Transcripts
1. Algebra promo final 2: Hi. My name is really sorry. I have prepared a cools and mathematics Their title of my courses Algebra one in algebra One you will learn what discarded execution on the whole to solve cord integration by a quadratic formula by fact arising and by completing scale hold a sword radical occasion and how to find the natural through self Quarterdeck occasion What ISS center Tickle division in the house so far in the questions and remainder incentive to television What our sets and hold to express search in Verne Diagram in case off union in case of intersection When one side is contained in another set what is function and home energy yourself function We will also define variation What is the director variation and what is in worst variation and what is adjourned Radiation Who should take the schools? The strangeness which are interested in and Deborah the shorting the scores The course is very interesting I have used so many examples and exercise to make her dizzy I assure you that you will enjoy the scores. One thing which is very important and variable for me is that please write documents After completing the course I hope that you will enjoy the scores. Thank you very much
2. solution of quadratic equation by completing square: example in this example, why affects you is corporal heard the eggs, so it will be life experience minus 30 X is the court of zero. Why effects is common. X minus It is. It is my six for their possibilities. Why affects is a little Tzeitel and X minus 60 you by his not its borders. It means X is equal to zero. Here, Exhibit six. What is their solution? Set it is zero and see Next girl next year seven X spear plus twits minus one is equal toe little So nobody find a solution of this quarter denigration by completing scale or to find the solution of quarter aggression by completing scare. The method is the metal is the coefficient off excuse should be one and the constant, um, on the other side. Once again, the coefficient off exc your should be one, and the constant dumb shouldn't be on other side. For what is the coefficient off experience? Seven. Here we will make one. And since construct is one, so it should be on the other side. Therefore so one X spear plus two x is equal to one to make one proficient off excuse would divide by seven system. It would be ex girl. Last tour say one X is equal to one over seven in our first step. What we do, the coefficient asks. X skirt is one, and the constant, um, is on other side. In a second step, bulls take us here off. We're taking the skin off. Half off skin will take the half off. The scale of the coefficient affects. So if we ever see there to the proficient off X is 27 proficient off excess Tour seven and it's off will be. Suppose I am boarding coefficient off expertise to almost seven and its office we went back to. So it is one of a servant. So 1/7 Scared aired on both sides. One a 17 scale beard on both sides, So excuse plus toe seven x plus 1/7 Skip would be aired on one of our seven plus one. Hope it will convert into the formula, which is a good to X plus one or seven. Here is a call to one of seven plus 14 to 9, so this will be good toe one over seven for the minus loads say one blast. One. It would be It turned 49. So it can be too scared or too. Andel toe did your cattle. Okay, X +117 He's a grown class. Fine. Us. You want to To schedule What? So excessive Called? Minus one by seven. Plus minus. Oneto this girl 77 in calcium, minus one plus minus. Tour promotion status minus one plus minus to scale for solution said by completing skill that would take another example for the completed scare. Yes, you three x squared plus seven access port. Uh, what does the first was? First thing we have to do over here. The coefficient of excursion Be one office turned off exclusively. One to make the coefficient of X square. One what we'll do. We'll divide by three off each term. On what site? So what? We get a look here, actually a plus seven by three exit. And the second step is what is a coefficient of X. It is set up by three. We will take half off. Seven battery It is so it is found by six and if scared, will be anchored on both side. So that's good love servant by two years. Plus seven by it'll be added on both sides. There's 1/4 7 by X plus seven six. It is a little seven by. Okay, so can finesse. X love seven by exit to a minor by Thanks. Couple Explore seven by six of the toe seven by six and x The bus seven by six. A little minor. Okay. Yeah, it is accident portal, of course. Plus around by 16 plus seven. Six will be cancelled on the last l invested minus seven minus two basics. So it is my enough. My enough seven by number six will b minus on the other side, minus 76 minus seven by six minus 27 by six. And with Qatar six, it is minus remotely. So our solution, that is you minor film, but
