Dr. Frederick W. Chapman

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13 years, 148 days
F.W. Chapman Solutions
Technical Consultant, Research Scientist, and Business Owner
Bethlehem, Pennsylvania, United States

Social Networks and Content at Maplesoft.com


Frederick W. Chapman, PhD

I am a research mathematician and an expert on mathematical software. I completed my PhD in Applied Mathematics with a specialization in computer algebra and symbolic computation in 2003 at the University of Waterloo. My PhD supervisor was Prof. Keith O. Geddes, co-inventor of the Maple computer algebra system. In my PhD thesis, I invented an infinite parameterized family of bilinear series expansions for multivariate functions, which I named Geddes series expansions in honor of my thesis supervisor.

Geddes series are more general than both Taylor series and Fourier series since the terms of a Geddes series can contain arbitrary functions. The Geddes series family is more versatile than traditional series expansions because the parameters of the Geddes series family are not numbers, or even functions, but rather linear functionals on function spaces. Geddes series have dozens of computational applications ranging from the fast and accurate approximation of high-dimensional multiple integrals to the automatic derivation and proof of multivariate identities for elementary and special functions.

To secure independent funding for my research program and provide the resources needed to develop Geddes series to their full potential, I founded F.W. Chapman Solutions, an interdisciplinary consulting firm which blends information technology with visual arts and mathematical sciences.

What can my company do for you?

My firm's Professional Services Division has the expertise and equipment to provide complete solutions which seamlessly blend four strategic areas:

1. Mathematical Software

• Consulting
• Onsite/Online Training
• Coding, Testing, Debugging

2. e-Learning

• Computer-Based Training
• Automated Quizzes/Tests
• Online Courses

3. Web Design & Database Applications

• Websites, Blogs, Photo Galleries
• e-Commerce, User Accounts
• Databases, Online Forms
• Online Marketing, Social Media
• Web Analytics, SEO

4. Digital Photography & Post Production

• Advanced Digital Imaging Lab, Online Photo Library
• Retouching/Compositing, Captioning/Keywording
• Online Searching/Browsing/Proofing/Ordering
• Mobile Photo Studio, On-Location Photo Shoots
• Business Portraits, Product Shots
• Architectural Interiors/Exteriors, Cultural/Social Events

My Commercial Products Division develops targeted information products to sell online and sells photos as digital downloads and prints. My Scientific Research Division does original research in mathematics and computing and uses the results to develop more powerful mathematical software and better digital image processing algorithms.

Why should you hire my company?

I am a university professor turned entrepreneur — a scientist, technologist, and artist with decades of experience solving complex problems in a wide range of disciplines. My company uses industry-leading tools to provide innovative, cost-effective, reliable solutions for businesses, professionals, artists, performers, educators, researchers, and other clients.

When you need proven solutions from an experienced professional problem solver, you need F.W. Chapman Solutions. I thank you for your business!



F.W. Chapman Solutions

F.W. Chapman Solutions is a vibrant synthesis of information technology, visual arts, and mathematical sciences. Founded by professor-turned-entrepreneur Frederick W. Chapman, PhD, the company provides an integrated suite of professional services on a freelance basis, develops its own line of targeted information products to sell online, and conducts independent scientific research for scholarly publication and future commercialization. Here is a brief overview of the company's areas of expertise.

Professional Services

• Mathematical Software Consulting
• e-Learning & Computer-Based Training
• Web Design & Database Applications
• Digital Photography & Post Production

Commercial Products

• e-Books, e-Courses, e-Manuals
• Photo Downloads & Prints

Scientific Research

• Computational Functional Analysis
• Multivariate Interpolation/Approximation
• Multilinear Algebra, Matrix Analysis
• Computer Algebra, Symbolic Computation
• Symbolic-Numeric Methods, Parallel Algorithms

For more information about F.W. Chapman Solutions, please visit the company website, blog, and photo library:





MaplePrimes Activity

These are answers submitted by fwchapman

Alec, thanks for making clear the differences between the various online Maple communities.  It is certainly important to understand the unique purpose of each one.

Chris and Alejandro, thank you both for pointing out the danger of having too many places to post Maple questions and answers.  For that very reason, I will steer LinkedIn group members to MaplePrimes for Q&A about Maplesoft products.

In general, I agree with all your concerns.  The Maple community is too small to splinter into separate groups without a good reason.  Furthermore, none of us can afford to waste our limited time by duplicating the efforts of others.

I started the Maple Global Network group on LinkedIn to fill an obvious void -- there was no international Maple group on LinkedIn.  There were already Maple and MapleSim groups to serve the local needs of Italian users, but there was no international Maple group until I started one.  We now have 46 members!

