...In this work, we present an extremely efficient approach for a fast numerical evaluation of highly oscillatory spherical Bessel integrals occurring in the analytic expressions of the so-called molecular multi-center integrals over exponential type functions. The approach is based on the Slevinsky-Safouhi formulae for higher derivatives applied to spherical Bessel functions and on extrapolation methods combined with practical properties of sine and cosine functions. Recurrence relations are used for computing the approximations of the spherical Bessel integrals, allowing for a control of accuracy and the stability of the algorithm. The computer algebra system Maple was used in our development, mainly to prove the applicability of the extrapolation methods. Among molecular multi-center integrals, the three-center nuclear attraction and four-center two-electron Coulomb and exchange integrals are undoubtedly the most difficult ones to evaluate rapidly to a high pre-determined accuracy. These integrals are required for both density functional and ab initio calculations. Already for small molecules, many millions of them have to be computed. As the molecular system gets larger, the computation of these integrals becomes one of the most laborious and time consuming steps in molecular electronic structure calculation. Improvement of the computational methods of molecular integrals would be indispensable to a further development in computational studies of large molecular systems. Convergence...
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...students with a solid foundation in mathematics, physics, general chemistry and engineering drawing and to apply knowledge to engineering, architecture and other related disciplines. To complement the technical trairung of the students with proficiency in oral, written, and graphics communication. To instill in the students human values and cultural rehnement tbrough the humanities and social sciences. To inculcate high ethical standards in the students through its intesration in the leamins activities. COIIRSE SYLLABUS 1. 2. 3. 4, 5. 6. Course Code: Course Title: Pre-requisite: M.ath22 Calculus 2 Math 21 None 3 units Co-requisite: Credit: Course Description: This course covers topics on dehnite and indefinite integrals of algebraic and transcendental functions, tecbniques of iutegration, applications of...
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...Calculus From Wikipedia, the free encyclopedia This article is about the branch of mathematics. For other uses, see Calculus (disambiguation). Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem [show]Differential calculus [show]Integral calculus [show]Vector calculus [show]Multivariable calculus Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits,functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modernmathematics education. It has two major branches,differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science,economics, and engineering and can solve many problems for which algebra alone is insufficient. Historically, calculus was called "the calculus of infinitesimals", or "infinitesimal calculus". More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus...
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...Calculus is the mathematical study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally considered to have been founded in the 17th century by Isaac Newton and Gottfried Leibniz, today calculus has widespread uses in science, engineering and economics and can solve many problems that algebra alone cannot. Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". The word "calculus" comes from Latin (calculus) and refers to a small stone used for counting. More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, calculus of variations, lambda calculus, and...
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...section. (Discuss) Proposed since May 2011. | Topics in Calculus | Fundamental theorem Limits of functions Continuity Mean value theorem [show]Differential calculus | Derivative Change of variables Implicit differentiation Taylor's theorem Related rates Rules and identities:Power rule, Product rule, Quotient rule, Chain rule | [show]Integral calculus | IntegralLists of integrals Improper integrals Integration by: parts, disks, cylindrical shells, substitution, trigonometric substitution, partial fractions, changing order | [show]Vector calculus | Gradient Divergence Curl Laplacian Gradient theorem Green's theorem Stokes' theorem Divergence theorem | [show]Multivariable calculus | Matrix calculus Partial derivative Multiple integral Line integral Surface integral Volume integral Jacobian | | Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more...
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...the function is a probability density function. b. Use the graph to find P(X < 3) c. Use the graph to find P(3 § X § 8) 1 Solution: a. Recall, a function is a probability density function if the area under the curve is equal to 1 and all of the values of p(x) are non-negative. It is immediately clear that the values of p(x) are non-negative. To verify that the area under the curve is equal to 1, we recognize that the graph above can be viewed as a triangle. Its base 1 is 10 and its height is 0.2. Thus its area is equal to 10 0.2 1 . 2 b. There are two ways that we can solve this problem. Before we get started, though, we begin by drawing the shaded region. p x 0.2 0.1 2 4 6 8 10 x The first approach is to recognize that we can determine the area under the curve from 0 to 3 immediately. The shaded area is another...
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...Families as Negotiators Tamiko Dawkins USC Human Behavior and Development SOWK 503 Sherry Blair February 6, 2014 Families as Negotiators As I read this article the main points the author were trying to make were psychological resilience on both the individual and family level. As a little girl growing up being raised by my grandmother who was a widow with seven children of her own, I can definitely see how my personality was affected by my environment. Resilience is defined as the ability to become strong, healthy, or successful again after something bad happens or the ability of something to return to its original shape after it has been pulled, stretched, pressed, bent, etc. (Merriam-Webster, 2013). I can remember difficult times in my life where my reputation was on the line because of things I had done or poor choices I made, however because of how I was raised I was able to overcome. As a little girl I found myself in many distressed situations because of family dynamics and because of all that I am the woman I am today. Psychological resilience on the individual level relates to an individual’s tendency to cope with stress and adversity. Resilience is most commonly understood as a process, and not a trait of an individual. Most research now shows that resilience is the result of individuals being able to interact with their environments and the processes that either promote well-being or protect them against the overwhelming influences or risk factors (Zautra...
