This portion of the W3Mall provides resources, software and tutorials for engineering, science and mathematics. Most of the resources are graduate curriculum.

There are many fine tutorials on the Internet. Many students must take calculus as part of their education in college but find the mathematics difficult. One of the best tutorials is called e-calculus. A link to this site is provided below:

Go to e-calculus tutorial.
The calculus of variations is very important branch of mathematics for physics and engineering. Unfortunately, this mathematics is often not taught at many colleges and universities. This mathematics is important for finite element analysis, physics and theoretical mechanics. Some links that provide information about the calculus of variations follow:

Calculus of variations from PlanetMath Organization
Calculus of variations from Wikipedia Organization
Calculus of variations resources
EZ Calculus of Variations
Professor Frank Firk at Yale University has written two books for physics students that are free. The first book, Essential Physics 1, is for potential physics majors. The second book, primarily for seniors, is Introduction to Groups, Invariants & Particles.

Firk's physics books
Another excellent physics book is available on the Internet for free. This book covers physics from the simple to the sublime. Many years ago at the university, I studied Dirac's theory of the relativistic electron using somewhat simplified mathematics by today's standards. I also have an understanding of the variational principle of general relativity. In my opinion, this is one of the finest physics texts that have ever been written. "M theory" which is at the fore front of contemporary physics will eventually be discussed.

Motion Mountain The Physics Textbook
A concise but good introduction to Lagrangian and Hamiltonian mechanics, which compliments the Motion Mountain The Physics Textbook, is next. These are two important aspects of theoretical mechanics.

Lagrangian and Hamiltonian Mechanics
The calculus of variations and Hamiltonian mechanics where utilized by the Russian mathematician Lev Pontryagin to optimize the operation of many systems including navigation systems and many complex manufacturing systems. More recently, the theory has been applied to optimize economic systems. The theory can be applied to continuous and/or discrete systems. This theory is called the Maximum Principle or more specifically Pontryagin Maximum Principle.

A link to a PDF document that describes the application of the Maximum Principle to control problems is next.

A Weak Maximum Principle for Control Problems with State Constraints
Click on the next link to download a 34 page PDF document that applies the Maximum Principle to economic theory.

Pontryagin Maximum Principle for Infinite-Horizon Optimal Controls
Unfortunately, calculus is only the start of the education of many people. Many students have to take tensor calculus and continuum mechanics. There are few good books on these two difficult subjects. Professor H. Heinbockel at Old Domininion University has written two excellent books on these topics in my opinion. An earlier version of the book is available at the web site listed below. A more complete version of this text has been published. Information about the published text is also available at the web site. Either of these books are an excellent resource for applied mathematicians, physicists and engineers.

Continuum mechanics book.
For an understanding of physics in general and mechanical engineering in particular, the work of Emmy Noether is very important but not generally known. I think she was one of the greatest mathematicians during the first part of the last century. Her theory relates the symmetry of a system to conversation laws for the system. Some historians of science believe that her general theory gave rise to the theory of general relativity. She presented her theory to Einstein and Hilbert during a discussion while the theory of general relativity was being developed. Hilbert published a paper on general relativity one month after Einstein. One mathematician stated that Hilbert understood General Relativity better than Einstein. Noether's theory is fundamental to an understanding of theoretical mechanics and physics to this day! A link explaining her theory in an somewhat elementary but satisfactory manner is next.

Emmy Noether's theory
A very large site that provides extensive links to information concerning chemistry and chemical engineering is next. The site is in English and Chinese!

Infochem
Chemists, engineers and physicists study polymers for many reasons. Furthermore, polymers are used in many forms for a variety of applications. Plastics are one type of polymer. Three good resources about polymers are next.

Polymer Tutorial
Polymer Chemistry
Polymer Chemistry Sites
Many problems in science and engineering are solved using finite element analysis (FEA) software. A good general site for FEA is next.

