GB Publishing
(Gunnar.Backstrom@physics.umu.se )
Books that demystify
algebra, statistics, calculus,
and partial
differential equations
Books on easy algebra and calculus at the end of the page.
SAMPLES of the following books may be downloaded for FREE.
Do you 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.
FlexPDE® is a finite-element program, written in C language for
Windows and other operating systems. 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 is
FREE!
You can download this software directly from here
--
and then start solving examples from the following two
books.
Rightclick to download
FlexPDE5s
Have You Ever Solved a Partial Differential Equation?
The numerical program FlexPDE solves PDEs in seconds on a simple PC. Electrical conduction provides an example of a non-trivial PDE in (x,y). The crucial equation expresses the conservation of charge by the relation div(J)=0, where J is the current density. In our simple example the conductivity is constant in space, which effectively reduces the PDE to the Laplace equation for U. The descriptor required for the FlexPDE program takes the following evident form.
TITLE
'Constricted Rectangular Plate'
SELECT { Settings }
errlim=3e-4 ngrid=1 spectral_colors
VARIABLES
U { Potential }
DEFINITIONS
L=1.0 d=0.3 cond=5.99e7 { Copper }
Ex= -dx(U) Ey=-dy(U) E=-grad(U) Em=magnitude(E) { Field strength }
Jx=cond*Ex Jy=cond*Ey J=cond*E Jm=magnitude(J) { Current density }
EQUATIONS
div( J)=0
BOUNDARIES
region 'plate'
start 'boundary' (-L,-2*L) value( U)=0 line to (L,-2*L) { Vanishing U on bottom side }
natural( U)=0 { Insulated sides }
line to (L,-d) to (d,-d) to (d,d) to (L,d) to (L,2*L)
value( U)=1.0 line to (-L,2*L) { Potential on top side }
natural( U)=0 { Insulated sides }
line to (-L,d) to (-d,d) to (-d,-d) to (-L,-d) close
PLOTS
contour( U) surface( U) vector( E) norm surface( Em) { Contour, surface, and vector plots }
contour( Jx) painted contour( Jy) painted contour( Jm) painted
elevation( U) on 'boundary' elevation( Jm) on 'boundary' { Elevations plots }
END
The plots resulting from the above descriptor demonstrate how the field deforms
on going into a narrower or a wider cross section. The figure shows the magnitude of the
current density.
Simple Fields
of Physics by Finite Element Analysis
by Gunnar Backstrom, PhD
Paperback
edition (311 pages,
sells on the web for $29.00)
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..
Update example sim214
The FlexPDE program yields plots in color,
whereas the copies in the softcover book are in black-and-white.
Once you have typed a problem descriptor (script) and run it, you will obtain
pictures in final quality. The e-books
below include color plots.
The only way of learning to use FlexPDE is to type
the scripts and find out what every line means.
A "must" for
physics and engineering libraries
ISBN: 9197555304
CONTENTS
Order: from
www.Amazon.com - Amazon.co.uk -
Amazon.de -
Amazon.fr -
Amazon.ca - Amazon.co.jp
Scandinavians can also order it through
www.adlibris.com (268
kr)
Booksellers: Please order
from www.ingrambook.com
in the US
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.
Right-click
here to download
the first 7 chapters for FREE.
Simple
Deformation and Vibration
by Finite Element Analysis
by Gunnar Backstrom, PhD
Paperback
edition (226 pages,
sells on the web for $29.00)
Solves problems in 2D and 3D
Update
example mex072e.pde
A "must" for
mechanics libraries
ISBN: 9197555320
CONTENTS
Order : from
www.Amazon.com - Amazon.co.uk
- Amazon.de,
- Amazon.fr - Amazon.co.jp.
Scandinavians can also order it through www.adlibris.com
(268 kr)
Booksellers: Please order from www.ingrambook.com
in the US
Right-click
here for FREE download of the first 7 chapters.
Fields of Physics by Finite Element
Analysis
E-book by Gunnar Backstrom,
PhD (279 pages
for
$19)
To read an e-book is simple:
Download the FREE Adobe® Acrobat®
Reader
Double-click on the icon for the book file *.pdf to start Acrobat Reader
View the list of contents by
pushing the F5 keyboard button (or click for
Bookmarks).
Toggle by
F5 to view the text
only.
This book uses the Student Version,
except in a few advanced cases. It comprises 120
examples, illustrated by color plots. The problems treated are
in the form of text files (scripts) that can be run by the FlexPDE program (see blue
example above).
The following list shows a few subjects from in the
table of contents.
• Plotting functions
• Fields of gravitation
• Fields around electric charges
• Electrostatic fields in (x,y) and (ρ,z) space, forces, and energy
• Magnetostatics in (x,y) and (ρ,z) space
• Heat conduction in (x,y) and (ρ,z) space
• Non-linear heat transfer
• Electron and hole conduction
• Fields in (x,y,z) space
• Vocabulary of FlexPDE
Download 10 chapters and the full table of contents for FREE.
Download the FREE FlexPDE program.
Order the PDF file from eBookMall.
After downloading you can print parts of
the PDF file for your personal use.
The best way of learning how to use FlexPDE is to type scripts line-by-line from
the book, while noticing the purpose of each command.
After purchasing the book, however, you may request a full set of PDE files from
the author. Just send a copy of the receipt by email.
Update example sim214
Waves by Finite Element
Analysis
E-book by Gunnar
Backstrom, PhD (194 pages for $19)
Please refer to the beginning of this site for a general discussion of
partial differential equations.
To read this e-book:
Download the FREE Adobe® Acrobat®
Reader.
This book uses the FREE Student
Version of FlexPDE, except in
a few advanced cases.
This volume is a sequel to the above Fields of Physics by FEA, which
introduces the most elementary facilities of FlexPDE.
