## Resources for Numerical Methods

Are you taking or teaching a course in Numerical Methods in Spring 2018.   If so, then look at all these resources.

Open CourseWare:

Blog:

## I thought Gaussian quadrature requires that the integral must be transformed to the integral limit of [-1,1]?

Question asked on YouTube: I thought Gaussian quadrature requires that the integral must be transformed to the integral limit of [-1,1]? The document in the above image is given here. This post is brought to you by

• Holistic Numerical Methods Open Course Ware:
• the textbooks on
• the Massive Open Online Course (MOOCs) available at

## Getting Started on Smart Sparrow Adaptive Platform

May 13, 2017

Autar Kaw

We are developing content for a course in Numerical Methods on the Smart Sparrow adaptive platform. There is a learning curve for you to get started but it does not have to be difficult.  To get going, we propose the following.

1. Watch this YouTube Smart Sparrow playlist to get an overview (22 minutes of video).
3. This tutorial from Learning Solutions magazine illustrates the authoring environment.
4. The knowledge base for Smart Sparrow is an essential resource and I would concentrate just on the creating lessons part first.
5. Then there is always the dependable support available by emailing to support@smartsparrow.com or by filling an online form.

In our future blogs, we will be illustrating our use of Smart Sparrow in the development of our lessons by creating tutorials based on generic content.

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This post is brought to you by

• Holistic Numerical Methods Open Course Ware:
• the textbooks on
• the Massive Open Online Course (MOOCs) available at

## A MOOC on Numerical Methods Released

After the rigorous and comprehensive development and assessment of the NSF funded innovative open courseware on Numerical Methods since 2002, we are offering a FREE Massive Open Online Course (MOOC) in Numerical Methods – Part 1 of 2 at https://www.canvas.net/browse/usflorida/courses/numerical-methods

The MOOC is Part 1 of a two-part course in Numerical Methods.  The course covers the mathematical procedures of differentiation, nonlinear equations and simultaneous linear equations.  We had the MOOC on Udemy but we are migrating it to CANVAS in two stages. CANVAS has a broader appeal for free MOOCs, it has a user friendly interface, looks familiar for many students using CANVAS, and has the capability of online quizzes that are algorithmic.

Start your journey today whether you are learning numerical methods for the first time or just need a refresher.  Unlike other MOOCs, you have a lifetime access to the course and you can pace yourself. Ask questions within the course and we will keep the conversation going! About: Numerical methods are techniques to approximate mathematical procedures (an example of a mathematical procedure is an integral).  Approximations are needed because we either cannot solve the procedure analytically (an example is the standard normal cumulative  distribution function) or because the analytical method is intractable (an example is solving a set of a thousand simultaneous linear equations for a thousand unknowns).

Materials Included: Textbook Chapters, Video Lectures, Quizzes, Solutions to Quizzes

How Long to Complete: About 20 hours of lectures need to be watched and estimated  time to read the textbook and do quizzes is 40 hours.  It is a typical 7-week semester length course.

Course Structure: For each section, you have video lectures, which are followed by a textbook chapter, a quiz and its complete solution, and automatically graded online quizzes.

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This post is brought to you by

• Holistic Numerical Methods Open Course Ware:
• the textbooks on
• the Massive Open Online Course (MOOCs) available at

## A Facebook Page for Numerical Methods

The Facebook page would be a place to keep the social media conversation going on – the one that has been going on via YouTube comments, twitter and this blog.

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This post is brought to you by

## Reconciling secant method formulas

Depending on how you derive the secant method, one gets the final formulas that are the same but the form is different.  This blog shows one how to reconcile the formulas.   _______________________________

This post is brought to you by

## A Grant to Study Flipped (Inverted) Classrooms

I will be leading a 4-institution team (USF, AAMU, ASU and Univ of Pitt) to improve and assess student learning in an inverted STEM classroom setting.  This is a 3-year study funded by National Science Foundation, and we will compare a hybrid classroom to the flipped classroom for a course in Numerical Methods.

Summary: Numerical methods are taught by many engineering disciplines throughout the nation and therefore more engaging and effective teaching of these methods could result in better prepared engineering graduates. When teaching numerical methods it is critical to cover not only theoretical concepts required for algorithm development and selection but also the precise language of computer programming required for algorithm implementation. This project is evaluating the efficacy of using an inverted classroom methodology to teach these diverse concepts.

Results from this project will include on-line materials that encourage and support use of active in-class pedagogical methods and assessments of these materials and methods. These results will inform the education community regarding the efficacy of teaching numerical methods using an Inverted classroom methodology. The materials will be readily available to engineering departments nationally and assessment results will help faculty better understand what aspects of numerical methods can be taught using an inverted methodology and also will give them the resources needed to teach in similar ways.

Multiple universities with diverse student populations are implementing the methods and materials of this project. Assessment and evaluation is performed by another university not affiliated with the implementers; therefore, evaluation is independent of the instructors. Evaluation of student performance is partially being assessed using a numerical methods concept inventory which is being developed by the program.

Successful results in this research could transform the way engineering programs teach numerical methods nationally.

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This post is brought to you by

## A MOOC on Introduction to Numerical Methods

After the rigorous and comprehensive development and assessment of the NSF funded innovative open courseware on Numerical Methods between 2002 and 2012, we are offering a FREE Massive Open Online Course (MOOC) in Numerical Methods at http://udemy.com/numericalmethodsguy

Start your journey today whether you are learning numerical methods for the first time or just need a refresher.  Unlike other MOOCs, you have a lifetime access to the course. Ask questions within the course and we can keep the conversation going! About: Numerical methods are techniques to approximate mathematical procedures (example of a mathematical procedure is an integral).  Approximations are needed because we either cannot solve the procedure analytically (example is the standard normal cumulative  distribution function) or because the analytical method is intractable (example is solving a set of a thousand simultaneous linear equations for a thousand unknowns).

Materials Included: Textbook Chapters, Video Lectures, Quizzes, Solutions to Quizzes

How Long to Complete: About 40 hours of lectures need to be watched and estimated  time to read textbook and do quizzes is 80 hours.  It is a typical 15-week semester length course.

Course Structure: For each section, you have video lectures, followed by a textbook chapter, a quiz and solutions to quizzes.

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This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://nm.MathForCollege.com, the textbook on Numerical Methods with Applications available from the lulu storefront, the textbook on Introduction to Programming Concepts Using MATLAB, and the YouTube video lectures available at http://nm.MathForCollege.com/videos. Subscribe to the blog via a reader or email to stay updated with this blog. Let the information follow you.

## Using Taylor polynomial to approximately solve an ordinary differential equation

Taylor polynomial is an essential concept in understanding numerical methods. Examples abound and include finding accuracy of divided difference approximation of derivatives and forming the basis for Romberg method of numerical integration.

In this example, we are given an ordinary differential equation and we use the Taylor polynomial to approximately solve the ODE for the value of the dependent variable at a particular value of the independent variable. As a homework assignment, do the following.
1) compare the approximate solution with the exact one, and
2) get another approximate solution by using a third order Taylor polynomial.  