Internet Finite Element Resources
The following site is a good introduction to the finite element method.

Finite Element Method Universal Resource
Information about two more free finite element analysis software packages follow. Just because some software is free, it does not mean the software is not useful. These systems are a good place to start learning this analysis method!

UNA finite element analysis program

FEIt software
Finite element analysis of polymers requires incorporation of their properties into the analysis software. The following site provides a variety of information required to perform this difficult analysis.

Polymerfem.com
Based on my industrial experience, I am of the opinion that many design engineers do not have a good understanding of the properties and design of composite assemblies. Manufacturing engineers may understand even less!

Ever J. Barbero at West Virginia University has written a text book - "Introduction to Composite Materials Design" (ISBN-1-56032-704-4). He produced a computer program that can be used with his book. The shareware called CADEC performs micromechanics, laminate analysis, failure predictions and has other capabilities. He has uploaded the software as shareware to www.simtel.net. No price is listed. Download his software to find out more about composites!

CADEC composite software
Unfortunately, the polymers in composites have very complicated chemistry. Consequently, they have complicated mechanical properties that are a function of the crosslink density and the glass transition temperature of the material. Both properties are greatly affected by the conditions during the cure of the polymer. Polymers are viscoelastic materials which are described by the sciences of chemistry, chemical engineering and continuum mechanics. A good but brief introduction to this very complex topic is next.

Polymer mechanical properties
The academic community has provided a variety of useful simulation software on the Internet for the benefit of industry and other institutions. The University of Delaware Center for Composite Materials provides simulations of composite manufacturing processes. The link to their site is next.

Composite manufacturing process simulation
Michigan State University provides a tutorial concerning polymer composite molding. Click on the following link.-

Polymer composite molding tutorial
Web-based composites analysis and repair design software (CARDS) is available on the Internet for free. Their site is next.

CARDS Software
Another site for composite design and analysis software at the University of Hawaii is next.

Composite analysis and design software
A report entitled "Exact and Variational Theorems for Fracture Mechanics of Composites with Residual Stresses,Traction-loaded Cracks and Imperfect Interfaces by John A. Nairn at the University of Utah is listed next. This is a PDF document which requires Adobe Acrobat. The Adobe Acrobat reader is available in the Free Software portion of this portal if you need to down load it.

Exact and Variational Theorems for Fracture Mechanics of Composites . . .
A report entitled "Micromechanics-based Failure Analysis of Composite Structural Laminates" by Professor J. Steven Mayes at Alfred University is listed next. The report requires the Adobe Acrobat reader and is 228 pages long!

Micromechanics-based Failure Analysis of Composite Structural Laminates
The IBM Almadem research laboratory provides chemical kinetics simulation software for professionals and students at the university for free. This software provides significant information about the properties of polymeric and other chemical systems.

Chemical kinetics simulation
The following website provides a variety of information concerning corrosion for industry and the military.

DoD Corrosion Exchange
The following site provides information about the R computer program for statistics and graphics which is available for free on the Internet. This is a very powerful statistical package.

R statistical software
The Samizdat Press provides free books about computers, engineering, mathematics and also links to other sites that have similar information. This site is well worth investigating.

Samizdat Press
Two excellent web sites have been identified and added to this portal. Both of these sites are produced by Eric Weisstein at Wolfram Research. This company produces the Mathematica software. These sites are encyclopedias for mathematics and for science. Links to these sites follow:

MathWorld
ScienceWorld
Museum sites are listed next:

Museum of Science and Industry
Smithsonian National Museum of Natural History
The following sites provide a great variety of tutorials on the Internet for free! Some of these sites are very technical.

Mathematics
Probability
Large Selection of Tutorials about Computer Programming
Streaming Media
JavaScript Kit
HotScripts.com
3D CAFE
Game Tutorials
Links to large software companies follow:

Sun Microsystems
Microsoft
Link to another page at this site follows:

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