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Interesting, did your class skip this unit? If that's the case I oddly had a similar experience when I first learned calc 3. The professor left this unit for us to teach to ourselves and skipped straight from vectors to multivariable functions. The whole class was going at mach 5 speed. Did a lot self-learning that semester haha

@ we skipped literally a lot, my Russian calc 2 professor decided to spend the last 3 weeks of class teaching us pre calc Hyperbolas Parabolas and Ellipse instead of teaching us Series and sequences which belong in calc 2 and that’s where the issue was, I learned that in Calc 3 instead of Calc 2. Lowkey the only thing we got up to was double intergals and applications of double integrals. I mean my Russian professor was old so he didn’t have that strength like he once did. Lowkey I hope my transfer college will accept my calc 2 and 3 despite not learning all of calc 3. I didn’t mean to skip it I just learned the material the way it was tought to me

@ Wow that sounds quite chaotic! Sorry to hear that was your experience. Hope I'm able to help fill in the gaps for you a little bit. If you ever have any questions about these topics as you get further in math and ever have to reference back, let me know!

@@JKMath I will probably self study these topics for future courses also thankfully my college is going to start teaching series and sequences in calc 2 again starting this spring semester meaning more of calc 3 will be able to be covered for future students who are gunna take it.

Glad to help! :)

Thank you sir! I appreciate the kind words :)

I don't necessarily think that one order is really better than the other. I chose to start with vectors because that's how I originally learned Calc 3, and the way the textbook I use to help me write the lessons lays it out. Now to be fair, I don't always follow the order of the textbook topic by topic, especially with the vector function unit, I have deviated quite a bit at times, but generally that's what I go by. I think sometimes a class might choose to go with the 3D coordinate system first because they are assuming you have already seen 2D vectors before and don't want to waste time on them (such as in physics 1 or 2). I decided not to make that assumption when starting this course, as I currently don't plan to cover physics with its own course (At least not right now). Hope this gives a little insight on my thought process!

Right now just math! Math is what I enjoy the most and what I went to college for, so that's my focus. Should keep me busy for a long time as there are a lot of math courses out there that I could cover! Appreciate the support :)

Can you provide the entire problem for me? It would help to see the wording in context as well as all the values of r, i, n, and F.

@@JKMath Sure! Here's the question: You are given the following information about a 20-year bond with face amount 7500: i) The bond has an annual coupon rate of 7.4% paid semiannually. ii) The purchase price results to the investor an annual nominal yield rate of 5.3% convertible semiannually. iii) The amount for amortization of premium in the fourth coupon payment is 28.31. Calculate the redemption value of the bond

@@LakshanaKalaiyalagan Ah I see now, thank you for providing this. So you have a couple options. One way to approach this is to remember that an amount of premium/principal will be the difference between the book values surrounding it. So the principal in the 4th coupon payment would be the difference between BV_3 and BV_4. (BV_3-BV_4) So you could set up the calculation for each of those BVs and then subtract those calculations, set them equal to 28.31 and solve for C. Another way to approach it is to write out how PR_4 would have been calculated. It would be PR_4= Fr-I_4, or the coupon minus the interest at time 4. You can then replace the interest at time 4 with BV_4*(interest rate), because thats how I_4 could be calculated, and then you'd have an equation where the only unknown is BV_4, so you can solve for it and then use that to set up the full calculation of BV_4 involving the bond price formula and solve for C that way. Hope this helps!

@@JKMath Ah alright understood. Thank you so much. Appreciate it!

Also, for the calculation of BV_3/BV_4, the extra formula shown at the end of the video is used, no? So (n-t) would be 40-3?

Hi! I'm currently estimating that once complete, this Calc 3 series will have around a total of 90 lessons, so approximately 60 left to make or so. I'm just one person, so I'm currently only able to work at a pace of about 1 new calc 3 lesson per week, but that could always change in the future. So by the end of this year it will be nearly complete is my expectation. Apologies for the wait, but I hope you can understand!

@@JKMath Of course, I understand and the fact you're doing all of this for free is an incredible achievement itself, tq for replying :)

Yes. It's ultimately a matter of preference. I like to change the integral back into terms of x most of the time, but if you prefer to change the bounds to be in terms of u that is totally fine. It can certainly make the evaluation at the end quicker at times. But both ways will produce the correct answer if done correctly.

