by Newton's law of motion. There are also chapters about
resonant vibration, eigenvalues and eigenstates in both 2D and 3D.
Order (Note the option "Location: Outside the U.S.?" just above the VISA card details.)
The first
7 chapters of the above book are
for FREE
FreeDownload
Includes table of contents.
This e-book sells on
the web for $19
Fields of Physics by Finite Element
Analysis (279
pages)
Based on
version 5 of
FlexPDE®
Uses the FREE Student Version,
except in a few cases.
Comprises 120
examples, illustrated by plots
Applications to Electricity,
Magnetism, and Heat Transport
Includes a chapter on 3D
problems
The first chapters introduce plotting
procedures by applications to vector analysis, gravitation, and electric fields
around point charges. Then there is a chapter on the Laplace and Poisson
equations without reference to any physical problems.
The major part of the book explains how to solve various partial differential equations occurring in electro- and magnetostatics, in heat transport, and in electronic conduction.
The parts dedicated to electricity and magnetism illustrate the influence of boundary conditions and materials properties. Field energy and forces on objects are also obtained by the FEA calculations.
The sections devoted to heat transport involve linear and non-linear PDEs, as well as simultaneous electric and thermal equations. Finally, there are examples of transient heat conduction and thermal waves.
One chapter deals with electron transport in metals and semiconductors, with an application to rectification in a silicon diode.
The last chapter addresses various 3D problems.
The problems treated in this work are in the form of text files (scripts) that can be run by the FlexPDE program. All of them, except a few, are compatible with the Student Version, which may be obtained for FREE from www.pdesolutions.com.
Order (Note the option "Location: Outside the U.S.?" just above
the VISA card details.)
This e-book sells on the web for $19
Waves by Finite Element
Analysis (194
pages)
Based on version 5 of
FlexPDE®.
Uses the FREE Student Version, except in
a few cases.
Electromagnetic Waves and Wave
Mechanics
This book explains how to
solve various partial differential equations concerning electromagnetic waves,
eddy fields and quantum mechanics
Includes a chapter
on 3D problems
CONTENTS
The problems treated in this work are in the form of text files that can
be run by the FlexPDE program. Most of the examples may be solved using the
Student Version,
distributed for free by www.pdesolutions.com
under Download.
The first part is devoted to
electrodynamics, and in particular to waves in one and two dimensions. Numerous
examples illustrate how to exploit this convenient technique to solve oscillatory
problems, even where conductivity, permittivity and permeability vary in space.
Examples of transient problems are also included.
The second part of the
book, which is about wave mechanics, treats barrier penetration and bound states in one
dimension, harmonic oscillators in one, two and three dimensions, in the latter
case after a single- variable separation. Two chapters are devoted to the
solution of the Schrödinger equation for the hydrogen atom and for the hydrogen
molecule-ion.
The final chapter deals with waves in three dimensions.
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Deformation and Vibration by Finite Element
Analysis (225 pages)
Based on version 5 of
FlexPDE®.
Uses the FREE Student
Version, except in a few cases.
This volume is an independent treatise, which assumes no previous
knowledge about finite element methods. It may be used as a teaching
tool in undergraduate courses.
The text deals with displacement, strain, and stress in solids. It comprises 120 examples, many in 3D.
The problems are in the form of text files that can be run by the FlexPDE program. Most of the examples may be solved using the Student Version, distributed for FREE by www.pdesolutions.com under Download.
This book begins by explaining the plotting facilities of FlexPDE by
simple examples. After an introduction to Laplace and Poisson equations it shows
how the definitions of strain, Hooke's law, and the relations of force balance
lead to 2nd-order partial differential equations, which may be solved
conveniently by the numerical software.
The first applications are elementary, but the following
chapter on beams involves an analysis of principal axes and the corresponding
stresses. Forces, bending moments and energy are also obtained without effort on
the part of the user.
Hooks, rings and tubes are first treated in 2D,
after which there is an analysis in cylindrical coordinates and in 3D. The static analysis
in (x,y) includes a discussion of torsion, warping, and thermoelastic deformation.
The dynamic analysis follows the same general pattern as the static counterpart, with the difference that the equations of equilibrium are replaced by Newton's law of motion. There are also chapters about resonant vibration, eigenvalues and eigenstates in both 2D and 3D.
Order
(Note the option "Location: Outside the U.S.?" just above
the VISA card details.)
After downloading the book, you may request a set of PDE files from
the author.
This e-book sells on the web for $19
Fluid Dynamics by Finite Element
Analysis (176 pages)
Based on version 5 of
FlexPDE®.
