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Mathematical Formulas

Mathematical Formulas. Ing. Jaroslav Bernkopf. Objectives. Math symbols Math operations Expressing uncertainty. Vocabulary. Math Symbols. Math Symbols http://www.youtube.com/watch?v=CG0Q0jo2v6k. Math Symbols. W e will avoid numbers and stick to the language .

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Mathematical Formulas

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  1. MathematicalFormulas Ing. Jaroslav Bernkopf

  2. Objectives • Math symbols • Math operations • Expressing uncertainty http://skola.bernkopf.cz jaroslav@bernkopf.cz

  3. Vocabulary http://skola.bernkopf.cz jaroslav@bernkopf.cz

  4. Math Symbols MathSymbols http://www.youtube.com/watch?v=CG0Q0jo2v6k http://skola.bernkopf.cz jaroslav@bernkopf.cz

  5. Math Symbols Wewillavoid numbers and stick to the language. The most basic symbolsare+ - x ÷ =. http://skola.bernkopf.cz jaroslav@bernkopf.cz

  6. Math Symbols = The firstof the common symbols is the equal sign. We say this as equals or is equal to. 1 + 1 = 2 http://skola.bernkopf.cz jaroslav@bernkopf.cz

  7. Math Symbols + This is the addition sign. We say it as plus or add. 1+2, 4+9 http://skola.bernkopf.cz jaroslav@bernkopf.cz

  8. Math Symbols - The next one is the subtraction sign. We say it as minus, or subtract, or take. 1-2, 13-12, 99-7 http://skola.bernkopf.cz jaroslav@bernkopf.cz

  9. Math Symbols x , ∙ Then we have the multiplication sign. We say this as times or multiplied by. 3x8, 26∙3 http://skola.bernkopf.cz jaroslav@bernkopf.cz

  10. Math Symbols ÷ , / The next is the division sign. You can also show division as /. We say this as divided by, or over. 3 ÷ 1, 10 ÷ 5, 6 / 3 http://skola.bernkopf.cz jaroslav@bernkopf.cz

  11. Math Symbols √ This one is the square root. We say the square root of. √4 = 2 http://skola.bernkopf.cz jaroslav@bernkopf.cz

  12. Math Symbols % This one is the percentage sign. We say percent. 67% (per cent = outof100) http://skola.bernkopf.cz jaroslav@bernkopf.cz

  13. Math Symbols 𝜋 This one is Pi. This is a constant which begins 3.141592653... This is an irrational number. c = 𝜋 x d The circumference of a circle equals 𝜋 times its diameter. http://skola.bernkopf.cz jaroslav@bernkopf.cz

  14. Math Symbols ° The next symbol is the degree symbol. We say degrees. 90° 360° http://skola.bernkopf.cz jaroslav@bernkopf.cz

  15. Math Symbols ∞ Then we have the symbol for infinity. http://skola.bernkopf.cz jaroslav@bernkopf.cz

  16. Math Symbols ± Lastly, we have the plus minus sign. We say plus or minus. 6 ± 2 http://skola.bernkopf.cz jaroslav@bernkopf.cz

  17. Math Symbols Math Symbols Today’s Daily Dose of English is a request from Albert, in Catalunia, Spain. Albert has written: I recently saw the "Computer Symbols" video and thought it'd be really interesting [to have] a video about mathematic operations. For example, it took me some time to find out that 3 x 4 was read "three times four" (in Spanish we say "three by four"). There are plenty of them: 3+3, 3-3, 3*3, 3/3, 3^3, sqrt(3), 3! and a lot more which I don't know how to write their symbols now. Many thanks for your videos!!! :-) Albert Mata. And many thanks to you, Albert, for making the request. It’s an excellent question and one that I’m sure many students are also unsure about. Unfortunately, Math was never my strong point. I’ve always been very good with English and always very bad with mathematics. However, if we avoid numbers and stick to the language, I should manage to explain this one reasonably well. From school, I remember the basic symbols that most people are familiar with, even if we're not particularly good at manipulating them. The most basic of these are... + - x ÷ =Let's start with the first one. This is the addition sign. We say it as plus or add. 1+2, 4+9.The next one is the subtraction sign. We say it as minus, or subtract, or take. 1-2, 13-12, 99-7.Then we have the multiplication sign. We say this as times or multiplied by. 3x8, 26x3The next is the division sign. I discovered that this is also called the obelus. You can also show division as /. We say this as divided by, or over. 3 ÷ 1, 10 ÷ 5, 6 / 3The last of the common symbols is the equals sign. We say this as equals or is equal to.Other symbols I remember from my schooldays are... √ % π ° ∞ ± so we can look at these, too.This one is the square root. We say the square root of. √4 = 2This one is the percentage sign. We say percent. 100%This one is Pi. This is a mathematical constant which begins 3.141592653 and apparently has no end. This is an irrational number, apparently, though I have always been of the opinion that all numbers are irrational.People seem to be fascinated by Pi for the reason that it has no end. The only thing I remember about it is that the circumference of a circle equals π times its diameter, or something like that.The next symbol is the degree symbol. We say degrees. 90° 360°Then we have the symbol for infinity. That's about all I know of this one. Lastly, we have the plus minus sign. We say plus or minus. 6 ± 2. I have absolutely no idea why anyone would want to do this, but then again I teach English.My dislike of mathematics stems from my teacher making me stay in class at playtime because I couldn't memorize my multiplication tables when I was about 7 years old. I'm 7x7 now and I still don't know the multiplication tables by heart and I still don't like mathematics. So, I'm afraid that's the extent of my knowledge of mathematical symbols and the end of this Daily Dose of English.I hope you enjoyed it and I'll see you again soon for another one.Goodbye for now. http://skola.bernkopf.cz jaroslav@bernkopf.cz