3. solution of quadratic equation by quadratic formula: it is X is equal to minus B past minus the scare minus. Who if he you want a bite? This is quartered formula. You know what to say. What is B C coefficient off experience? E coefficient off executed. They and crawfish turned up excess me and constant honest see love, that same police. The example is life experience. What makes you the last safety checks plus one is equal to zero. What is the value offi what is really on me and what is the body off? See? It is life and he's it and see it's one play the formula families Excellent. Goto my enough to be That's my skill minus four isi a little by really putting the value What is will be it is mind set plus minus Be scared me in a spirit minus full isi Why? Man sees one 12 to a on what is a very offi It is five minus it plus miners 64 20 doing the by 10 My new suit plus miners and will be 44 Scared by 10 is equal to what we can write toe here mine if it one multiplied by four. The word about 10 so it will be called to a pull toe. Minor saved plus miners two into one. The weather by 10 after taking two comin over here minus four plus minus There one. Oh, thanks So much solution Thirties minus four plus minus 11 Scarecrow toe five. Not to take another example by the formula to the X Q plus itics. Class two is a little the very office when your bees record toe it and sees ical too. A critic for Malays. Excessive gold toe minus B plus minor Least here my four ways. See water about Tooley out there putting the value Whoa! Putting the value a to minus me. What does it mean? Mine If it plus minus, Be scared. I want you to this It's good. Minus four is see if he's and these two do it away To weigh on Is my physical minus minus 64 Minus wonderful. Little by six. It is my state of mind. I want to Good. What? I I think so. How much? Russian cities minus it plus minus. Martin scheduled the world away. I think
4. Radical Equation: Warlick allocation and a question allocution in warming in awarding expression under the radical fine. It's called a heart condition. Under the Ready Go sign and aggression, which is under the radical sign is called American Aggression. It was sold were illegal aggressions. Take an example to express wife, is it go through, say one explode 16 This is an on a regular Christian resolve it taking scare on book site creating on world site The next most wife here is equal toe several next plus 16 What is the spirit of this one? Two X Pierre? Yes. Here. Last baby me and Buick land. Why last these? You mean there will next plus 16. It will be four Expert It is 20 experts 25 miners. So one X minus 16 So who experience it will be 13 Thanks 20 x minus seven X is equal to 30 necks and 35 minus 16 is plus mine is a or a zero. So once again we murdered by four By nine it will be 36. I will be 36 on was separate Carty next central to numbers into two times such that when we add us a ghost towns over answer Should be authority were murdered by those times. I would answer the 36 so those terms are for nine. So full X plus my next plus Rex plus nine of you. So what is common over here is well, excuse us. It is excess common. It will be who express my It is also okay. It's common one who? X plus My So you know what X last night is common? Next, plus one, you cool it in my is the court of Appeal and X plus one is a portal exit minus nine from enough for line by
5. Cube root ofunity: Hubble electric car. This Greenman ache. It is the Notre Birdie. The call to be scared. My policy. You know, What are the nature of roofs? Are these positive means and the better fix here then? And westman and corn you be? Yes. Less than ideal. This in place that rule saw imaginary. These little zero, then groups. Yeah, equals these better than zero on the is not the XP, then rubes. Good. Good education. Uh, irrational. And Tommy, - I learned on the screaming and all my next my yes plus 20. My physical zero. Your hair's a court from my on these a minus people, I What does discriminate musical toe this mind or C get a B minus 30 minus four. Yes. Life ces 25. They want to 900. Imagine the ropes of the nature Rock looks over here. Imagine ity. I could take in a little dimple. Particular nature of our roads. Love your Knicks lineup. The pain is real years. Pretty her pain? No. Measly little minus Leo, please. Please. If 13 years are 39 13 Thanks. Was it a bit is not a perfect sphere, Not a next year. But it's positive and lice rule the national and on equal kindled of unity. Excuse one. So I saw this aggression. Exp u minus a little X minus one. Yeah, Excellent. One is love One table by the quadratic formula A play over here a line that I ordered from above will get well what we learned That would be minus one less minor. You need looks We want go. Yeah, minus one Mine Really scared. What do So it is the totem There could note by poster come by and well there Thomas made. So you know it works. Exit the cultural solutions that rich in the oceans that as solutions did one can make no one rulers lots of liberalism ago and other orders Biggest fear negative is scared. And also there that would take the steel off. Negative one of it, one minus omega minus may go Our seven like one made up lost. You know these are these doors are by using these stories. You see that one miner, Magal? My God, Problem seven is a one Make a plus May go. Plus will make us feel is equal to minus one one. Love is 1/4 1 20 chicken of the example. I heard the sale one plus a man. Go of the years minus. Why watch make I think love here. Mango 38 36 minus wife Major 36 is common. So Maga plus my minus, which is a Colorado mega tortoises can go through our on. This is a good one. Minus flight. My basic oracle. Long one minus one minus life. Which is? It would go minus one. My life, minus six some of and directed son was notably. Yes, it is minus Woody. And But I would like to go hopes, Director. It is a country might be Leo. Example. Suppose we have 1/4 division next year minus wife last Crazy. A little No Sundays. What is equal to minus? What is that? B minus? Life is is one and Bernard. What? You know Did the quarter do you want? - So that is an aggression. If we want we want to find out what it is vision when the roofs are given, When the rules are given and we want to When the credit ignition then this formula Carmela xq minus as X plus three. You know, it all started here. We use this form. Suppose we have a wonderful life. The their tools. 