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Solved: In each of 1 through 8, determine whether the given function is periodic. If so

Elementary Differential Equations and Boundary Value Problems | 10th Edition | ISBN: 9780470458310 | Authors: William E. Boyce ISBN: 9780470458310 168

Solution for problem 3 Chapter 10.2

Elementary Differential Equations and Boundary Value Problems | 10th Edition

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Elementary Differential Equations and Boundary Value Problems | 10th Edition | ISBN: 9780470458310 | Authors: William E. Boyce

Elementary Differential Equations and Boundary Value Problems | 10th Edition

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Problem 3

In each of 1 through 8, determine whether the given function is periodic. If so, find its fundamental period.sinh 2x

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Music Appreciation—Marc Dickerson **NOTES FOR EXAM II: March 24** Middle Ages • The Monarchy and the church held the power of music • The Queen and the Pope has all the power (the following is in descending order of power) arch-bishop • • bishop • common people • A vassal owned land from the Lord to whom they owned alliance • Knights were there to protect the Monarch • A serf is like a sharecropper because he would do manual labor in exchange for a plot of land where he can live with his family and grow food for family • Townspeople were free but still had to work; probably closest to the merchant class • A peasant had a very hard difficult life • You stayed in your class rank, so if you were born in the Monarchy, you stayed in the Monarchy • During the day when the knights were fighting the Crusades, they saw fabric and head music in Jerusalem and brought it back with them. This was the beginning of trade and the merchant class • The Middle ages were also known as the Dark Ages because the light of knowledge was gone due to the plague. People turned to the Church and monarchy for help. The only way you were given an education was to be in the Monarchy or the church • Sacred vs. Secular Music Sacred: the mass was one of the main influences in this type of music. Pope • Gregory developed the calendar and came up with the idea of putting music on lines and spaces • Secular: based on the monarchy and usually the songs would be about the King and how great he is. This is the start of what we know as love songs • Syllabic: one pitch per syllable/word Nematic: 2-5 pitches per syllable • • Melismatic: more than 5 pitches per syllables i.e. Alleluia • Hildegard of Bingen • wrote Alleluia • very influential in sacred music • She was a nun from Germany was the 1st real woman’s voice of Western music • • considered to be a saint • She would have these dreams telling her what to write and claimed they were from God • She wrote over 700 hymns from these dreams • Guillaume de Machaut known in secular music • • Was a Frenchman, with popular, advanced music of this time • Many of these musicians were travelers and their music was very often improvised • Music Instrument types of the Middle ages • Bas soft sounding music • • played inside • Haut • loud sounding music • played outside The Renaissance (1450-1600) • The rise of polyphony became widespread • The time in history is when they figure out the plague was carried by fleas in the fur of vermin and found a way to cure the problem • Often used pre-existing chants with added lines of melody during the time of Reformation and counter reformation • • The Crusades opened up trade routes which had an influence on music of the western world (development of merchant class) • Dance music used at court became very popular • So now people can start thinking about their lives again, the nuns and monks were closed off and kept culture going The Baroque Period (1600-1750) • one that lasted for the longest time, very ornamented, uses as many notes as possible • Centered in Germany • Greater use of polyphony Increasing conflicts between the church and monarchy • • Most courts had their own choirmasters • Churches began employing musicians full time • Widespread use of instruments in church music • Bach • Was born in Germany During his lifetime, he never traveled more than 50 miles from where he was born. • He was born into a musical family but lost both parents at age of 8. He moved in with his older brother and while his father let him play music, his brother thought he was too young. Bach kept nagging him about it until finally his brother brought down a music book and they went over the first page. After that, Bach snuck into the room where the books were kept and copied every single page. The night he finished copying all the books, his brother caught him and threw the pages into the fire. The next day, Bach came home from school and started practicing the pieces he copied from the book perfectly. His brother came in and heard, and asked him to play certain parts in the book to make sure Bach really didn’t have the pages in front of him but had it all memorized. After that, his brother gave him the books and told him that he would learn from him. Bach had 20 children and worked at least 5 jobs at once. • • He started going blind and went to several surgeons and went through many failed surgeries. He probably died because of infection • When he died, his music died with him until another composer found it many years later. • Bach viewed his music as utilitarian, to use for practical reasons. He didn’t consider himself a great composer • Equal temperament: making some of the notes out of tune to match the rest • Bach came up with music theory—if you are writing music and using cords to do it —and all of its rules. A toccata is where you can show off your talents. Fugue is polyphonic • • Antonio Vivaldi • Wrote “Spring” • He had a hunchback, very long unkept hair and a bright red beard, his nickname was the “Red Priest” • He became a priest to get an education Took a job at a girls school (where pregnant young girls can get an education) and • created a choir out of them • Handel (This Handel is Baroque) • Church came to him and asked if he could come up with a new hymn • Wrote “Messiah”; was written when he had dreams • Each syllable fit perfectly