Prototype web based resources have been developed for an undergraduate course in Numerical Methods. The web modules are holistic, that is they include pre-requisite information, real-life applications, presentations and notes, simulations, and selfassessment. The student interest and learning are maximized by providing customization of content based on a student's engineering major and computational system of choice.
KeywordsNumerical methods, web enhanced courses, Mathcad, Maple, Matlab, MathematicaHolistic but Customized Resources for a Course in Numerical Methods 1
Figure 1: Higher Order Interpolation is a
IntroductionBelow is one of the many conversations (The acts and the names of the characters are real! Resemblance to persons and incidents, past or present, are true and not coincidental) the first author has had with undergraduates using numerical methods and computational systems [1][2][3][4] to solve problems in engineering courses.Peter: "Dr. Kaw, I am taking a course in Manufacturing. We need to find an efficient and smooth path that a robot could traverse to inspect holes at 10 specific locations on a 12"x12" square plate. I am using Maple [2] to fit a ninth order polynomial through the 10 points. But, when I plot the polynomial, it is oscillatory! It is a smooth path but by no means does it look efficient."Kaw: "As I recall, you took my course in Numerical Methods. What was that -one year ago?"Peter: "Yes, your memory is sharp but my retention from that course -can we not talk about that!" Kaw: "Come into my office. I wrote this program using Maple [2]. See this function, f(x) = 1/(1+25 x 2 ). I am choosing 9 points equidistantly between -1 and 1. Now look at the eight order interpolating polynomial and the original function (See Figure 1).See the oscillations in the interpolating polynomial. In 1901, Runge [5] used this example function to show that higher order interpolation is a bad idea. One of the solutions to your problem is to use quadratic or cubic spline interpolation option in Maple. That will give you a smooth curve with no oscillations."Most experienced engineering faculty will attest to have had conversations similar to these with current and former students. In engineering courses, we want our students to gain a comprehensive and conceptual understanding of engineering principles and not have to struggle with the mathematical and numerical aspects of engineering problems.When it comes to applying numerical methods, why do our students in upper level engineering courses face problems like these [6,7]? The following are the main reasons. All the above reasons become all the more critical when 43% of the 5000 engineering professors surveyed [9] believe that students drop out of engineering because they have not mastered difficult mathematical skills.
ObjectivesTo address the above concerns as well as to enhance the quality of teaching and learning numerical methods, a prototype project [10] of holistic web-based modules for numerical methods has been developed (http://numericalm...
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