1/4. You want to find out what medications? So I have these some of the routes. These brutal bubbles. One marquee. Why get a life on? Um, one class wife. Thanks. That's your mind. Is it a lot of you? So explain. What is the value affects next? Scared you? Just like yes s. Except what I speak These physical life this is the border division were not hopes are you would were taken of the December. The roots are one last iota. And the war in the minor yoga So s is a quote from some of the roofs. One plus your plus one minus you. We did the car on these little one plus your cup on one. It is the little one minus your last year. I don't know that. And we know that one minus your total minus one. It is a little one. Their whole Where medication is xq minus six. Love is the little next year minus If really, offices too value our peace. Also, this is an admission
6. Synthetic Division: in division he's got is a process finding the question Tremendous polynomial is devoted by is wanted by so that we moved under example in this event. Probably. Right. That's good. So next minor. For a word about it, X plus one X plus one is equal according to the method. Right? Explosive political zero for the central Division X is equal to minus one. So what are the coefficient? Are the variables the highest part of the variables to Scottish in this one? So right, one over here on the coefficient off. Exes seven Standard this minus one. There will be minus one. According to the method were you know, over here in each sensitive division, one plus one want a murky but minus one of minus one and seven minus one of the 4 to 6. So six months by the minus one minus six, it will be minus seven. Okay? Yeah, yeah, yeah, yeah, but I don't know So what has remained of our Mandarin? My. - And the question is, since it is exp you so over questions will be one power less means it is one at I love thanks. This is questioned
7. Sets : a set is, uh, well, define collection off objects. And you just did Notre by kept the letter. It does be three. You hear? This sets seconds of very defined collection off objects. And it is the neutral by capital letters A B C there to see a sit, having no element scored. Empathy is it, I suppose. And no element it is. The neutral by the Empress up is denoted by just like us. So the 30 has no element there who it is, embodies it. Single, Done that. No, sit. Every one element is gored. Single, done set. Suppose either effect and is another coffee? Yeah. Is single insect union Oh, sex the union off. You know, Prue, sex, you and re means that is the set that consisting or all the winners Which are I? That And here all in me example suppose we have it is equal to 12 city and B is set using google or by hand the union off. The envy is by union be which is a little one. Go to me four. While you six you can see that the numbers 12345 and six are ill attorney either than be so the union is actually combination off six All the elements you condense, all the limits that contention Both are way have research than all those elements which in distant those two concerts, it's called the Union Intersection Offsets intersection offsets intersectional closer It's A and B Oh crucifix. And the yes is the is a set consisting go common elements in you aren't be example Woman element Suppose is equal to want to today on music True, did he? And four. So the intersection off here and be is the neutral by intrasection which is ical group common element in Vienna be We see that one and go. These two elements are common in A and E They re writes one true difference off different So six If he and they uh through sex, then they're different is did not go by the elements is not the by uh okay so example that is a little one through three on a breezy oneto two and three The difference difference Oh no you and be all right Through service then there the class is You know the way am I must be e minus is a set, which is equal to 12 Okay. And these are What is it? Cool and really a minus means that I don't does everyone coffee which are not in me. We right. Only those element coffee. We thought market. So there is only one element offi we just started me beautiful, right? Only one difference off e And these one you you is you knew all sorts. And a is a subset of you off you them compliment and come in. And dolls. Yeah, is the certainly both elements those elements off you off you, which are we don't not. It's hard not contained. And a Cipel's use that he was upset. So a complete mint is equal to u minus. What a simple U is equal to one to to me after stolen. Yeah. Then on a Z quartile for six to and yeah, he compliment is a total U minus. So what are those elements? It's ordered you, but not any. I think that is one on three off course, five, seven. My and, uh
