Submitted By tleadmon

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Words 530

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...Formula, Power Series, Zeroes and Singularities(Simply Connected and Multiply Connected Domains) Cauchys Theorem, Cauchys Integral Formula, Power Series, Zeroes and Singularities(Cauchys Integral Theorem) Simply Connected and Multiply Connected Domains Knowledge of Basics White Board Teaching Week 4 Lecture 10 Cauchys Integral Theorem Development of Concept White Board Teaching Week 4 Lecture 11 Cauchys Theorem, Cauchys Integral Formula, Power Series, Zeroes and Singularities(Cauchys Integral Formula) Cauchys Theorem, Cauchys Integral Formula, Power Series, Zeroes and Singularities(Taylor Series) R-1:Ch 20 Calculus of Complex Functions Topic 20.14 T-1:Ch 12 Power Series Taylor and Laurent Series Topic 12.5 R-1:Ch 20 Calculus of Complex Functions Topic 20.16(1) T-1:Ch 12 Power Series Taylor and Laurent Series Topic 12.6 R-1:Ch 20 Calculus of Complex Functions Topic 20.16(1) T-1:Ch 13 Zeroes Singularities and Residues Topics 13.1 13.2 R-1:Ch 20 Calculus of Complex Functions Topic 20.17(1) T-1:Ch 13 Zeroes Singularities and Residues Topic 13.3 T-1:Ch 13 Zeroes Singularities and Residues Topic 13.4 R-1:Ch 20 Calculus of Complex Functions Topics 20.18(2) 20.19 Cauchys Integral Formula Numerical Applicability White Board Teaching Lecture 12 Taylor Series Numerical Applicability White Board Teaching Week 5 Lecture 13 Cauchys Theorem, Cauchys Integral Formula, Power Series, Zeroes and Singularities(Laurent......

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...Modeling Assignment – 1 2013 Answer all questions. 1. When the deflections of a statically determinant beam are calculated using singularity functions, it is necessary to know the values of 2 boundary conditions. For each of the beams below, what are the boundary conditions? 2. Calculate the reactions and draw the SFD and BMD for the cantilever beams below. Using singularity functions, calculate the deflection at 2 metres, the deflection at the tip, and sketch the deflected shape. The cross section of the beam is 300 mm deep by 200 mm wide, and it is made of concrete with a Young’s modulus of 30,000 MPa. 4. Using singularity functions, derive (in terms of P) the equation for the upwards deflection at midspan of the beam below. EI = 10 x 106 Nm2 5. Determine the location and value of the maximum deflection for the beam below. How far from the centre is the point of maximum deflection (expressed as a percentage of the span length)? EI = 10 x 106 Nm2 6. Calculate the reactions and draw the shear force and bending moment diagrams for the beam below. EI = 10 x 106 Nm2 (Note that this has four reactions, so the 3 equations of equilibrium do not give sufficient information to solve the problem – it is statically indeterminate. The answer requires you to use the results from questions 4 and 5). 7. For the beam below, use singularity functions to determine an equation for the deflected shape, expressed in terms of x (measured from the left) and EI. If the......

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...194-195 Sunlight output is about 10^17 watts, and we only need 10^13 watts. This is 10k more then we currently need. Increased effectiveness of nanotechnology implies energy requirments will only oncrease to 3x10^13 by 2030. We can meed this energy need with 0.0003 of the sun's energy. Solar panals have been relatively inefficient and expensive, but technology is rapidly improving. Stedily advanced for silicon photovoltaic cells from 4% in 1952 to 24% in 1992. Currently around 34% efficiency. Effectiveness above 60% seems attainable. Today it costs $2.75 per watt. The price will fall, and once it does fall below $1.00, it will be competitive for directly supplying electricity to the nations grid. Currently, the price sits as low as $0.70 cents per watt. Once we have molecular nanotechnology based manufacturing, can produce solar panels extremely ineffictively, basically at the costs of raw materials. Could eventually be as inexpensive as a penny per square meter. Could put solar panels everywhere, on buildings, majority of human surfaces. Could put solar satellite into space and beam to earth via microwave. Each unit could provide billions of watts of electricity. Medicine 213 New ECG analysis for long-term unobtrusive monitoring, detect early warning signs of heart disease. AI programs to do pattern recognition and intelligent data mining in development of new drug therapies. Intelligent datamining tools to find new ways to distupt......