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...1. In my opinion, using the partial recognition approach (as did Circuit City) to account for extended warranty and service contracts is the most consistent with the actual sales transaction involving products extended warranty contracts. This approach is the most consistent for four reasons as we can see with Circuit City Stores, Inc. First, pricing of the sale of an extended warranty is an integral part of pricing of related products. As we can see with Circuit City the joint sale of products and warranties was indeed an integral part of their corporate strategy and by selling extended warranties and service contracts to a portion of their customers, Circuit City could price their products more competitively. [p2] A second reason why the partial revenue approach is more appropriate is because the sale of such warranties and contracts almost all the time accompany the purchase of a related product (as with Circuit City). A third reason, Circuit City could see that the profit margin on selling extended warranties was high in comparison to the profit margin of selling just the product itself as in the following example about Circuit City’s warranties. Example: Sales price of warranty- $100 Actual cost of warranty- $20 Profit = $80 Lastly, similar to the previous reason, the estimated costs to be incurred to render services or repairs under the warranty could be estimated with a high degree of reliability. As in the above example, Circuit City was very confident...
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...Ghbkhkgg2223543 The third approach is most consistent with the actual substance of sales transactions involving equipment and an extended warranty contract. Revenue from warranty has to be recognized when a period of a warranty is fulfilled. It would be wrong to consider revenue from the sale of an extended warranty or product maintenance contract at the time of sale since the company is still liable or obliged to the customers with the warranty. All are major elements of Partial Revenue Recognition on the sale of extended warranty and product maintenance contracts were applied in the Circuit City case since it was mentioned in the text that the sales has rapidly grew from $705 million in 1986 to $2.1 billion in 1990. This is when the company had introduced the extended warranty contracts and the profit margin form the extended warranty sales were high in comparison to the profit margin from the sale of products. The warranty contract relates to the product sold by Circuit City where the pricing of the sale of the extended warranty is an integral part of pricing the related product The third approach is most consistent with the actual substance of sales transactions involving equipment and an extended warranty contract. Revenue from warranty has to be recognized when a period of a warranty is fulfilled. It would be wrong to consider revenue from the sale of an extended warranty or product maintenance contract at the time of sale since the company is still liable or obliged to...
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...CHAPTER ONE INTRODUCTION In terms of etymology, the word system is actually derived from Greece, namely “Systema”, which in English is known as "SYSTEM", that had a meaning as a set of parts or components that are interconnected on regularly and it is a whole that cannot be separated. According to the Institute of Public Administration: “System is essentially a set of components, elements, which are related to each other, interplay and interdependence, so that the whole is an integrated unit or a totality, and has a specific role or purpose.” The following are the definitions of system according to some experts: 1. Stoa System is a combination of heaven and earth who work together, so that we can see that system consist of elements that work together to form a whole and if one element is missing or not working, then the overall combination cannot be called as a system. 2. Buckley System is a whole that functions as a whole by virtue of interdependence of its parts. 3. H. Kerzner System is a group of components consisting of humans and or non-human who organized and arranged so that the components can act as a unity in achieving its objectives, common goals or outcomes. This meaning implies the importance of aspects arrangement and organizing the components of a system to reach the common goal, because if there is no proper coordination and synchronization, then the activities of each component, sub–system, or areas in an organization will be less support each other. Furthermore...
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...developing sectors. This diversified approach is what makes Al Hanoo a pioneer and an integral facet in the economic hub of various countries in the world. As of today, Al Hanoo Holding Company and its subsidiaries are pioneers in their own areas of expertise, and continue to achieve success after success with projects that make difference in people’s life, such as Nujoom Islands City. A project embraced by the sea from every side and covers a massive 60 million square feet. Group of Companies Marsa Al Nejoum : The landmark Blue Bay Project is brought to you by UAE based Marsa Al Nejoum Real Estate, a subsidiary of Al Hanoo Holding Co (UAE's leading real estate company), a pioneering group with impeccable real estate development credentials. Established in 1972, with its headquarters in KSA, Al Hanoo Holding has become one of the leading real estate master-developers in the UAE and other GCC region. Al Hanoo Holding has already established its credentials in the region, when it launched the successful Emirates Industrial City in Sharjah; this success has ensured the launch of the iconic Blue Bay Project, to be the beginning of a series of successes. Besides real estate investment and development, Al Hanoo Holding also focuses on large scale infrastructure construction and trade with a strong presence in contracting, gas and electricity network installations, agriculture, trading and other developing sectors. This diversified approach makes Al Hanoo...
