13.1: Vector Functions & Space Curves

Objectives:
1. Define a vector-valued function.
2. Graph certain space curves defined by vector-valued functions.
3. Write the vector form of a line segment.
4. Define the limit of a vector-valued function.
5. Define continuity for a vector-valued function.

[@JHaas117]

wow its really like night and day when looking for different teachers to explain things. thank you for uploading this ive found my current prof just expects people to know alot of the ideas he is teaching with out giving even the briefest of reviews. new flash students forget the small stuff ALL the time!

[@Mary-mj7le]

lmao what is going on with these replies

[@JHaas117]

@@Mary-mj7le uhh looks like spam i guess? i would report it if you can.

[@sgt.sargent3242]

You have no idea how much these are helpful, especially when reviewing for big exams. Great lecturers like yourself are a BLESSING. Thank you🙏

[@being____sharma]

Being honest I'm watching this video after 2 years since it was uploaded and I'm following the series of your videos from ch-12 and I bet I'm getting a better clarification and the level of understanding about these topics had increased much more than it was before. Thank You Ma'am for creating these lectures...😄

[@oxord1111]

Why doesn’t my professor explain like this 😭. I have to pay my classes just to teach my self from KZbin. Thanks for this video really helpful!

[@aishasaed2454]

I’m like you😢

[@kyoutobi6051]

I am a Chinese student, and your courses have helped me a lot. Other teachers can’t be as clear as you said！

[@kyoutobi6051]

Your pronunciation and spelling are very standard, which makes me sound very relaxed!!!

[@Wawadish]

Waow, this helped a lot! Thanks for teaching me this, I hate commuting to university so I try to study from home. Knowing that there are great online resources like this helps me a lot. Thanks for making your lectures available.

[@NulliusInVerba8]

You are AMAZING! Thank you. I kept resisting opining this video, because I couldn't understand vector functions so I hated them and wanted to just avoid this topic! but thanks to you.. it's now nice and clear .. thank you very much.

[@didemaydogan1307]

Joining that class from another country feels great. I wondered their ages because we get this course at the second year of the mathematics department in Turkey.

[@alexandraniedden5337]

This class is a high school junior/senior class (dual credit offered through a local university). This is a highly advanced class though - calculus 3 in high school is not the norm!

[@Dave-to5it]

@@alexandraniedden5337@alexandraniedden5337 Wow calc 3 in high school is crazy. Definitely not the norm, I don't think they even offered that at my highschool.

[@parthomondal3663]

I saw the whole class from Bangladesh. It has been very helpful for me. Note that my course teacher cannot teach like this.Thank you ma'am for presenting me so beautifully. And yes, can I know the name of the book you are reading from?

[@alexandraniedden5337]

Hello! I teach from Stewart's 8th edition Multivariable Calculus.

[@my2b54]

At 30:09 , is it supposed to be (1-cost)/t? Because that would give us a 0/0 form. If we had 1-(cost/t), the limit would not be defined

[@humaamsaid3282]

You are helping me out so much in multivariable thank you so much

[@StockaOfficial]

I think that l, | and 1 shouldn't be written all like vertical lines.

[@fllh100]

Hi miss, thank you for your wonderful explanation 🌹 but I have a note in example 7 I think there is a mistake with the 1-cos/t We first should do common denominator After that at the end we will get I think 1/0 If I am wrong plz correct me and thank you 🌹

[@alexandraniedden5337]

Hi! Thank you for your comment. For Example #7, I'm not sure what you mean when you refer to a common denominator. We can substitute 0 in right away, getting 0/0 and then using L'Hopital's Rule.

[@fllh100]

What I meant is before substituting the t with 0 we could first join 1-cost/t by common denominator The 1 will be t/t After that we will do t-cost/t And the final answer will be 1/0 which i think is doesn’t exist And plz correct me if I’m wrong I’m just seeking knowledge And thank you for being kind and responding to me

[@alexandraniedden5337]

@@fllh100 Ah, yes, I understand now. I meant that fraction bar to extend, so 1 is actually in the numerator of the fraction. I apologize for my poor notation. That being said, if 1 were not in the numerator and were standalone as you read, then yes, you would be correct that we should find a common denominator first.

[@fllh100]

@@alexandraniedden5337 ohh ok. Sorry for my misunderstanding. And thank for your brilliant explanations on your channel. Good luck!

[@kyleschwab1114]

You are the GOAT.