Uses the FREE Student
Version, except in a few cases.
This is the second volume on the fields of mechanics, occasionally referring to
the preceding one on Deformation and Vibration. The present treatise is devoted to liquid flow
in 2D and 3D. Here, the graphics tools are assumed known from previous books.
The problems studied in this work are in the form of text files that can be run by the FlexPDE program. Most of the examples may be solved using the Student Version, distributed for FREE by www.pdesolutions.com under Download.
The first chapter deals with simple potential flow. The second chapter extends this mode to irrotational flow with circulation around an obstacle, which may cause transverse forces. The next chapters systematically treat viscous flow in (x,y) according to the Navier-Stokes equation. An additional PDE yields the solution for the pressure and also assures a divergence-free velocity field. These principles are extended to cylindrical (r,z) and to three-dimensional coordinates (x,y,z).
The first part of this book concerns problems at small Reynolds number, but later chapters include the terms necessary to proceed to Re>>1.
One chapter is devoted to percolation in porous materials. Such problems are solved by the simple, conventional theory as well as by an extension of the Navier-Stokes equations.
The last chapter presents an alternative formalism without a
pressure equation.
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Must we learn mathematics as in the 1800s ?
Teach yourself by MATLAB®!
Price $39.00
/ £20.00 (209 pages)
Undergraduate mathematics is difficult mainly because it is presented in the form of derivations and proofs. These impressive underpinnings made by professional mathematicians may now be taken for granted, and if you only want to make practical use of the theory you may use a shortcut. Trust the verifications of generations of mathematicians and proceed directly to applications, involving only the well-known rules of arithmetic. This is the goal of the present book, which also confers understanding of both algebra and calculus.
The Student Versions of MATLAB may be
ordered from MathWorks Inc. by colleges and universities, which in turn can sell CDs to their students, or simply give them away. The full price is around
$75. These educational versions are practically identical to the professional
MATLAB program, and the restrictions are of no importance in undergraduate work.
Of course, the Professional MATLAB program may also be used, if it includes the
Symbolic Math Toolbox.
The MATLAB program evolves regularly , and every two years or so there is a new
version number. Fortunately, the enhancements do not concern the elementary
functions and procedures used in first-year mathematics. The author of this book
has verified that the examples involved run under the versions 5, 6 and
7. An enormous number of MATLAB CDs now exist in the world, and these programs
may be borrowed or purchased second-hand.
Without committing yourself you may test the first 11 chapters and view the full
Table of Contents, as announced below.
Review
of a previous edition by a British mathematician
Review
in
Internationale
Mathematishe Nachrichten (Nr. 193, 2003)
This book may be obtained from Amazon.com,
Amazon.ca,
Amazon.co.uk,
Amazon.de,
Amazon.fr,
and
Amazon.co.jp.
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www.ingrambook.com/start/
in the US
www.gardners.com/,
www.bertrams.com/BertWeb/public/search.do
in the UK
Scandinavians can also order it through www.bokus.com
The first 11 chapters of the above
volume are
for FREE
FreeDownload
Includes a table of contents.
This e-book sells on the web for $16
Simple
Mathematics
Using Student
Versions of MATLAB®
(209 pages)
Compatible with several versions of MATLAB®
This e-book exploits MATLAB to illustrate the concepts and results of first-year college mathematics in the form of numeric examples. MATLAB was chosen for its remarkably simple syntax. The reader learns a primitive but useful subset of MATLAB commands while he proceeds to apply mathematics. Some chapters apply the powerful symbolic mathematics included in the Student Versions.
The Student Versions of MATLAB may be
ordered from MathWorks Inc. by colleges and universities, which in turn can sell CDs to their students, or simply give them away. The full price is around
$75. These educational versions are practically identical to the professional
MATLAB program, and the restrictions are of no importance in undergraduate work.
Of course, the Professional MATLAB program may also be used, if it includes the
Symbolic Math Toolbox.
The MATLAB program evolves regularly , and every two years or so there is a new
version number. Fortunately, the enhancements do not concern the elementary
functions and procedures used in first-year mathematics. The author of this book
has verified that the examples involved run under the versions 5, 6 and
7. An enormous number of MATLAB CDs now exist in the world, and these programs
may be borrowed or purchased second-hand.
Without committing yourself you may test the first 11 chapters and view the full Table of Contents, as announced below.
Order
(Note the option "Location: Outside the U.S.?" just above
the VISA card details.)