8. Venn Diagram: on D. Morgan be more what? A stew Mogul Law. The G border loss wouldn't concert cnd the envy compliment is the cardinal you compliment in section be complete mint Uh, in no section the complimented quartile. Yes, Bloomer Union compliment. This is demon. Both D and B Do this design six. This don't mean that there is no common element in E and B. Then there ven diagram then Yes, Julian s union be diagram can be you just like this is You also said you onda certain And that be so since there is no element common element in a video For though Grand Island was introduced like yes and, uh waas a The sex are distinct than there Intersection in context Water of intersection e intrasection e What intersection? The man died. Ramis, Is this universal set? Yeah, this is But we will not see it because there is no common element. Therefore, intersection e and B B m pretty set, but you're gonna be the set of ounces. He answered me, but there is no common element. That's, uh Well, let me if the search start overlapping, then usually and when Diomedes, This is what does that this e on this artist to be so your envy means that all those elements which are in a or I didn't be Therefore their union is represented by they will share both e and And if we watch inter sexually then this is You know what? Yeah, in this gifts, Richard, only the Kama region. So the common region in E and B is basis Coma region. Here is the some certain be Then what? Adrian B. Yes. You're gonna be close the door and I promise he's the sensor. This is And this is the since union is the combination of closets Didn't is element off. Certs eat me means we combined the elements off Surks here. Our union is assert that you convinced that America it's all other than what? I didn't be so in case off union When is the sub certainly be sheer? No religion. You Will this be? No If is the sub certainty and is the subset Toby, He's the sub sir. Copy On what intersection? Learn by. This is me on. This is so in this case, only the region is common because it just actually means that the comment region So the home origen in e And these if he's the sub circle the Kama region in he envies only suppose the us again beginning also set you know you complement is equal to u minus e And on the very diagram No, this is you And of course it is so hellish is equal to human Assume use that will right on those elements off you which are not any through a common region is our formal region is excluding committed a law off here Julia, the is equality be union come great of law in this case, Lamis. I suppose this is Yeah. Andi, this is me. For me on that issue. The streets are if the sex are over. Let me, then. Is the uncertainties Well? Does it the elements without either an A or B? I mean civilian a junior minister, the elements to which are either any What I didn't be for We see that in figure one and in figure two the regions are common
9. Variation: Simon. And yes, exhibition Simultaneous occasion. A system of occasion having a common solution. Common solution. He's going a system of his goals are system Oh, mission that were taken Example. The example is Oh, yes, that's why it before. And did he have a spear? Bless. Last year is equal toe through. This is a good one from this is speculation through wrong one. Why the chortled Why is equal to or minus? Yes. Under this three, we're going in putting the above aggression. And so any experience but awesome widescreen. Yes, Yes. Pickle. Yes. We're must both. Yeah, the extra mile. Oh, man. Yes, it is mortal to the experience. 0 16 last night Experience from Triple X. My God, you So you see you next year minus from people X minus 36 16. My husband is a physics still here minus lives and its mast Extremely with monthly extra minus two x My. Take it, you experience it. Experian minus three X close X minus Living Gordo. Excess woman So x minus T Wonder woman X minus X minus These woman And if one is going their whole Xel minus two years ago, the people zero on here political ability. And after the little one, no ex article 23 What was a way within the accessibility? Accessibility? Negligently, what was evidently why is equal to minus PX Woman is the expense, and it's warm nine. And of course, we get, uh, acceptable. We did my sleeve. Look at this video and minus five while I was working was with his wife. X is going to nice one. What is the Goto four minus three minus one city? Let's get minus wander. So So what's the oceans? It is Gideon. Last night Fiction Correction. The question off numbers are your biggest lashing is a reflection. National election, The rational fiction insulation off the form in ethics. Do everybody effects were enough extent. Dfx are longer you. Next I put it on your the next with the Inquisition. The effect is not a disease called National direction in America with a little group of animals. So no, no, no infection. This can affect any of you. Yes, definition is the external Brazil, and this is a national rep affection or a selection or rational correction, and I'll fix it away. The axe. The affects is not he scored a national election. If dealio, the video and the optics it's less than video, many of the the way they don't know. I don't know what. And in in FX or the Office, this is a national fiction. This is a national fiction radio, and the Knicks is there to the video. He's there for them.