A customer wrote:
"Your Ebooks are good quality,
practical, and priced very reasonably.
I especially like the full color
screen captures that PDF files permit."
The following list shows a few subjects from in the
table of contents.
• Electromagnetic waves and resonators in (x,y)
• Wave guides
• Vector potential and eddy fields in (x,y) space
• Vector potential in (ρ,z) space and radiation
• Elementary wave mechanics in one dimension
• Harmonic oscillators in (x,y) and (ρ,z) space
• The hydrogen atom in (ρ,z) space
• The hydrogen molecule-ion
• Waves in three dimensions
• Vocabulary of FlexPDE
Rightclick to download 4 chapters and the full table of contents for FREE.
Download the FREE FlexPDE program.
Order the PDF file from eBookMall.
After downloading you can print parts of
the PDF file for your personal use.
The best way of learning how to use FlexPDE is to type scripts line-by-line from
the book, while noticing the purpose of each command.
After purchasing the book, however, you may request a full set of PDE files from
the author. Just send a copy of the receipt by email.
Deformation and Vibration by
Finite Element Analysis
E-book by Gunnar Backstrom, PhD
(227 pages for $19)
This volume is an independent treatise, which assumes no previous knowledge of
finite element methods.
It is suitable as a teaching tool in undergraduate
courses.
To read this e-book:
Download the FREE Adobe® Acrobat®
Reader.
The book uses the FREE Student Version of FlexPDE, except in a few advanced cases.
The following list shows a few subjects from in the
table of contents.
• Graphical facilities and fields of gravitation
• “Curly” velocity fields
• Laplace and Poisson equations
• Elementary elasticity in (x,y) and straight beams
• Hooks, rings, and tubes
• Elasticity in (ρ,z) space
• Torsion and warping
• Thermo-elasticity
• Deformation in three dimensions
• Waves along a beam
• Eigenstates of a membrane
• Eigenstates in (x,y,z)
• Waves in fluids
• Vocabulary of FlexPDE
Download 7 chapters and the full table of contents for FREE.
Download the FREE FlexPDE program.
Order
the PDF file from eBookMall.
After downloading you can print parts of
the PDF file for your personal use.
The best way of learning how to use FlexPDE is to type scripts line-by-line from
the book, while noticing the purpose of each command.
After purchasing the book, however, you may request a full set of PDE files from
the author. Just send a copy of the receipt by email.
Update example mex072e.pde
Fluid Dynamics by Finite Element
Analysis
E-book by Gunnar
Backstrom, PhD (177 pages for
$19)
Please refer to the beginning of this site for a general discussion of
partial differential equations.
To read this e-book:
Download the FREE Adobe® Acrobat®
Reader.
This book uses the FREE Student
Version of FlexPDE, except in
a few advanced cases.
The above Fields of Physics by FEA introduces the most elementary facilities of FlexPDE.
The following list shows a few subjects from in the
table of contents.
• Irrotational flow of liquids in (x,y) space
• Circulation around an obstacle
• Viscous flow in (x,y) Channels
• Viscous flow past an obstacle
• Irrotational flow in (ρ,z) space
• Viscous flow in (ρ,z) space
• Seeping through porous materials
• Viscous flow at Re>>1 in (x,y) space
• Viscous flow at Re>>1 in (ρ,z) space
• Transient viscous flow at Re>>1
• Viscous flow in three dimensions
• Simplified PDEs for viscous flow
• Waves in fluids
• Vocabulary of FlexPDE
Download 4 chapters and the full table of contents for FREE.
Download the FREE FlexPDE program.
Order the PDF file from eBookMall.
After downloading you can print parts of
the PDF file for your personal use.
The best way of learning how to use FlexPDE is to type scripts line-by-line from
the book, while noticing the purpose of each command.
After purchasing the book, however, you may request a full set of PDE files from
the author. Just send a copy of the receipt by email.
Must you learn
mathematics as in the 1800s ?
Teach yourself algebra and calculus -- and learn to use MATLAB®
at the same time!
You may download samples of the following books for FREE.
Undergraduate mathematics is difficult mainly because it is presented in the form of derivations and proofs. These impressive underpinnings once 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 under- standing 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 $100. These educational versions are practically identical to the professional MATLAB program, and the restrictions are of no importance in undergraduate work. An enormous number of MATLAB Student CDs now exist in the world, to be borrowed or purchased second-hand.
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.
Read a review
of a previous edition by a British mathematician
Read a review
from
Internationale Mathematishe
Nachrichten (Nr. 193, 2003)
This book may be obtained from www.Amazon.com
(ISBN 9197555312)
Amazon.ca,
Amazon.co.uk,
Amazon.de, Amazon.fr, and Amazon.co.jp.www.amazon.com
Scandinavians can also order it from www.adlibris.com (ISBN 9197555312, 180 SEK).
Booksellers: Please order from www.ingrambook.com
in the US
Download
the first 11 chapters of the book (including table of
contents).
Practical Mathematics using
MATLAB®
by Gunnar
Backstrom, PhD
E-book, Adobe® PDF (239 pages for $15)
The following list shows a few subjects found in the table of contents.
• MATLAB® as a calculator
• Geometric applications
• Vectors in (x,y) and (x,y,z)
• General vectors
• Systems of linear equations
• Plotting functions
• Zeros and extreme points
• Symbolic algebra
• Limits and derivatives
• Sums and integrals
• Symbolic calculus
• Random events and statistics
• Fitting a function to data
• Ordinary differential equations (ODEs)
• Symbolic solutions of ODEs
• Complex numbers and functions
• Fourier series
• Fourier transforms
Download the first 11 chapters and the full table of contents for FREE.
Order the PDF file from eBookMall.
After downloading you can print parts of the PDF file for your personal use.