# Orthogonal polynomials

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have been proposed and investigated for treating these problems. The most common method is the use of polynomials that are orthogonal over unbounded domains, such as the Hermite and Laguerre spectral methods [10, 11, 12, 13]. Guo [14, 15] proposed a method that proceeds by mapping the original problem in an unbounded domain to a problem in a bounded domain, and then using suitable Jacobi polynomials to approximate the resulting problems. Another approach is using the domain truncation method by choosing

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quadratic formula for solving a quadratic equation. In the eighth century, the great Persian mathematician, Al-Kharizmi, offered a solution to the quadratic equation by completing the square. But solving the cubic equation or finding the zeroes of the polynomials of degree three evaded the great mathematicians. Omar Khayyan, the Islamic poet, astronomer, and mathematician attempted to find a general algebraic solution to the cubic equation but was able to only offer a geometric solution for a specific cubic

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removed called Frobenius Method) of differential equations. We present a few examples on this method by solving special second order ordinary differential equations. Key words ; Power series, differential equations, Frobenius Method, Lengendre polynomials 1.0 INTRODUCTION 1.1 BACKGROUND OF THE STUDY The attempt to solve physical problems led gradually to Mathematical models involving an equation in which a function and its derivatives play important role. However, the theoretical development

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Patience is the key in accomplishing anything. My most challenging class this year would be my Math Analysis Honors course. My main struggle was fully understanding the curriculum that I avoided my sophomore year, with Algebra 2 Honors. The curriculum was knowing the domain and range of a graph, I assumed that this notion would stay in Algebra 2 and not follow me into my next math course. Starting off the year, the class was simple as it was review of Algebra 2, however days later I am faced with

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Fig. 10 compares the switching instances between – (i) CSFSVPWM and VSFSVPWM, and (ii) CSFDPWM2 and VSFDPWM2. It also shows the shape of the switching frequency variation for each sector. The following can be noted: - The VSFSVPWM reduces 3 switching instances per cycle compared to CSFSVPWM, a 13.6 % reduction. - The VSFDPWM reduces 2 switching instance per cycle compared to CSFDPWM, a 12.5% reduction. Hence, the proposed variable switching frequency PWM reduces the switching instances within a

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“Slightly and squeaky!” The door to the classroom flew open as I burst into the room and sat in my usual seat. This was the day I was going to learn how to do polynomial long division. “Good morning.” The professor said, as she walked into the classroom. Almost every one of the students had at least a pencil and notebook, copying notes that the teacher had put on the board. After writing the notes down, I said to myself, let me try to do one of the problems that the teacher had put on board. Surprisingly

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Many people around the world have used medication to treat a medical issue, many individuals use medication daily to treat various issues and reasons including but not limited to diseases, disorders, for life, and pain management. Pain is an interesting concept, as the sensation is subjective to each individual, making it difficult to define. Anatomically, pain can be explained in steps: contact, reception, transmission, and receiving. First there is a stimulus; it can be pressure, puncture, a burn

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During the years of high school, students are exposed to multitudes of branches of mathematics. Each math prepares you for college and different careers; however, algebra is the basic math every person will use throughout their life. Algebra will play a role in my life throughout my college career and adult life by means of taxes and shopping. . During college, students must take specified required classes- math, language, science, and social studies especially- as well as classes designed for the

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When I was in fifth grade, I was taking third grade math. I could not, for the life of me, figure it out. Math was a huge struggle, and it still is. However, now, I am in Algebra II. Algebra II is a junior class and I am taking it as a sophomore. I have worked very hard to get where I am. This situation has made me realize a couple things. Number one: it is OK to ask questions. Number two: If you work hard, you will accomplish something. First off, I learned that it is not a sign of weakness to ask

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