The point I was trying to make at the end of this video is that Exact Matching does not meet the requirements to be classified as a method of Redington immunization or Full immunization, not that exact matching is not an immunization method at all. Exact matching is sort of in its own category of immunization methods. Immunization as a concept just refers to a strategy of risk-management for assets and liabilities. Exact matching can be used for immunization, but is not the same as Redington or Full immunization. My wording at the end of this lesson is not particularly great, and I would change it if I were to make this video today to make that more clear. I might make a pinned comment about this to clear up potential confusion in the future, but I do apologize for not making this more clear from the start. It is definitely a flaw in the explanation, and I own that. Now, with regards to SOA 148, that problem is particularly tricky and I would argue a bit misleading in its wording. Notice that it never mentions what method of immunization is being used, just that the objective is to be "fully immunized." So, we want the assets to be fully immunized, but it isn't specified that they are to be immunized using the Full immunization technique. From my experience, it seems that SOA sees the term "fully immunized" as a way to indicate that assets are protected using some form of immunization (costs that need to be paid are met completely), not necessarily that the strategy of Full immunization is used. It could be the case that it is (and most times it is), but it is not an automatic assumption that can be made without considering the context of the problem in full to see if a Full immunization strategy is being implemented or not. In the majority of exam problems involving Redington or Full Immunization strategies, the problem will explicitly state that those strategies are being used (using the words "strategy" or "technique"), and will also include an interest/yield rate being used for the immunization strategy. SOA 148 does not include an interest/yield rate for which the assets are being "fully immunized" and also does not mention either strategy by name (Redington or Full). Generally, if you are not given an interest rate like this and are not given enough information to find it, you probably need to use exact matching like is done for the solution of this problem. It's the only option. I will say, this particular problem is unique in this way. I've never seen another SOA problem involving immunization be this unclear, so I would not expect to see this happen a lot in future problems. I apologize for the lengthy response, but I hope this helps clears things up a bit and makes up for the confusion I may have caused at the end of the video.

You're welcome!

You're welcome! Glad the video is helpful :)

In the context of Calculus 3 it is pretty standard for a vector using the bracket notation <x,y> to represent a position vector, or a vector whose initial point is the origin and terminal point is the coordinates (x,y) from the vector components <x,y>. The word "position" referring to the "standard position," which is the origin. This is how I was taught, and how my Calc 3 textbook lays it out. So unless otherwise stated in a problem, I always assume the brackets imply a position vector. As a side note, there is another way to represent vectors using standard unit vectors, which I cover in a different lesson in calc 3, but usually you learn the bracket notation first. Putting that aside, you'd have to give me more context on how you asked your question or how the professor answered it in order for me to fully clear things up. Perhaps he has a different way of defining position vectors or maybe there was a miscommunication. Also if you are learning about vectors in a course that is not calc 3, the notation might be different.

In u substitution you use both differentiation and integration. Whatever you set equal to u, you will need to take the derivative of. In this case we set u=4x^3+1, so we have to take the derivative of that du/dx. The derivative rule for powers is to multiply the exponent down and then subtract one from the exponent. Thats why we get 4*3x^2=12x^2. The opposite is true when integrating a power. That is where you add one to the exponent and divide by the new exponent. Hope this helps!

Awesome! Glad I could help. Calc 3 can be tough, but you've got this!

Don't worry, I'll get there! A lot of the applications show up in later topics of Calculus 3. So you'll see them in future lessons.

Comp is the magnitude of the projection. So proj finds the vector w1, and comp would find the magnitude or length of vector w1. Hope that helps!

@ oh ok. Just wanna double check. So comp is used to find like the length/magnitude of W1 and W2. And Proj is used to find the vector <x,y,z> for W1 and W2?

@@Exceliear The comp formulas I boxed in and highlight at 21:18 are for finding the magnitude of W1, or the projection vector while the proj formula is for finding the actual vector of w1, <x,y,z>. To find the magnitude of w2, you would have to use the magnitude formula on v-proj (square root of sum of the components squared). The naming is similar so I can see where the confusion comes in, w2 is called the orthogonal vector component, which is different from the comp formula for magnitude of w1.

@@JKMath got it. Thank You

@@JKMath just one last question. So we would use comp if a problem ask us about magnitude(in vector projection) and proj if they ask us for vector components correct?