  18. Math Symbols http://skola.bernkopf.cz jaroslav@bernkopf.cz

  19. Math Symbols List ofmathematicalsymbols http://en.wikipedia.org/wiki/List_of_mathematical_symbols http://skola.bernkopf.cz jaroslav@bernkopf.cz

  20. TheTipping Point I give you a large piece of paper. Fold thepaperover. Takethat folded paperand fold it over again. Refoldthe original paper 50 times. How tall is thefinal stack? Mostpeople guess: The pile would be as thick as a phone book, or it would beas tall as a refrigerator. Therealheight of the stack approximatesthe distance to theSun. Foldedit over one more time. The stackwould be as high as the distance to the sun and back. Thisis called a geometricprogression. Epidemics are another example of geometricprogression. Avirus spreads through a population. It doubles and doubles again. We have a hard time with thiskind of progression. The end result isfar out of proportion to the cause. http://skola.bernkopf.cz jaroslav@bernkopf.cz

  21. TheTipping Point MalcolmGladwell: TheTipping Point Consider, for example, the followingpuzzle. I give you a large piece of paper, and I askyou to fold it over once, and then take that folded paperand fold it over again, and then again, and again, until youhave refolded the original paper 50 times. How tall do youthink the final stack is going to be? In answer to that question,most people will fold the sheet in their mind's eye,and guess that the pile would be as thick as a phone bookor, if they're really courageous, they'll say that it would beas tall as a refrigerator. But the real answer is that theheight of the stack would approximate the distance to theSun. And if you folded it over one more time, the stackwould be as high as the distance to the sun and back. Thisis an example of what in mathematics is called a geometricprogression. Epidemics are another example of geometricprogression: when a virus spreads through a population,it doubles and doubles again, until it has (figuratively)grown from a single sheet of paper all the way to the Sun in fiftysteps. As human beings we have a hard time with thiskind of progression, because the end result — the effect —seems far out of proportion to the cause. http://skola.bernkopf.cz jaroslav@bernkopf.cz

  22. TheTipping Point Odpovězte anglicky: Jak vysoký by byl stoh přeložených papírů, kdybychom jeden papír přeložili 50x? Jak vysoký by byl stoh, kdybychom papír přeložili 51x? Popište, jak se množí virus. Přeložte do angličtiny: Dám ti velký kus papíru. Stoh by byl vysoký jako lednička. Znovu se zdvojnásobuje a zdvojnásobuje. 6x3 http://skola.bernkopf.cz jaroslav@bernkopf.cz

  23. PaperMagic PaperMagic http://www.youtube.com/watch?v=N1sOcD2vITQ http://skola.bernkopf.cz jaroslav@bernkopf.cz

  24. Apiece of string How long is a piece of string? http://www.youtube.com/watch?v=oqcTspe3efc http://skola.bernkopf.cz jaroslav@bernkopf.cz

  25. Apiece of string Hello, how long is a piece of string? Here is a piece of string, a long piece of string. Here is another piece of string, so a medium length piece of string. And here is another piece of string, it's a short piece of string, or pieces of strings of different length. There‘s anexpression in English which is „Howlong is a piece of string?" if you ask a question about a quantity, but given the information we have, there is no way to give an accurate answer: How long is it going to take to get there? How long is a piece of string? How much do you love me? How long is a piece of string? http://skola.bernkopf.cz jaroslav@bernkopf.cz

  26. Q & A Thankyou. Questions? http://skola.bernkopf.cz jaroslav@bernkopf.cz

  27. Container beta times higher current – beta-krát větší proud calculate the current - vypočítat proud calculate the values – vypočítejte hodnoty Can you derive the equation? - Umíš odvodit ten vzorec? derive the equation - odvodit vzorec explain the equation - vysvětlit vzorec given the following conditions – jsou-li dány následující podmínky given the values - s danými hodnotami it consists of the sum ... - skládá se ze součtu ... many times - mnohokrát minus sign - znaménko mínus plus sign - znaménko plus resistance is equal to - odpor je roven resistance is zero – odpor je nulový simplify the above explanations – zjednodušit výše uvedená vysvětlení solve the task – řešit úlohu substitute the known values - dosadit známé hodnoty the gain is equal to zero – přenos je roven nule The gain is never lower than 1. - Zesílení není nikdy menší než 1. the gain is reduced by 3 dB − přenos je nižší o 3 dB the gain is reduced by 3 dB − přenos je nižší o 3 dB The output polarity is the same. - Výstupní polarita je ta samá. the output voltage is the same as the input voltage − výstupní napětí je stejné jako vstupní napětí the resistance is equal to - odpor je roven the resistance is practically infinite - odpor je prakticky nekonečný the voltage gain is equal to unity − napěťový přenos je roven jedné Thevoltagegainisinfinite. - Napěťové zesílení je nekonečné. thevoltagesaddtogether - napětí se sčítají this implies that - z toho vyplývá, že Childrenlearnmultiplication tables by heart. numbers_cardinal_ordinal.ppt model_numbers.ppt http://skola.bernkopf.cz jaroslav@bernkopf.cz

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