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...star’s core reaches a certain mass it will overwhelm it self and implode. The second type of supernova is formed when a white dwarf star accumulates gas from a companion star. Eventually the white dwarf star becomes compressed. It will ultimately “set off a runaway nuclear reaction inside, that eventually leads to a cataclysmic supernova outburst.” In other words some black holes are formed when massive stars go through supernova explosions. The supernova compresses stars over nine solar masses into extremely small volume of space and this is the reason why black hole gravities are so strong, strong enough to trap light. A black hole is composed of many parts. The point in the center of black holes is called a singularity. At a certain distance around the singularity the gravity will be strong enough to trap everything, light included. This is called the event horizon, also known as the point of no return. A general misconception is that people think the black hole just keeps on sucking everything in and nothing will escape. If this is true then the whole universe will eventually be swallowed by black holes. The reality is that entities that are farther and outside of the event horizon will simply orbit around it, much like how earth orbits around the sun. How big and how heavy are black holes? Astronomers believe some black holes can be as small as a single atom but weighs as much as mountains. There are also stellar black holes. Many of these black holes exist in......

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...information I present. Ray Kurzweil, author of “The singularity is near” explores the possibility and firmly believes that the singularity is nearly here. The technological singularity is a hypothetical moment in time when artificial intelligence will have progressed to the point of a greater-than-human intelligence, radically changing civilization, and perhaps human nature. Since the capabilities of such an intelligence may be difficult for a human to comprehend, the technological singularity is often seen as an occurrence (akin to a gravitational singularity) beyond which the future course of human history is unpredictable or even unfathomable. Included in this technological boom would be the capability to extend human life. (Kurzweil, 2005) With the rate at which technology is progressing, it is not so farfetched to consider such a possibility. Many scientists are working towards the goal that will lead us to this, the first step is computers that can think, learn and evolve. That alone is cause for pause, and a subject all in its own. We are within a decade of reaching such technology at our current pace. Once this happens, computers will evolve all areas of science at a rate that Humankind cannot begin to fathom. The possibilities would then expand out in every field. We are on the nexus of the greatest expansion of technological growth in all of Human history. The cons against Human mortality and the singularity is a very long list. While at first thought,......

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...your shopping cart will be active until you leave the store. All Tutorials will be E-mailed immediately after the Payment, Please Check your inbox or Spam Folder and can also be downloaded by clicking on Tutorial Bucket. For Any Other Inquiry Feel Free to Contact us: studentsoffortunes@gmail.com For More Tutorials Visit: ( http://www.studentsoffortunes.com/ ) (Product Description) INF 103 Week 1 DQ 1 The Future is Now Pretty Soon, at Least After reading Chapters One through Three, review the videos Ray Kurzweil on How Technology Will Transform Us and Ray Kurzweil: A University for the Coming Singularity. (Interactive transcripts are also available on the TED web site.) Based on what you have learned, which of Kurzweil’s predictions do you agree with, and which do you doubt? Why? Please be specific. Are you thrilled or worried about the coming singularity and exponential technology advances? Make your case with specific supporting materials. INF 103 Week 1 DQ 2 Research Project Brainstorming You must begin working on this important assignment this week. To get started, you will select a theme/topic from the suggested list found within the Research Project section of this Course Guide or under Week Five of the left navigation panel in the online course. If you have a theme/topic other than one listed, please submit it to your instructor for approval. After selecting a theme, begin brainstorming a plan on how to approach this exercise publicly......

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...INF 103 Computer Literacy Entire Course Follow Link Below To Get Tutorial http://homeworklance.com/downloads/inf-103-computer-literacy-entire-course/ Description: INF 103 Week 1 DQ 1 The Future is Now Pretty Soon, at Least After reading Chapters One through Three, review the videos Ray Kurzweil on How Technology Will Transform Us and Ray Kurzweil: A University for the Coming Singularity. (Interactive transcripts are also available on the TED web site.) Based on what you have learned, which of Kurzweil’s predictions do you agree with, and which do you doubt? Why? Please be specific. Are you thrilled or worried about the coming singularity and exponential technology advances? Make your case with specific supporting materials. INF 103 Week 1 DQ 2 Research Project Brainstorming You must begin working on this important assignment this week. To get started, you will select a theme/topic from the suggested list found within the Research Project section of this Course Guide or under Week Five of the left navigation panel in the online course. If you have a theme/topic other than one listed, please submit it to your instructor for approval. After selecting a theme, begin brainstorming a plan on how to approach this exercise publicly through this discussion forum. The discussion post must include the following information in a couple of detailed and descriptive paragraphs: a. Select a topic and explain why you chose the theme/topic (what interests you about this......