10. direct and inverse variation: variation Relation between two quantity of us Empire. All the same planned this garden natural relation between true unity of the same kind asshole. Initial 200 and so 100 which is a miracle. 100. Really? So 100 floor district total seven. It is a popular official. What would take a look? Simple. One kilometers 600. You don't that one kilometers So 601. Give me a minute. Show 600 meters Another run Climate physical proposal 1001 it doesn't. And 600 The arsenal we're gonna be which is equal to six under. It could be freezer. This is a little over three. And so that little by special no portion abortion is Our statement is a statement of it is expresses, huh? The justice Miss Dance and give us our division again. It's off. Given intellectually, give himself The show is called abortion. It is a life or doctors like proportion and initial is because of poor doctors Like the proportion is it isn't Connect these dots notes. I ve be you. Why next 60 Official 90 compulsion empty. Enjoy X. The latest 61 of my 90 is equal proportion 20 or next. So you have to go and three days are pretty country. Oh, excellent to better the corridor 60 Next photo, actually. Okay, So, Jake, another limp if city Until who? X minus very light. Is it going? Two X minus seven away, then point. Look, from this people. Is that Parenteau? Oh, excellent. Broadway. Rex Elaina's heavily It is a little bit then. What? Some way. Globex, Elena Stories in light of done away. Listen, waiting for you. It is finished, minus 10 way Afghanistan last three way. This most of what is mine. Why? So he liked next is equality anyway. And, uh, that's a little way. Excellent way. It's equal Videla. And I'm like a blanket. Excellent lady. Exponential. What? What is it? Probably on any issue and in association. Malaysian. But what is not division? No committees do quantities. Uh, the letter and such a There. These are, please in one. Pretty because Okay, uh, decrease in dignity for that one. Dirty. And this nation's heart The commission, this radiation If medical nobody's dickering essentially, that increase under these greens are decrease in a 100 us and please our decrease. In other words, dispose it isn't crazy. Then a 2nd 1 Results of using it is not relation. On one hand it is that easy in this location. But other countries also using it means that the same big that means that is called operation on the 2nd 1 is in West region. In what a bit of indigenous? 100 please. One 20 in please. Other places other degrees, 1 20 degrees London country 100 at least. And then base. This is God in vaccination.
11. Fourth,Third, Mean and continued Proportion: then it is in. Why raise with X So with us, why is directly what it takes? Why is the carnal GX support this occasion is one video where next is given? Why is equal to it? And X is a cordial No. But in this very room above a question Why is it called Gates parquet? Why is he going toe is a key on access to you Told many scales Ekotto? No, my friend Oneto way. Want to find a life when accesses a portal life? Okay, I'll take this aggression. Gin. Why is the little BX putting the value? Why is Gordon fee the value of gains for excess? Why, yes. Look. Next my car. Where is the card? Gets Boise Little gifts and the case. Cool. We went to my next. What is it? What is your body? It so printing beautiful is equal. Next ones what? Seconds off X? Come no pushing. Take one of these B and C on literacy. Just like the official proportion. Beautiful and sees card. See these called go proportion that we do an example Wonderful and terrible. Pushing off explosive way. And next year, minus so in a publisher it would be two explosions throughout the base. National True, you know the publishing. Let see be the huh proportion, then right X plus initial F minus west. Actually, my I m. C. What? It means that next plus way you want to buy next year. Last graph is quartile. We'll see. Well, the college. It's most way explosive labor. Excellent wife, and it's the most extreme in its last year. Using the physical this mostly his wife. He's Goto again. X plus Williams. Well, we'll see. So it's always gets a lot. Makes most Rizzi. It's not his wife. Their marketing play with X minus are gonna be extra minus Why skill and text us. This is of any FC good we have when it is a easy handy be. These are four quantities on this one. This will be Bush here. These are the four promotion de yes, God cool proportion. These girls or proportion involved proportions. The three numbers three guns, expressions, maybe is like wife. It's looking force these for promotion, then get right by special. It's essential what's interesting and what tenderness. While we wait this quarter lifting a look, we can't wait. Beaton's 50 month. Bye bye. You don't like I want some by three. So easy, Plentiful I mean proportional. I mean proportional. And the question is, did you have any kind of business like it be Dempsey and this quantity or Liberace artists ? E I shall be proportion Beashel. Then he's got a mean the the score. I mean proportion. Start with a simple this like we have a number company end 45. We want to find a new promotion off the end. So net exit the I mean he fixes a publishing research according X proportion X and 40 i, so it will be turned. Elex is equal to excellent parking flight by the close identification extra 45 countries are it is 900. No, that's 930. So X is a mortal heartiest group that is, according to X is equal to recognize it continued proportion and the continued promotions. We have taken these a b and C. He's got your letters of that. Hey, I'm sure people portion the initial See it's season then this implies that and see, uh, come dance. We start with an example 20. You good. Bianca, I love you so we want 100 cautious about the definition of you. All right, club. This will be bushing initial this drug therapy between people being so what's he playing? Be scared of the gargle and he's really Please, Please Goto. That's nice. Six years joint radiation. A commission. Let it, Dan. Motivation. We're not more than one, Not I told them one of a table. What isn't looking all right? Why scared that national dress? And why is inversely proportional? You see, the tradition is why is I'm pushing? Excellent. Is this a SS Medically abortion? A little scared and as it you know what city? But then there's a combination is you hear what? Yes, this that actually, because you're scared and sec wasn't pleasure to be so drunk Business have a venues argument U s acquittal. All right, we were right s is equal to get, you know? So what is it? The very low prices given? Yes, that is a key part of seven. There is one and isn't very often who is also Let's go. He's also given Store seven is equal to Okay, line up. Gave the portal What? We're gonna look fine. Okay, Mope. We want in front of you Off? Yes. I want to find the video. Yes, I'm using for six years the world. Thanks and musical. So how did you take this occasion? Once again? Yes, As a candle. You Philip. So what? Escape please for another night and really offer you is given that his next six years. And we used him so pretty wielding overnight market bribery, my ones up nine. And that's is the brutal the samples from beautiful.