The PV for a set of cashflows represents the amount of money that would need to be invested today (t=0) in order to get a desired amount or amounts in the future. Another way of thinking of it is that the PV is just the value at t=0 of any future payments being received. It's what those payments would be worth combined today. So in the case of example 2, Lily will be receiving payments of 3000 at the end of the next 5 years, the PV represents what those 5 payments would be worth today. She doesn't necessarily have to make that investment herself, but regardless that is what those payments would be worth at t=0. You can also look at it like this: A common scenario for PV is paying off a loan. The amount of a loan is represented by PV, or the amount that all the payments in the future need to add up to (including interest) in order to pay off the loan. The value of all the future payments at t=0 (PV) should be the same as the loan amount, so that it is entirely paid off in the future. Does that make sense? I think you may have just confused the wording of the problem. It is not saying that Lily will receive the PV. The problem is asking to find the PV of all the payments that she will receive in the future.

@@JKMath Ah i get it now. Tysm you've been very helpfull

You're welcome! Glad to help :)

When you use semiannual rates for both r and j and solve for n in the equation, it will naturally be in terms of semiannual periods. So there is no need to convert it by multiplying by 2. If you instead used annual rates for r and j in the equation, then the n you solved for will be in terms of years and so then you would need to convert to semiannual periods. Its all based on the frequency of the rates that you use. Does that make sense?

You're welcome!

It's important to remember that while a converging series will have a limit of 0, the reverse is not necessarily true. A limit of 0 does not guarantee that a series converges, it can still diverge. This is why the divergence test only produces a result if the limit does not equal 0. If its not 0 then we know for sure that it does not converge, but if it is 0 we do not know. We will need to use other convergence tests to decide that. So that's why I say we can't say anything for that last example. Hope this helps!

You can always do either. Integrating with respect to x or y is ultimately a choice that is up to you, because as long as the integrals are set up correctly, they will produce the same answer. With that being said, often times one way will be easier than the other. Integrating with respect to x is easier when you look from the top down over the region and only see ONE top & bottom function each. If the function on top switches at some point, then you have to use two integrals to set up the area like I do in example 3. Integrating with respect to y will be easier when you look from right to left over the region and only see ONE right most & left most function each. If the right most function switches, then it has to broken up into two integrals. So the bottom like in this: if you can avoid needing to set up 2 integrals, then that's the way you probably want to do it. Although, sometimes using 2 integrals will be unavoidable depending on how the region is formed. The region in example 3 requires more than 1 integral no matter how you decide to approach it. Working with respect to both x and y results in the need for 2 integrals. Hope this helps! (Also glad you like the outro music haha. I'm no musician but I'm proud of making that little jingle)

Not until I finish the Calc 3 series. I can only manage working on one higher-level math course at a time. Since regular Algebra topics are simpler in nature, I can manage covering it alongside Calc 3. Those are the only two courses I plan to work on this year. I'm just one person, so I'm doing what I can! Thanks for your patience!

@@JKMath I'm not going to be taking Calc 3 and Linear Algebra until next year. Hopefully, at least the Calc 3 playlist will be complete by then. We need you, Joshua-please don't give up on us! I honestly can't thank you enough for the Calc 1 and 2 playlists. Thank you very much!

@ You're very welcome :) As long as the channel continues to grow I should be able to keep making videos for a long time!

@@JKMath Live long and prosper! 🖖

You can expect about 1 new Calc 3 lesson a week. It takes a lot of time to put each video together, so that's as fast as I can do it without overworking myself. Thanks for your patience!

@ thank you sir

Yes, I believe that would also work! Everything gets multiplied together in the end anyway, so if you want to multiply by the PV factor earlier that should be fine. I believe you would still get the same answer of 202.40.

You're welcome, glad I could help!

As of right now I have not made worksheets for calc 2 like I did for calc 1 and financial mathematics. Those worksheets are very time consuming to make, so if I ever do make them it will be far into the future. I am just a one man operation, so there’s only so much I can do at one time. Right now, my top priority is making more videos, so I won't be working on Calc 2 worksheets anytime soon. There is not enough time in the day for me to do both at once unfortunately. My apologies, but I hope you can understand!

@@JKMath yup i understand. it's all good, i'm still learning and getting better at my classes from ur video. you doing a great job. i wish you all the best.

You're welcome! I appreciate the kind words :)

Will do! 👊

d^(m) represents a nominal rate convertible m times per year. To get the respective non-annual effective rate that is compounded m times per year, you divide d^(m) by m. So d^(m)/m would be the non-annual effective rate compounded m times per year. In example 2, that means d^(12) is a nominal rate convertible monthly, while d^(12)/12 is the effective monthly discount rate. Hope that helps!

Thank you sir! I use an app called Goodnotes on iOS.

Thank you!