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...Superintelligence Reflection There are many differences in this paper compared to my first draft. In my first paper I tended to overuse the same pronouns when referring to the author. I also did not compare and contrast the authors as well as I should have and did not supply any possible solutions to the problems the authors wrote about. In this draft I tried to do a better job of inserting quotes without using sentences starting with “this quote…” or “this quote highlights”. Also I gave my view on how we should approach singularity as my solution to the problems and uncertainties discussed in this paper. As a whole I believe this paper is way better than my first. The biggest thing I took away from this assignment is how vital technology has and will be in mankind’s existence today and continued survival. Also my researching skills have improved after the continued practice I had throughout this assignment. Superintelligence A Superintelligence is “any intellect that vastly outperforms the best human brains in practically every field, including scientific creativity, general wisdom, and social skills”; however, this definition leaves open how the super intelligence is implemented – it could be in a digital computer, an ensemble of networked computers, cultured cortical tissue, or something else. The ethical issues surrounding the creation of these machines with general intellectual capabilities that far outstrip those of humans are very different and have far......

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...INF 103 Computer Literacy Entire Course Follow Link Below To Get Tutorial http://homeworklance.com/downloads/inf-103-computer-literacy-entire-course/ Description: INF 103 Week 1 DQ 1 The Future is Now Pretty Soon, at Least After reading Chapters One through Three, review the videos Ray Kurzweil on How Technology Will Transform Us and Ray Kurzweil: A University for the Coming Singularity. (Interactive transcripts are also available on the TED web site.) Based on what you have learned, which of Kurzweil’s predictions do you agree with, and which do you doubt? Why? Please be specific. Are you thrilled or worried about the coming singularity and exponential technology advances? Make your case with specific supporting materials. INF 103 Week 1 DQ 2 Research Project Brainstorming You must begin working on this important assignment this week. To get started, you will select a theme/topic from the suggested list found within the Research Project section of this Course Guide or under Week Five of the left navigation panel in the online course. If you have a theme/topic other than one listed, please submit it to your instructor for approval. After selecting a theme, begin brainstorming a plan on how to approach this exercise publicly through this discussion forum. The discussion post must include the following information in a couple of detailed and descriptive paragraphs: a. Select a topic and explain why you chose the theme/topic (what interests you about this......

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...So why does the mention of artificial intelligence conjure scenes of destruction like we just watched? Many of us take a pessimistic view when asked about AI. Today I want to explain to you the biggest fear associated with artificial intelligence, share examples of this technology that is already in successful use, and describe why you should support the development of artificial intelligence. I.) Having already mentioned a few movies that seem to give very negative connotations to the use of artificial intelligence, let’s begin by looking at one of the biggest oppositions facing artificial intelligence, the argument against singularity. a.) What is singularity? According to Merriam-Webster’s Dictionary, singularity is “the quality or state of being singular.” (Merriam-Webster). i.) Pertaining to the field of artificial intelligence singularity is the moment when machines reach a level of intelligence that surpasses that of human intelligence, thus becoming a singular entity void of the necessity of human interaction. b.) In a recent interview with BBC British Physicist Stephen Hawking states “The development of full artificial intelligence could spell the end of the human race”. (Cellan-Jones). The problem with this statement is the fact that most of you know who Stephen Hawking is and his status in the scientific community. This means that most people just accept this statement as a truth, instead of what it is; a hypothesis. i.) Another lesser known, but......

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...happened during and after that moment. According to the standard theory, our universe sprang into existence as "singularity" around 13.7 billion years ago. What is a "singularity" and where does it come from? Well, to be honest, we don't know for sure. Singularities are zones which defy our current understanding of physics. They are thought to exist at the core of "black holes." Black holes are areas of intense gravitational pressure. The pressure is thought to be so intense that finite matter is actually squished into infinite density (a mathematical concept which truly boggles the mind). These zones of infinite density are called "singularities." Our universe is thought to have begun as an infinitesimally small, infinitely hot, infinitely dense, something - a singularity. Where did it come from? We don't know. Why did it appear? We don't know. After its initial appearance, it apparently inflated (the "Big Bang"), expanded and cooled, going from very, very small and very, very hot, to the size and temperature of our current universe. It continues to expand and cool to this day and we are inside of it: incredible creatures living on a unique planet, circling a beautiful star clustered together with several hundred billion other stars in a galaxy soaring through the cosmos, all of which is inside of an expanding universe that began as an infinitesimal singularity which appeared out of nowhere for reasons unknown. This is the Big Bang theory. Big Bang Theory - Common......