I knew about MaplePrimes and wanted to avoid duplicating what already exists here.  I am trying to steer the LinkedIn group in directions which are complementary to MaplePrimes.  I do not want to compete with or attempt to replace MaplePrimes.

I was unaware of the Maple Wiki, but I know about it now.  One of the things I propose to do if I build an independent website for the Maple Global Network is to "direct traffic" -- to have a well-organized directory of Maple resources which clearly explains where to go for each kind of resource.  I can mention MaplePrimes and the Maple Wiki, for example.

As for the role of Google Apps in the Maple Global Network, I'm still thinking about that and discussing it with the group on LinkedIn.  I was going to require people to open LinkedIn accounts before signing up for Google Apps accounts (as a way to authenticate the membership), but perhaps I will reconsider that policy and offer the services in an a la cart fashion -- some members may be interested in one but not the other.

Nothing is set in stone at this point.  I appreciate your comments, which are definitely helping me to evolve my plans in a better direction.

Thanks again,


Frederick W. Chapman, PhD (Waterloo), MMath (Waterloo), BA (Lehigh)
Research Mathematician / Mathematical Software Specialist / Maple Expert
Full Credentials & Freelance Consulting Services:  linkedin.fwchapman.info

My first programmable calculator was a TI. It used algebraic notation. Many years later, I bought an HP. The RPN took getting used to and required a very different way of thinking, but now I like it much better—RPN requires fewer keystrokes than algebraic notation and is ultimately simpler. I think Maple is much too big to run on a handheld calculator. It would probably require a palmtop computer, at least. -- Frederick W. Chapman, Postdoctoral Fellow, University of Waterloo http://www.scg.uwaterloo.ca/~fwchapman/
Rich, As far as I can tell, the read asterisk means that the post contains material which you have not seen yet—either you have never read that post before or it has changed since you last read it; e.g., someone may have added a new comment or edited an old comment. There's an interesting twist to the red asterisk for the Sent-messages folder in your private messages: In that context, a red asterisk seems to mean that the recipient of your message has not read it yet! Fred -- Frederick W. Chapman, Postdoctoral Fellow, University of Waterloo http://www.scg.uwaterloo.ca/~fwchapman/
Hi Axel! Whenever an integral takes too long to evaluate numerically using evalf/Int in Maple, I try the method = ... option. This bypasses the standard evalf/Int polyalgorithm, which generally includes some symbolic preprocessing—that's where Maple sometimes gets bogged down. (This symbolic preprocessing is generally a very good thing, however.) If you want to see exactly where Maple gets bogged down, increase the infolevel before calling evalf, like this: > infolevel[evalf] := 1; If you want to see even more details, set the infolevel to a higher number. If you no longer want to see any extra information, set the infolevel to 0. There are many different numerical integration methods which you can specify in Maple 10. There are five native Maple methods for single integrals: method = _CCquad -- Clenshaw-Curtis quadrature method. method = _Dexp -- adaptive double-exponential method. method = _Gquad -- adaptive Gaussian quadrature method. method = _Sinc -- adaptive sinc quadrature method. method = _NCrule -- adaptive Newton-Cotes method "quanc8"... There are three external NAG methods for single integrals: method = _d01ajc -- for finite interval of integration... method = _d01akc -- for finite interval of integration... method = _d01amc -- for semi-infinite/infinite interval... There are two methods for multiple integrals: method = _cuhre -- multiple integrals over a hyperrectangle... method = _MonteCarlo -- Monte Carlo method over a hyperrectangle... Please see the ?evalfint help page for full details. For your integral, changing the upper limit to infinity and using method = _NCrule yields a result within a few seconds (on Maple 10.00 with the classic interface): > evalf(Int(2.9992571251988*(kappa-.89988751406074)/Pi* > exp(3.3571035419740-12.0624756920228897*ln(kappa))* > BesselK(1,26.1571648648044217*(.13147587176957e-1+(-.57683186342273e-1+ln(kappa))^2)^(1/2))/ > (.13147587176957e-1+(-.57683186342273e-1+ln(kappa))^2)^(1/2)/kappa, > kappa = .89988751406074 .. infinity, method=_NCrule)); 0.1061064735 Your 18-digit answer was 0.106106473481553262 Maple's result is your result correctly rounded to 10 digits. Note that I have Maple 10.00. Does this help you on Maple 10.02? All the best, Fred P.S. Thanks for visiting my blog. I posted a reply to your questions about multiple integration last night. -- Frederick W. Chapman, Postdoctoral Fellow, University of Waterloo http://www.scg.uwaterloo.ca/~fwchapman/
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