12. What are Differential Equation: What is the French elocution? Our differential occlusion is an aggression with our function, and one are more offer distributors. What other use our differential equations? The French allocations have a remarkable ability to predict the water on us. They are used in a white for TR disciplines from biology, economics, physics, chemistry and trend changing. They can describe exponential growth and turkey the population growth off species. Are the change in investment in turn over time? Why did the French electricians are important? The term orderly ISS used in contrast with the term partial differential equation, which may be with respect to more than one independent variable lena differential equations are the defense allocations that are linear in the unknown function and its distributors. The type of differential equations, an open defence, elocution or tea is the most common type. A limited slip differential overcome. This problem are lacking Differential means Locker is able to lock the to drive ills on an excel together. Our school is an open differential in which the Exel's have been mechanically fastened together. Partial differential equation. Partial differential equations are used to mathematically formal it, and thus at the solution off physical and other problems involving functions off Several variables, such as the propagation off heat, are sound fluid flow a loss to city electrostatic electrodynamics. Use a partial differential equations in mathematics. A partial differential equations is are the French allocution that contains beforehand unknown multi variable functions and their positive bitters. Partial. Different educations are used to formulate problem involving functions off several variables and are either sold by hand. I used to create a computer model order and degree off a defense education. The order is the highest, Um attributed in the occasion What the delay is the highest power to which a derivative is raised. Quite simple white, double prime plus y prime musical toe Why is first degree second order defense Shin occasion. Okay, White double prime wide double time plus y prime musical. Why means that the highest tribute ofhis wide double prime. So it means order is to order after the French allocation is too. And since the barber exponent exponent off wire prime is one. So this means that it still is one and in why prime scale was See over here we see that why prime scared is equalled. Why me instead, the tribute of his 1st 1st riveter. The highest derivative is the first riveter, so it's order is one. And since the ah yes, tribute of exponent is too this is too. So this means that it's tickety is too. So it is second degree first order differential equation. I look at this ready of examples for first off, while divide Body X is equal to five x plastics. In this case, you can see what is the highest tribute. Um, the highest illiteracy T y by D. X. So it means order off this Over here it means order is one inches one and since it's exponent is also one So it still is one. And in this example you can see that what is the highest tribute of the highest treatment of disco? Why about DX care? So it means that it's order is to order off this defence allocation is too and you know it's exponent. Is the order off Highest tribute of the exponent off. Ah yes. Tribute of is since one therefore Estili is one. And in the next example you can see that I take you. Why, by t x Cube? The highest riveter is Tiki Weber TX cume. So since it is third out attributed, it is third ordered Riveter. And since the exponent off, it is one. So we can say that it's It's degree is one. So in the next example do Abati X is equal to five x plus six. Since this is First Artillery Witter, this is first order tree better. If it is first ordered Riveter, then it means that art is one. So it's exponent. You can see that it's exponent is too, so it's degree is, too. And in the next examples you can see here it is an extra symbol. What is the highest spirit? Um, the highest tribute of us Describe about t excuse So artist, too. And it's exponent exponent off highest relativist seven, therefore urges STDs seven. And in the next example, you can see the highest derivative is Diego about the X Cube. So it's order is Street and its exponents since two. Therefore, degree is, too to solve the first order differential. A question by separating the variables method. The method is you can see over here for Why d why is it goto G affects the affects? What does it mean? by. From here, you can see in the left hand side is a pure functional Why and the right hand side is the pill from benefits in the separating the variables. What we do, we separate the variables, the variables off extra to be in one side and the variable of why I should be on other sites. So this is example in this example you can see X squared d y is equal toe. This is the example X scare d Y is equal to minus X squared minus one y could be X. So what we will do And the left hand side we can see that extra is multiply Bharti y And in the right hand side we can see that minus X squared minus one y group means variables are mixed variables. So retort need, Mr Variables, We will separate the variables extra being one side And why should be on the other side? So what we'll do since d y. This is t y. And you know this is why Cube. So when we shifted y kube on the left hand side, it will off course will come in the denominator and the venal is shifted this excuse on the right hand side. Then of course, it will take the place and the Terminator off the right hand side. Okay? No, you can see that now. You can see that on the left hand side. The pill function away on the right hand side is the pill function affects when we get this condition. Just like left hand side. Is that bill functional? White and the right hand side? Is that your function effects than what we do? We will integrate to find a solution. So integrate it