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...I truly believe that we are a lot closer than we think to achieving artificial intelligence and singularity due to the constant and ever changing advancements of computing, speech recognition, optical recognition, and real-time translation of languages on mobile devices. I do kinda think and feel that true AI and singularity can never be truly achieved based on the fact that a live human has to do all the programming within the computer in order for them to really have AI. If you really think about it a human programs the computer to run commands and when you think about it the only reason a computer can win at Jeopardy or Chess is because a person programmed all the different possibilities for each game. If you believe that makes a computer smarter than a human then I think you need to go back and do a little more research before you can make a qualified argument that a computer is smarter than a human. Think about when you see those commercials or news stories about facebook, they all show people sitting on computers writing code. A computer can not simply go beyond what we program it to do. I have seen the movie IRobot and that does not faze me at all. I also think that if singularity really becomes what I think it will then we as humans are better off without it. This brings to mind an episode od The Big Bang Theory where Lenord asks Shelton why he doesn’t keep his money in the bank and Sheldon came back with, “ I believe that when robots begin to think for themselves the...

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...what initially put Stephen in his wheel chair. While all of this was happenign to Stephen, he was also fortunate enough to meet a young woman by the name of Jane Wilde. They were married in 1965. He finished Cambridge in 1966 with a doctorite. He then was employed by Cambridge and started his teaching career. While working at Cambridge, his research was first noted with his theory of singularity. The theory of singularity is when a place in space or time at one point becomes infinite. The best example of this is a black hole. He worked with Roger Penrose during his work and Roger finally was able to prive the singularity theory. Using what he had found in Penrose’s work along with the famed earlier work of Albert Einstein, Stephen was able to find that all of the origins of the universe were in singularity. This means that the universe started in one concentrated place and eventually grew and is still growing to infinity. This is just further proof of the big bang theory, Hawking was just able to help solidify the previous thoughts regarding how the unverse was conceived. The theory of singularity didn’t stop there, it was taken to another level with black holes. We all know they exist but until Stephen was able to apply his theory and do research, nobody knew exactly what it was or did. He was able to prove that the edges of a black hole (called the event horizon) was growing over time instead of shrinking or gettign sucked into itself. He was also able to prove that......

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...happened during and after that moment. According to the standard theory, our universe sprang into existence as "singularity" around 13.7 billion years ago. What is a "singularity" and where does it come from? Well, to be honest, we don't know for sure. Singularities are zones which defy our current understanding of physics. They are thought to exist at the core of "black holes." Black holes are areas of intense gravitational pressure. The pressure is thought to be so intense that finite matter is actually squished into infinite density (a mathematical concept which truly boggles the mind). These zones of infinite density are called "singularities." Our universe is thought to have begun as an infinitesimally small, infinitely hot, infinitely dense, something - a singularity. Where did it come from? We don't know. Why did it appear? We don't know. After its initial appearance, it apparently inflated (the "Big Bang"), expanded and cooled, going from very, very small and very, very hot, to the size and temperature of our current universe. It continues to expand and cool to this day and we are inside of it: incredible creatures living on a unique planet, circling a beautiful star clustered together with several hundred billion other stars in a galaxy soaring through the cosmos, all of which is inside of an expanding universe that began as an infinitesimal singularity which appeared out of nowhere for reasons unknown. This is the Big Bang theory. Big Bang Theory - Common......

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...reserved. (8) (9) 3 20 f(ζ) 0 −20 0 5 10 15 20 f(ζ) 0 −20 0 10 20 ζ 30 40 50 Figure 2: Plots of f (ζ ) = 1 − ζ cot(ζ ) − Bi for Bi = 5 showing roots (*) and singularities (o) of Equation (10). Upper plot shows the range 0 ≤ ζ ≤ 15. Lower plot shows the range 0 ≤ ζ ≤ 50. The ζn are the positive roots of 1 − ζn cot(ζn ) = Bi. (10) Equations (8) through (10) provide a compact representation of the solution. Obtaining numerical values from these formulas is a nontrivial eﬀort except in the case where Fo 1 when a one term approximation is suﬃcient. In general, at least the ﬁrst few terms terms in the series are needed. 3 Evaluating the Solution in Matlab In this section, a procedure for evaluating Equation (8) is presented. The Matlab programs, or (for long programs) the function prologues, are listed in the appendix. 3.1 Finding the Roots of Equation (10) The ﬁrst task is to ﬁnd the roots, ζn , of Equation (10) for a given Bi. This is a standard root-ﬁnding problem, with two important complications. First, there are an inﬁnite number of ζn on the positive real line. To evaluate Equation (8) a large number of roots must be available and sorted in order of increasing ζn . A missing root will cause erroneous evaluation of the series. The second complication is that Equation (10) has a singularity between successive roots. Copyright c 2011, Gerald Recktenwald. All rights reserved. 3.1 Finding the Roots of Equation (10) 4 Figure 2 shows the function f......

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