[@kbsjourney1341]

can you explain more at 16:23 on how you got (1 - 6t)? and the difference between r and r(t)

[@kotp7147]

idk if you need the answer still but she just used the vector notation of vector r and she made into a parametric equation with the original point

[@malihasabir3605]

thank you so much!!!!God bless you

[@neutral7474]

Thanks you very much for this.. this is really helped me a lot.. which book is best to visualise and learn this concept??

[@alexandraniedden5337]

I teach out of Stewart's Multivariable Calculus, 8th edition. I can't say that this book is best, but that's where I am aligning my content to.

[@neutral7474]

@@alexandraniedden5337 thanks for replying.. really appreciate your work.. According to you which is the one best(your favourite too) book for Vector calculus or multivariable calculus for complete beginners??

[@alexandraniedden5337]

@@neutral7474 I have not looked at many textbooks but believe Stewart's is pretty good - very reader friendly. Good luck!

[@menzincube2845]

Where can we find your notes😭, it would be much easier to take all this in

[@alexandraniedden5337]

I don't have my notes posted. Sorry!

[@Karuska22ps]

is there a reason why it is x=cos(t), y = sin(t)?

[@alexandraniedden5337]

I'm using the unit circle.

[@ompavankoushik8959]

no man,actually there isn't any reason ,just that cos(t) and sin(t) makes things easier we can also take it as x=t,y=square root(1-t^2) and there are many other ways but it doesn't seem to be convenient in these ways

[@plasmarim170]

32:49 I think limit t approachs to 0 of (1 - (cost)/t) it consider lhopital only cost/t so it have to 1 - 0 = 1 on j vector

[@plasmarim170]

anyway love u teaching it help me understand a lot

[@romanticclips.]

So nice explained

[@0100hem]

great flow! btw what is the name of the book? and what is the class year?

[@alexandraniedden5337]

I work out of Stewart's 8th edition Multivariable Calculus. This is a high school dual credit Calculus 3 & Differential Equations class (mostly high school seniors).

[@0100hem]

@@alexandraniedden5337thank you, i appreciate your efforts and wish you good

[@curiousOrk11]

thank you

[@jerryjerry666]

Nice videos, thank you!

[@naveenvenkatesan7004]

Which book

[@jonathansanchez2854]

why would x^2+y^2 = 1 become x= cost and y= sint ???

[@alexandraniedden5337]

This is the parametrization for the unit circle. For all points on the unit circle (x, y) = (cos(theta), sin(theta)) (normally use theta in place of t).

[@shaunmasuku9779]

is this a college class?

[@r.kamali4767]

Thank you so much ........

[@romanticclips.]

Can you share me link of chp 12

[@ngawangr5324]

29:35 i dont understand how -2cos(pi)0 is equal to -2. I can see that if you multiply cos by 0 first, then you'll end up with an answer of -2. but if you multiply in order, like -2 times cosine times pi times 0, you end up with 0. how the hell do u do math??

[@kotp7147]

you multiply the cos pi and t first which is 0, cos pi is 1 then times 0 = 0, then she just left -2 alone and thats how she got -2k

[@LOG2007]

Why do we restrict t from 0 to 1? Can it be any domain or must be from 0 to 1?

[@alexandraniedden5337]

That's the way I have constructed the segment. When you substitute t = 0, you get one endpoint. Using t=1 gives the other endpoint. This will always work for a line segment. That being said, this is not unique.

[@alabatchi1]

Are you studying advanced engineering math?

[@alexandraniedden5337]

@@alabatchi1 No, sorry!

[@apersiannihilist5632]

@@alexandraniedden5337 on the 5th example , the main domain must be t>1, since x= ln | t-1 | , t-1>0.....t>1 , we can't take negative values in the natural logs , its undefined , I believe you must have forgotten about the natural log

[@alexandraniedden5337]

@@apersiannihilist5632 You are correct that the argument of a log must be > 0, but remember that we must consider the absolute value. Therefore |t-1| > 0 which is true for all values except t = 1. This is represented graphically using the number line.

[@1999Joseph1]

thank you so much (:

[@2infinity1gamer17]

in your (EX 3) (1-3=-2 not 4)

[@loganabounader2995]

this the teaching that make students hate math

[@jsaba197]

can u be my professor please

[@khansamimakram]

wonderful

[@rafikamin6617]

Bro are you from apc collage??

[@froilanarias2292]

Would you pleaseeeeee stop using that pen!! The sounds of it skeeves me out. Other than that, your video is great!

[@angiolg2]

Agree

[@Junior4466]

sounds like a you problem

[@froilanarias2292]

@@Junior4466 lol you're a cool guy. Your profile pic is also very original, too, cool guy.