with the King James Bible from prophesies of Isaiah to the resurrection of Jesus. When he played for the King, everyone stood (because the King stood). So that is why we still stand today. The Classical Period (1750-1825) • a similar approach to harmony • Classical architecture is more like Greek, not very ornamented. Everything is extremely symmetrical • The musicians are still attached to some type of patron • The Age of Enlightenment: during this time, musicians started to write not just a symphony but their symphony. However, they don’t have complete freedom yet • Franz Joseph Haydn (“Papa Haydn”) • known as the father of the symphony The members of his own orchestra were very well taken care of • • He died shortly after Napoleon invaded Vienna • His father was a miller (he grounded wheat into flour) but he heard a little boy sing in a choir and made his son try out for the St. Steven’s boys choir. He had ragged clothes on compared to the nicely dressed boys but his voice was so pure that the choir master gave him a place in the Vienna Boys choirand a spot in the school for an education • People started falling asleep during his performances so he made a loud symbol and used dynamics to get people to stop falling asleep. This was called his surprise symphony. • Mozart • He was an Austrian musician • by the age of 3 he was playing melodies on the piano. By age 10 he wrote his first opera • His father had a plan and made Mozart perform because he saw money based on his amazing talents • Mozart wrote thousands of music sheets with ink and there was no sign of mistakes. It was perfect (it had to be perfect or else he wouldn’t perform it!) • He wrote the opera of the Magic Flute. In some of the scenes many people speculate that Mozart exposed some of the secrets of the Masons. Many Masons were killed because of this A musical bioptic is a movie about a composer or group. ex. Amadeus is a movie • about Mozart’s life • Mozart was witty and smart and silly and just wanted to play music. He hung out with common people and played for them • A concerto is a way for a performer to show off their ability. It has 3 movements. Mozart wrote one for each wind instrument except the trumpet (he would play the trumpet only if he wanted to pass out). • Most of his pieces were lost because he only wrote one copy • The notation for Mozart’s pieces were in chronological order. Example: K.191 means he was young when he wrote that piece. • He really liked to have fun with the concertos and sometimes when he wrote them for other people, he would throw all the pages (not numbered) into the air so that they would have to figure out the order again. • His father was very controlling, however, when he died, Mozart was left lost. He didn’t know how to manage his money or do other things for himself. He went into a deep depression and started dreaming and a figure came to him and asked him to write a requiem for someone who has died and that they would pay him more the faster he wrote it. Some people say this figure was his father helping him out with money, but others say it was the composer Salieri trying to steal Mozart’s work. Mozart worked to his death to try to finish this piece. On his death bed, Salieri even tried to help him finish it but Mozart’s wife comes in and tells him to go away and locks the piece up. They were completely broke when Mozart died so they had no money to bury him. His body lay in a Pulpers Grave and only about 20 people came to his funeral. He probably died from lack of Vitamin D, but some speculate it was the Masons. • • Cool Fact: in some of Mozart’s operas, he would use a technique called “singspiel” which literally means “singing/speaking” in German. This meant that instead of the entire opera be performed in song, there would be some dialogue to it • Ludwig Van Beethoven • Stands between the Classical and Romantic period. He was a transitional composer because some of his earlier pieces were Classical and the later ones were more romantic • He became deaf because of his father’s abusive nature. When his dad came home he’d make Beethoven practice and if he messed up, he would get a beating. Beethoven could listen to the music by putting the piano on the ground and feeling the vibrations. • Napoleon Bonaparte was one of Beethoven’s heroes (like many people in that age), so he wrote a song dedicated to “a hero.” Only later did Beethoven realize that he was a tyrant and so he changed the dedication to “in memory of a beloved hero.” A metronome (used to keep time) was invented just for him • • One day a prince asked him to come and play and when he got there he was told to go around because he was a musician (they put him with the servants). Beethoven did not like this so he cause such an ordeal that the prince eventually had to come out himself. Beethoven asked him along with all the servants if they could do what he was about to do. All of them said no and Beethoven was allowed in through the front door. This paved the way for all musicians to stand up for their talent and for themselves • Beethoven started to realize he was going deaf in 1800 and by the time he finished his final piece, he had gone completely deaf. • He decided to write one more symphony (he wrote a total of 9) and in the last movement of the symphony (the fourth part, usually all orchestral), he added the entire chorus. This is called the “Ode to Joy” • All he could sense was the vibrations but at the end of the performance, one of the musicians turned him around so he could see the standing ovation. • Beethoven only wrote on opera and 9 symphonies. • Unlike Mozart, Beethoven died a wealthy man. He died during a violent thunderstorm and when he was very sick he heard thunder struck and put his fist in the air toward the heavens like a final gesture—what else do you have for me

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Chapter 10.2, Problem 3 is Solved
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Textbook: Elementary Differential Equations and Boundary Value Problems
Edition: 10
Author: William E. Boyce
ISBN: 9780470458310

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Solved: In each of 1 through 8, determine whether the given function is periodic. If so