on. Both 30 are taking the Antigua. You can also right over here taking the integer on both side. Okay, after taking the integral on both. So you know the integration? Our widest of minus three is we had one in the exponent. And Dwight, by that exponent, is the rule off in volition. So the debate a uav widest of ministry is virus trip ar minus two letters to the bar Ministered whereby minus two and the intuition off extra to a par minus two is we add one in the exponent two minus to plus one here. Okay. The role suffered division. You sure know it. ISS miners Extra toolbar minus one minus to plus one means extra the minus one divided by minus Wonder toe that it is. We get minus sign over here so the irritable minus one is minor sex, and this is constant off integration and after multiplying by miners. So after Marty playing by minus, it will be positive. It will be positive. It was positive, and it reports the other Tom will be posted. So this is our solution by separating the variables what is homogeneous? The French television Alina. The French allocation is homogeneous if it is homogeneous leaning allocution in the unknown function and distributors in this example, you can see that on the right hand side, do a Body X is equal to execute classics Weather My wife scare during the by exc you're here. You can see that in the nominator. There are three terms XK plus X y plus y scared and you know the Diggory off each term is to and the duty off Eastern in the terminate is also to hear the degree is too. And in X y. The degree is also told, because X plus the exponent affects is one and exponent of why is one so one plus one is equal to two and here also y plus y skimming is toe means to delete off Eastern in the nominator and tournament for both Dealing off Eastern is same since the degree off east, Um is saying therefore, it is homogeneous accretion because in a homogenization, the deal is off East, um is seem so next. So what is the method? Hopefully solve the homogeneous the French allocution. The method is we put why is equal toe the effects why physical vfx and one overtake the tree Vito off. Why it will be d Weber DX. And when we take the tree Vito off. Why Vieques? So what is the attributable? Vieques by the product rule on the V first as it is and derivative off X is one plus X as it is on the direct or obvious dearie, over DX. Therefore we can write do about dx are we can put this way we can put this value supports. This is accused in one and this is a question one. Okay, put in accusing one. Why is equal to Vieques in occlusion one? And you know why is it Corvex and what is delivered e x, it is the Weber D X is equal to this one. So this will be equal to this one means by putting over here we get this. So excuse is just like us and the very off again X y Y is equal to the exit Vieques scared . And why is the court of Vieques mean this great execute whereby excuse. And we it's can see or hear excuses common in the nominator and so that X scribble begins on we get this one Okay after that, you know, on the right, left hand side is the plus X V and this week will begin salute and we get this occasions know what will to buy separate in the variables one plus v skill than one plus Freescale shifting the left inside. It will be in the to nominate him and then we shift X in the right hand side. It will be also in the nominator, No integrating both sides after interrogating on both side what we will get we get the derivative by integrating by integrating it is just like integrating. You know the integration of one plus whiskers Terran was sweet. It will be 10 in once we and the interrogations off excess natural effects. Norway put value off week. What is the value of these in? So why Isaac orto Vieques. And from here from here, Why Zika will be X from here. V is equal to is equal toe wire works. Why works musical toe? Why or X? Okay, No opening here. Dannon waas me then Then it was the means that it is y or X And this is our solution by which method by homogeneous defence allocation Hopeless older, homogeneous differential equation What is non homogeneous differential Occassion? He called that second order leaner The French allocation with the constant coefficient have the form irritable prime B y prime plus See why is it called g effects will solve equations were G affects isn article zeal which have not homogeneous differential occasion So any differential equations off the form This one is is non homogeneous Differential occasion foster defense solution of the farm It one affects the web Body X plus in order fix why physical g affects It's sort of a leaner the French allocations in the dependent variable Why and if Dfx is called zero. Then it is homogeneous differential equations. And if he affects isn Article zero then it is non homogeneous. Differential occasion? What show? What? The sister Linear regression One off x. So here will be X multiplier de weber the axis Multi! Bye bye. Function affects And here will also be function affects with multiple able Why and the right hand side will be the function of your function effects. If it is the farm, then it is leaner differential occlusion no See the difference between second order Leaney and nonlinear differential equation. So the general farm off leaning and only differential equation is wide, double applying plus fx Why prime blast effects? Why is it called war effects? So here we can see white double prime means Here, Here, maybe any kind off constant and no, this is ffx Do your fix and or effects. So in case off ffx it maybe this any constant and in d effects it may be geo affects our any other constant. And in case off or effects, it may be any constant. Any constant are or effects. So the example off Alina question is wide double Brian plus X y prime plus extra. Why Isaac orto egotistical minus X and the second example is rideable prime plus C y is equal toe zero. So here we discuss why it is lenient and the first we see the example