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...TLFeBOOK WHAT READERS ARE SAYIN6 "I wish I had had this book when I needed it most, which was during my pre-med classes. I t could have also been a great tool for me in a few medical school courses." Or. Kellie Aosley8 Recent Hedical school &a&ate "CALCULUS FOR THE UTTERLY CONFUSED has proven to be a wonderful review enabling me t o move forward in application of calculus and advanced topics in mathematics. I found it easy t o use and great as a reference for those darker aspects of calculus. I' Aaron Ladeville, Ekyiheeriky Student 'I1am so thankful for CALCULUS FOR THE UTTERLY CONFUSED! I started out Clueless but ended with an All' Erika Dickstein8 0usihess school Student "As a non-traditional student one thing I have learned is the Especially in importance of material supplementary t o texts. calculus it helps to have a second source, especially one as lucid and fun t o read as CALCULUS FOR THE UTTERtY CONFUSED. Anyone, whether you are a math weenie or not, will get something out of this book. With this book, your chances of survival in the calculus jungle are greatly increased.'I Brad &3~ker, Physics Student Other books i the Utterly Conhrsed Series include: n Financial Planning for the Utterly Confrcsed, Fifth Edition Job Hunting for the Utterly Confrcred Physics for the Utterly Confrred CALCULUS FOR THE UTTERLY CONFUSED Robert M. Oman Daniel M. Oman McGraw-Hill New York San Francisco Washington, D.C. Auckland Bogoth Caracas Lisbon...
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... ASSESSMENT PHILOSOPHY Some lecturers I appreciate so much in school presented their subjects in a way that caught my interest, clarified difficult topics and led me through complex areas, and put knowledge into context so that its relevance was apparent. These lecturers have influenced my approach to teaching: I view myself primarily as a facilitator of learning. Feedback from students has been vital to the process of growth since I began teaching: I learned from them, for example, the pacing of lectures, and effective ways to help them learn in small group discussions. According to Geyser (2004:91), assessment is the most powerful strategy that influence the way students learn and as a result, assessment practices for learning should be based on sound assessment principles. The following assessment principles are discussed below a. Assessment as an integral part of learning that should focus on deep, active learning and involve high order cognitive skills The paradigm shift distinguished between traditional/conventional and alternative assessment and further indicated that, the assessor, as the agent/source of assessment and, as an integral part of learning, must focus on deep active learning and involve high order cognitive skills rather than surface...
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...referred to as Cain’s notes), that I served as a primary text for an undergraduate level course in complex analysis. Throughout these notes I will make occasional references to results stated in these notes. The aim of my notes is to provide a few examples of applications of the residue theorem. The main goal is to illustrate how this theorem can be used to evaluate various types of integrals of real valued functions of real variable. Following Sec. 10.1 of Cain’s notes, let us recall that if C is a simple, closed contour and f is analytic within the region bounded by C except for finitely many points z0 , z1 , . . . , zk then k f (z)dz = 2πi C j=0 Resz=zj f (z), where Resz=a f (z) is the residue of f at a. 2 2.1 Evaluation of Real-Valued Integrals. Definite integrals involving trigonometric functions 2π We begin by briefly discussing integrals of the form F (sin at, cos bt)dt. 0 (1) Our method is easily adaptable for integrals over a different range, for example between 0 and π or between ±π. Given the form of an integrand in (1) one can reasonably hope that the integral results from the usual parameterization of the unit circle z = eit , 0 ≤ t ≤ 2π. So, let’s try z = eit . Then (see Sec. 3.3 of Cain’s notes), cos bt = z b + 1/z b eibt + e−ibt = , 2 2 sin at = eiat − e−iat z a − 1/z a = . 2i 2i Moreover, dz = ieit dt, so that dt = Putting all of this into (1) yields 2π dz . iz F (sin at, cos bt)dt...
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...is to present a theoretical framework that helps to conceptualize ethics and to clarify the characteristics and limits of the different ethical theories. In other words, students without philosophical background will find here a synthetic “road map” of ethical approaches. This framework has been previously published in a book in Spain2. In this paper, authors will describe the model and discuss how it has been successfully tested in two different contexts: a University of Catholic Inspiration and a State University. The framework proposed offers sound and solid philosophical foundations, consistent with Catholic social tradition. It allows students to engage with different business ethics traditions, mapping the territory with a critical approach, and showing their limitations. Authors of this paper strongly believe...
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