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Text moved. Here! >>>Click Here<<< https://EditaPaper.com Simon Business School â&#x20AC;&#x2039;hi everyone I've shown you some pure mathematics before so I thought it would be a good idea to show you what some applied math looks like and I have another exam here and this is supposed to be an example of what you could expect to see if you studied say engineering mathematics it's going to cover two topics linear algebra and differential equations and because it's covering these two topics neither of them are going to be too in-depth but it will give you sort of a view of what both of these topics looks like and the questions that are in here are things that I think you can expect to see if you major in physics math or engineering in my opinion this isn't going to be too hard of an exam the questions are a bit more straightforward there are less proofs which is one of the things I struggle the most on in math and the math does have a lot more applications I will post the full exam with worked solutions down the description so you can download that and I hand wrote these solutions myself this time so let's have a look at the questions I hope me opening this exam doesn't give you too much flashback anxiety if you've set lots of exams yourself but first of all we're showing some pretty easy I guess linear algebra questions a bit of an

overview linear algebra really deals with lines planes and rotations it's really useful in modeling or computing various systems because you can make approximations of more complicated nonlinear systems to be linear and then you can use any algebra on them it really talks about how things relate to each other in space so first we asked about the requirement for a set of vectors or lines to be linearly independent of each other so to have no redundancy there when describing a system number two is dealing with a matrix so that's this collection of numbers here a matrix is an array of numbers that in this case are used as a transformation what is the transformation being done by this matrix and the answer here is that this is essentially a rotation by a hundred and fifty degrees in space moving on we're asked a question compute a to 2011 essentially take that matrix of numbers and apply it to something 2011 times now that seems really difficult because that's such a big power but really you need to look at it and figure out that okay if this matrix is rotating by 150 degrees then if you do it 12 times in a row you're going to end up back where you started back at the identity so essentially a to the 12 is the identity since 2011 is 12 times 167 plus 7 really all you need to do is do a to the power of 7 then were asked to create or find the inverse of a matrix and this is our matrix here the way that we're going to find the inverse is by doing Gauss Jordan elimination which essentially means we're going to do a whole bunch of operations on the rows and the matrix so here we have I guess an example of how linear algebra is used in a practical context we have a system of linear equations so I guess three equations in x y&z if you look at this what is given here is actually our a matrix before if we look at a and we know that that is XY and Z then we can see that these equations here are all the coefficients are encoded in that matrix a the system is a times X which is just x y and z this our space mate Victor so that's what X is a times X is equal to B so this here is our victor B if we want to solve the system of linear equations what we want to do is solve this equation here for X so we know a from before and we know B because it's here if we want to solve this it involves writing it like X is equal to a inverse B so we know a inverse we calculated that in the previous question that's B so if you do some similar row column operations on this here you would end up with this victor which is our x y&z solution being able to compute actually quite large systems of linear equations becomes really useful in engineering or lots of other disciplines and you might find yourself doing it much more on the computer on something like MATLAB then on paper pen and paper but it's good to be able to know and understand what's happening behind the scenes when you ask MATLAB to solve a system for you we're moving now into the differential equations part of the exam and we're dealing over here with partial differential equations often abbreviated to PDE s so these partial differential equations involve an unknown multi variable function and it's partial derivatives we're asked here to write down the heat equation and any initial and boundary conditions needed to find a unique solution this here is the heat equation and it pretty much tells you about the distribution of heat and space over time again very useful in a lot of engineering applications then we've got some more I guess conceptual questions about PDE s the heat equation and boundary conditions so talking about the physical meaning of some boundary conditions in this case I believe they're talking about if spatially at the edge of your distribution your boundary conditions are zero physically it implies you've got total insulation at those end points here we've got a similar thing asking about the heat equation but also the wave equation which is similar in a lot of ways except that it describes the movement of waves through space and then we've got these questions that are asking you to show that certain solutions satisfy certain differential equations so in this case you're asked to show that this value of U fits within here and then it works out again a very similar problem here just being asked to find out U of T and UX so we're doing a couple more partial derivatives and finding out that they are consistent with this equation here is the I guess longer and more difficult PDE question in this exam but it's something that you'll definitely face if you're doing a lot of PDS and really we're given a differential equation and we're given a whole bunch of initial and boundary values and we're asked to find a formal solution so the first thing that you do in a question like this is actually use separation of variables so we take what we've been given which is U of X T so we've got you in two different variables and what we want to do is find a V another function of X and T it's our solution that can be described as a function of x times a function of T a product solution if you will if we can separate out separate out our problem into this then it means we've separated our partial differential equation into two ordinary differential equations and those are going to be much easier for us to solve I won't go through all the details here but of course you can download this full solution and the description so I encourage you to do that many people watching this video may be considering studying or are currently pursuing engineering math and physics if that's the case and you want to teach yourself these ideas or you've seen the content before and find these questions a bit daunting then you should check out some courses on brilliant org you master the concepts by solving fun challenging problems you're guided to break down a problem into its component pieces think clearly through each part and then build back up to a conclusion brilliant can walk you through courses on both linear algebra and differential equations as well as lots of other math and science topics this exam might look a bit easier when you truly understand how these concepts relate to each other if you are considering

studying engineering math or physics go to brilliant org slash Tibby's and sign up for free also the first 200 people that go to that link will get 20% off the annual premium subscription thanks for liened for supporting my channel and thank you for watching I'll be down in the comments answering as many questions as I can bedford university registration.

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