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Books that demystify 
partial differential equations

 

SAMPLES of the following books may be downloaded for FREE

 

Distributors and book shops may order directly from the publisher in batches of at least ten copies, 
comprising at most three different titles.
Please contact info@gbpublishing.se for net prices.                      

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.

Click to download FlexPDE5s

 

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 the 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 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' { Elevation 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. The central part of the plate exhibits only two colored areas, and hence the magnitude of J is nearly constant there. The neighboring color extends somewhat into the constricted region, and the inner corners are points of very high field.

 

 

 

 

 

 

 

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..

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, however,  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,

Click to download the first 7 chapters for FREE (including the table of contents).

Order from amazon.com and amazon.co.uk

Scandinavians can also order it from Adlibris  

 Distributors and book shops may order directly from the publisher in batches of at least ten copies, 
comprising at most three different titles.
Please contact info@gbpublishing.se for net prices.                      

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
Similar equations for vibration as for deformation
Entirely based on the FREE Student Version of FlexPDE®

Comprises 95 examples, illustrated by plots.
End-of-chapter exercises are included.

A "must" for mechanics libraries

Click for FREE download of the first 7 chapters

Order  from  amazon.com or amazon.co.uk               

Scandinavians can also order from Adlibris

 Distributors and book shops may order directly from the publisher in batches of at least ten copies, comprising at most three different titles.
Please contact info@gbpublishing.se for net prices.                      

 

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

Click here to download a sample of the e-book.

Click to 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.

 

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 partialdifferential 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.
The first part of this book is devoted to electrodynamics, and the second part applies the FlexPDE program to wave mechanics.

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

Click to download 4 chapters 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.

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.

 

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.


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.

 

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