off Nonlinear which is avoidable. Prime y plus y prihn plus X Y is equal to zero. Of course it is linear y double prime minus y prime Last one is called zero. So why these two occasions are no linear and why the first two occasions are linear Hell, you can see when why's multiply here You can see why is multiplied by white double prime then And if we see here, X is multi Bible Why prime if why is multiply by y plane Our exes multiply by means X is if excess multi Piper Why prime then it is linear And if wise multi bible wide double plane then it is not linear And since this is in sort of form sort of form, if it is in sort of form, then off course it is not linear. Any questions off differential equation which is inserted form is not linear but these differential equations why it is not linear because why is multiplied by avoidable brain? Okay, why is multi bye bye y doble prime due to this season's It is nonlinear. And suppose Suppose if I say why is multiplied by the way it is again nor linear. It is a lean, not linear notes exacta, French allocation exact and in exact differential, especially used in Perma dynamics to express if a partial differential Christian is dependent on pot or not, Executive financial aggression represent the given. A function is independent off. They depend upon their initial and financed it, and therefore they are called state our Point Function. Executive. French television. If M and an R functions off X and y, then partial m durable partial, why is it called a partial and will a partial X? If this condition is satisfy, then it means that the given differential equation is an executive French locations. And if the differential equation is an exact a French allocution than if solution will be, um and DX plus and into t y plus and into do y is equal to see No, you can see this example. Three Experian minus two y skill plus one minus four X Y Y prime is equal to zero. Here, you can see three X squared minus two y scale. Yeah, this is M okay. And one of minus four x Y. This is why? Because we can work for us toe y prime physical to divide body X. So it is m everything. The partial derivative off em parceled Rippetoe off em with respect to X, it will be, uh, yes and respect way partial derivative off em. In respect away, it will be, you know, Bush and partial derivative If you're taking the possible suspect, this is constant and the partial derivative are two y squared Is is minus two West is mindful for by And if you're taking a derivative help one minus four x y with respect to X and the attributable of one will be zero and attributable minus four x y is minus four way Therefore partial m develop a partial y derivative off m davidoff em with respect a why and tribute off and with respect to exile. Same Therefore, the given different elocution. This differential equation is an exact differential equation Integrating factor off for started a friend celebration of the form Be off X wire the X plus Q affects worldly wise equals zero is not exact, but it will be exact supposing for this not accept, and it will be exact every multiply our function. And what is that? That function maybe the function affects and maybe the function of way after multiplying by this function. If affects, why the given? The French delegation will be exact different location after multiplying the entry Fichtner factor. Actually, we find the integrated factor for what purpose? Only for one purpose. We want to make the differential equation exact. Our differential equation of it is looking non exact. What we do with multiply the integrated factor to make that difference secretion exact. So suppose if this the differential equation is non exact, this is a differential equation is not exactly and what it will do with multiply by integrating factor After multiplying the integrated factor, The integrator factor will be a function what kind of function it will be f off ex wife like function After multiplying dysfunctions, this differential equation will get exact and if it is exact than it is easy to find a solution of difference. Locations, maybe by the homogeneous method, are better separating the variables hotel Make a first order differential equation. Exit to the French allocation by finding the integrating factor. So in this example X y squared plus four x squared y in through the X plus three extra y plus four x scoob And in Todi Y is equal to zero off course it is. This is equal to M and this is And in this case, if we think the partial genital off em with respect to why then what will be the answer bustled riveter off em. With respect to white, it will be two x y and plus four x gear. And what is the here? Every c Partial derivative off animal respect weeks What really the partial digital off And with respect to X, it'll be six x y plus 12 x scared. So what? This means that partial, debatable family respect why and partial derivative off en with respect to X are not same. So it means that this is not exact. We want to make it exact what we will do. We will find the integrating factor. There is a special methods so hard to find the indicative defectors. There are four different methods to find the integrating factors I have discussed in the next lectures. There are brief descriptions in the scores. Hard to find the integrating factors in the next lecture, so you will understand how to funder intended defectors. But here, just father short descriptions for the short review off the course. I am just telling you if I find the integrative factors suppose the integrator affection defector is y or X. Why Onex? We will multiply the integrating factors after multiplying the integrated factors. This differential equation will be exact means partial derivative, our family respectful why and partial derivative off animal respect to X will be seem sort of means that this is exactly what this is affect. And you know how to find a solution off executive for interrogation that we're discussing them last victim.