Chap-04 B.V.Ramana August 30‚ 2006 10:13 Chapter 4 Calculus of Variations function of the independent variable y(x)‚ which is a function. Thus L{y(x)} = Y cn c2 A O c1 X B x2 x1 4.1 INTRODUCTION Calculus of variations deals with certain kinds of “external problems” in which expressions involving integrals are optimized (maximized or minimized). Euler and Lagrange in the 18th century laid the foundations‚ with the classical problems of determining a closed curve in the plane
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Dream Summaries Day Dreaming: When your imagination carries you away. Daydreaming is a classified level of consciousness between sleep and wakefulness. False Awakening Dreams: You dream that you wake up and your day starts‚ but then you actually wake up. Lucid Dreaming: Where you realize you are dreaming during your dream‚ and then have the ability to control your dream and what happens inside of it. Nightmares: A nightmare is a disturbing dream that causes you to wake up feeling anxious and
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Dreams In the Greek and Roman eras‚ dreams were seen in a religious context. They were believed to be direct messages from the gods or from the dead. The people of that time look to their dreams for solutions on what to do or what course of action to take. They believed dreams forewarned and predicted the future. Greek philosopher‚ Aristotle‚ believed that dreams were a result of physiological functions. Dreams were able to diagnose illness and predict onset of disease. During the Middle Ages
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Dream my Dream Without dream‚ there can be no courage; without courage‚ there can be no action. What Wim Wenders said indicates the importance of the dream‚ which no one can deny. Most people’s dream is not stable and changes with the time going by‚ but the critical point is that they do have a dream. I’m the person with a dream. I once romantically dreamed to be an excellent diplomat at early age and later‚ I was looking forward to teaching undergraduates in a historical university. But now‚ I’m
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Reflection – Why we dream. Dream is a very interesting phenomenon that occurs every time we sleep or at least once at a time. Till now‚ dream remains enigma for us about its capability to be virtually shown to the other person. Scientists discoveries up till today has bring up our exitement to study more about our dream. Me myself‚ has been a little bit enthusiatic after watching the potential‚ importance and benefits that dream can do throughout the documentary. Rem sleep was
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"Dreams are the touchstones of our characters."- Henry David Thoreau Dreams have fascinated philosophers for thousands of years‚ but only recently have dreams been subjected to empirical research and concentrated scientific study. Chances are that you’ve often found yourself puzzling over the mysterious content of a dream‚ or perhaps you’ve wondered why you dream at all. What is a dream? A dream can include any of the images‚ thoughts and emotions that are experienced during sleep. Dreams can
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Dreams are very different from waking life‚ but it is extremely difficult clearly to define in what the difference consists. When we are dreaming‚ we are nearly always convinced that we are awake‚ and in some cases real experiences have been mistaken for dreams. The latter mistake forms the subject of a celebrated Spanish play called Life a Dream‚ and of an amusing story in the Arabian Nights‚ in which a poor man is for a jest treated as a mighty monarch‚ and it is contrived that he should afterwards
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Dreams Introduction Dreams are successions of images‚ ideas‚ emotions‚ and sensations that occur involuntarily in the mind during certain stages of sleep. The content and purpose of dreams are not definitively understood‚ though they have been a topic of scientific speculation and a subject of philosophical and religious interest throughout recorded history. The scientific study of dreams is called oneirology. Scientists believe that other mammals‚ birds and reptiles‚ also dream. Dreams mainly
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Ruoqi Xu Psychology Professor Dude 11/22/12 Dream and Its Meaning Dream can be happy‚ delightful‚ absurd or even fearful. Dream is what we experience when we sleep; it “involves an integration of perceptual‚ emotional‚ motivational‚ and cognitive processes performed by various brain modules” (Passer and Ronald193). However‚ the content of the dream and the reason why we dream specific content still remain a mystery till today. Although many scientists have been attempting to find the answers
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individuals are the characters Katherine‚ Clara and Beethoven in Moisés Kaufman’s 33 Variations. These three characters although each of their challenges have different risks and rewards‚ had the courage to move out of their comfort zone. This is significant because these characters did something different than the average human‚ which gives a view into what can happen if we follow their footsteps. In the play 33 Variations‚ Moisés Kaufman shows how humans who do extraordinary
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