To read an e-book is simple:
Download the free Adobe® Acrobat®
Reader from
www.adobe.com/products/acrobat/
Double-click on the icon for the book file *.pdf to start Acrobat Reader 5 (or later version).
View the list of contents by
pushing the F5 keyboard button (or click for
Bookmarks).
Toggle by
F5 to view the text
only.
After downloading you may annotate and print the PDF file for your personal use.
This e-book sells on
the web for $16
Alternative Mathematics Using
MATLAB 7
(239 pages)
This volume shows how to illustrate the concepts and results of
first-year university mathematics in the form of numerical exercises. It may be
used in parallel with conventional lectures in mathematics to enhance
understanding, as well as to provide tools for applying theories to scientific
problems.
The standard language used in this book is MATLAB, chosen
for its remarkably simple syntax. The student learns a primitive but useful
subset of the MATLAB commands while he proceeds to apply mathematics.
This arsenal suffices to let him solve
large systems of linear equations (even with complex coefficients), approximate derivatives and integrals, and solve
ordinary differential equations up to 2nd order.
This book also contains chapters of applied symbolic mathematics. This facility is included with the Student Edition of MATLAB. The latter may be purchased by academic institutions and distributed to its students.
Contents
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A Rational System of Musical Notation
This article (7 pages) explains how the upper, conventional line of notes may be transformed into the more rational lower one. The latter is not only easier to read but also expresses the intervals between the various tones in an intuitive fashion. Download free of charge to read and print by Acrobat 4 or later version.
Praktisk matematik med MATLAB
Förenklad svensk upplaga
(240 sidor) StudentlitteraturMånga moment är förenklade i förhållande till tidigare upplaga. Editering och
körning av filer kommer inte förrän i kapitel 7, och i största allmänhet ökar
svårighetsgraden mycket långsammare än i den tidigare texten. En bruksanvisning
ingår numera i inledningen.
Boken är avsedd som handledning vid självständiga studier i tillämpad matematik, motsvarande första årets kurser för teknologer och naturvetare. Den kan antingen tjäna som inledning till den akademiska matematiken genom att presentera begreppen på ett slående sätt, eller som parallell konkretisering av de kurser i abstrakt matematik som normalt serveras vid högskolorna.
Texten bygger på programmet MATLAB 5, som ger unika möjligheter att utforska matematiken med ett minimum av kommandon och syntaktiska regler. Studentversionen av MATLAB (Prentice Hall), som finns att köpa i bokhandeln, är fullt tillräcklig för ändamålet. Versionen 5.3 från MathWorks Inc., som inte är kopieringsskyddad, är idealisk för grundutbildningen.
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Alternativ matematik med
MATLAB 7
Version 7 av MATLAB är förbättrad i flera avseenden, främst ifråga om grafiken.
Vissa moment i denna bok är förenklade i förhållande till tidigare upplaga. Editering och körning av filer kommer inte förrän i kapitel 8, och i största allmänhet ökar svårighetsgraden mycket långsammare än i f'örsta upplagan. En bruksanvisning ingår numera i inledningen.
Boken är avsedd som handledning vid självständiga studier i tillämpad matematik, motsvarande första årens kurser för teknologer och naturvetare. Den kan också tjäna som inledning till den akademiska matematiken genom att presentera begreppen på ett slående sätt, eller som parallell konkretisering av de kurser i abstrakt matematik som normalt serveras vid högskolorna.
MATLAB ger unika möjligheter att utforska matematiken med ett minimum av kommandon och syntaktiska regler. Studentversionen av MATLAB 7, som köps och distribueras av högskolorna, är fullt tillräcklig för ändamålet.
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Den amerikanske
massageterapeuten Clair Davis, tillsammans
med dottern Amber Davies (vänstra bilden),
har på ett pedagogiskt sätt prese
nterat en ny metod att bekämpa smärtor, som
går ut på att söka upp och behandla
roten till det onda.
Deras bok har översatts till svenska av Gunnar Bäckström (högra
bilden), som givit ut den på eget förlag (GB Publishing) under titeln Massera
själv bort dina smärtor!
Har du
någonstans ?
De
flesta har ont på något ställe i kroppen. Smärtan kan vara så stark att den
hindrar en att tänka på något annat, och man kanske oroar
sig för att den kan tyda på något allvarligt fel i ett inre organ, i en led
eller i ryggraden.
Misstänker man något organiskt fel bör man naturligtvis söka
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musklerna, och då kan smärtan lindras eller helt tas bort genom enkel massage.
Om man drabbas av värk
eller brännande smärta, får man lust att massera just där det gör ont.
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