Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate




Q. What is Holistic Numerical Methods Institute (HNMI)?  

In 1985, while pursuing his doctorate in Clemson University, the lead investigator of this project, Autar Kaw revised a WPAFB Apple IIe based BASIC program for laminate analysis of composite materials.  Since migration to PCs was not an easy task then, in 1988, he and a few hardworking independent study students wrote a completely new laminate analysis program called PROMAL.  This tool was then used in teaching graduate level and senior elective course in Advanced Composite Materials course.   Since 1988, PROMAL, which is now written in VB2010, has evolved into a product that is used in over 75 universities worldwide, and accompanies the Mechanics of Composite Materials textbook (1997, 2005).


Naturally, the success of this idea of developing these computational tools was extended in 1990 to a course in Numerical Methods.  At that time, we started developing simulations for Numerical Methods using Microsoft Quickbasic3.0, and then in Visual Basic for Windows.  We unsuccessfully applied to get funding from NSF in the early 1990s for developing and distributing (via floppy disks) the simulations and textbook chapters for a comprehensive course in Numerical Methods. However, when MIT unofficially announced their open courseware initiative in 1999, our passion for the project resurfaced. In 2001, we received the first of the five NSF CCLI grants to develop, assess, refine and revise a comprehensive open courseware in Numerical Methods.


The courseware is distributed free of charge to anyone in the world. 


To quote the OCW initiative at MIT, we are strong believers in "having open dissemination of educational materials, philosophy, and modes of thought, that will help lead to fundamental changes in the way colleges and universities utilize the Web as a vehicle for education."  We are continually looking for self-sustaining avenues of dissemination, and we have been fortunate so far to find sponsors to keep it free.

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Q. What does it mean that this is a developing website?

The core of undergraduate numerical methods consists mainly of eight topics/mathematical procedures, namely, 

1) approximations, errors & modeling 2) nonlinear equations, 3) simultaneous linear equations including Eigenvalues/eigenvectors, 4) interpolation, 5) regression, 6) differentiation, 7) integration, 8) differential equations


Under the NSF funding for the prototype (2002-03), we developed modules for

    1. Nonlinear Equation
    2. Interpolation


Under the second NSF grant (2004-07), we developed four more modules.

    3. Integration

    4. Ordinary Differential Equations

    5. Simultaneous Linear Equations
    6. Regression


Under the third NSF grant (2008-12), we developed five more modules.

     7.   Introduction to Scientific Computing

     8.   Differentiation

     9.   Fast Fourier Transforms
     10. Partial Differential Equations

     11.  Optimization


Under the fourth NSF grant (2013-16), we used the developed modules to compare a flipped class with a blended class.


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There is no registration needed to use the course material.  We are keeping it purely open access without any hassles or obstacles such as payment of use, registration, downloading, buying expensive software, etc.  But drop me a note to tell me how you are using the resources.  However, I am requiring faculty members who use any of the the course material to send me brief info and put link(s) to HNMI on their web site.

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Faculty members can use the materials to enhance their classroom lecture by using the power point presentations and simulations.  They can ask students to quickly assess their knowledge by taking the online assessment of multiple choice questions.   They can ask students to pre-study the topics so that class time is used for discussion purposes.

However, I am requiring faculty members who use any of the the course material to send me brief info and put link(s) to HNMI on their web site.   This will help us to keep this site unrestricted and at the same time show where it is being used.

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Q. How can a student use the course material?

A student can use it to review background information on a topic, perform their own simulations, review course material, go for self-assessment of knowledge, learn how other engineering majors use numerical methods, have seven different examples to illustrate each method.

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This courseware would only be possible with the web.  We have taken a holistic approach where users can review the background information as well as see the higher level application of what they have learned.  We have also taken a customized approach because had the contents been written in a a book form, one would have to write 28 versions of the book.  But with this courseware, a student has 24/7 access and can work at his own pace with help from text book notes, simulations and assessment.

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Q. What intellectual property policies govern the materials?

The materials given on the web site are original and written by the faculty and students at the University of South Florida, Florida A&M and Old Dominion University.  Any other material is either in public domain, or permission has been given for its use and is acknowledged.  If you have any questions about the ownership of the materials, please contact us.

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Q. How do we define non-commercial use?

The material on the web site or its derivatives can only be used for nonprofit purposes in educational institutions of any grade level.    Providing direct links on user's website are critical in fair use of the materials.  For full details, see the creative commons license.

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Q. How was the courseware developed?

The course was developed using Microsoft FrontPage and JavaScript for the web pages, Studymate for  assessment tools; Microsoft Office for the text notes and lecture presentations;  MathCAD, Maple, MATHEMATICA and MATLAB for the worksheets; Acrobat Pro for making of the PDF files; Adobe Photoshop for editing images; Flash for drawing sketches; and Microsoft Publisher for advertisements.

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Q. What are the system and technical requirements for the course materials?

Read all the system and technical requirements.

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Q. How do I search the course material I am looking for?

  • If you know a topic and have a language of choice, the best page to find the course material is the resource page.

  • You can also use google search that searches the whole website.

  • You can also go to the site index.

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Q. How is HNMI supported?

The Holistic Numerical Methods Institute was funded by National Science Foundation through their CCLI program.  Support also came from 

  • the Mechanical Engineering Department at USF via faculty release time and conference support, 

  • the College of Engineering at USF via undergraduate students through their REU program,

  • the Engineering Computing at USF via software support and web site maintenance,

  • the University of South Florida via offering the PI sabbatical in Fall 2002 and Fall 2010 to develop the web site and form a basis for a full development proposal granted by NSF in December 2003 and a national dissemination proposal submitted to NSF in January 2011 , 

  • Academic Computing at USF via support of software training and Blackboard access,

  • Maplesoft

  • MathWorks

  • MathCAD

  • Milwaukee School of Engineering

  • Florida A&M University

  • Old Dominion University

  • Arizona State University

  • University of Pittsburgh

  • Alabama A&M University

  • Mississippi Valley State University

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Q. What are the long-term goals of HNMI?

The long term goals of HNMI are to develop course materials for all the main topics taught in a course in Numerical Methods.

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Q. How does a faculty member contact a real person from HNMI?

Contact the Principal Investigator - Autar Kaw via telephone, e-mail, fax or mail.  Any inquiry, especially from instructors of Numerical Methods, will be answered.  We welcome your questions, comments, and suggestions.  We would like to help you in incorporating the contents of the website in your course.

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Q. Why are the worksheets, especially ones written in MATLAB, not modular?

The worksheets, especially those written in MATLAB, at first might appear not well written; they do not take advantage of modular programming.  However, in our website modules, we wanted to keep all subroutines and functions within a single script file. This might not seem logical at first glance. 


But, it is important to note the overall goal of the worksheets is to provide the student only one file.  The content is in one file for simplicity.  Otherwise, there would be dozens of files that the student would have to manage and understand-- not just one. 


Also we want to show a numerical method worked out step-by-step as if the student was working it out by hand.  This is why many of the worksheets show each iteration separately as opposed to in a loop.


We hope that you would ask your students to write procedures (subroutines, functions, etc) and use modular programming techniques as part of the learning process of Numerical Methods.

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Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.