MAthematics question: Doing vector..then waht?

[Goosemaster]

Well, I started Vector Calculus(calc III) today, and was told that it will last about 7 1/2 weeks: it wll finish too late to perhaps start another math course this summer.

Seeing as how I am going to be at my community college for a while('till next spring if not more, depending on how long it takes me to get my associates in EE), I was interested in continuing math indefinitely.

I was interested in recommendations concerning the next math course I will take:

Linear Algebra
Differential Eqns
Discrete Mathematics


From friends, I have heard that Linear and Discrete math deal with topics that are quite different from my Calculus perspective.


Personally, I assumed that taking diff eqns right after vector would be nice since integration and differention would be fresh in my mind.


Thanks

 

[Goosemaster]

Nevermind.. iasked someone who knows their sh!t and they said diff eqns



thanks

 

[silverpig]

Vector Calc is calc IV
Multivariable is calc III
Integral is II
Differential is I

 

[Goosemaster]

Originally posted by: silverpig
Vector Calc is calc IV
Multivariable is calc III
Integral is II
Differential is I

at my college vector and multivariable are both covered in calc III. Vector calc is just the name of the class.


What I will do is just ask the univs I want to transfer to.

 

[simms]

Originally posted by: silverpig
Vector Calc is calc IV
Multivariable is calc III
Integral is II
Differential is I

Sounds right, even for Canadian Universities.

<--- UToronto

 

[silverpig]

Originally posted by: simms

Originally posted by: silverpig
Vector Calc is calc IV
Multivariable is calc III
Integral is II
Differential is I

Sounds right, even for Canadian Universities.

<--- UToronto

Better sound right for Canadian universities...

<--- UBC

 

[Goosemaster]

After consulting staff at my college, and finally staff @ Virginia Tech, which is where I would like to transfer in the future, I have been advised to take Linear Algebra first, followed by diff eqns and discrete math.

That person that "knew their sh!t" appearantly didn't .

 

[silverpig]

Lin alg and diff eq aren't really related. You can do them at the same time. Actually, the same goes for discrete math. They are so different that knowing lin alg won't help you with diff eq or discrete at all.

 

[apac]

Originally posted by: silverpig

Originally posted by: simms

Originally posted by: silverpig
Vector Calc is calc IV
Multivariable is calc III
Integral is II
Differential is I

Sounds right, even for Canadian Universities.

<--- UToronto

Better sound right for Canadian universities...

<--- UBC

Whiskey...?

I only have 3 calcs:
Calc I is basic differentiation/integration
Calc II is advanced diff./int., sequences and series and polar
Calc III is multivariable and vector

 

[rgwalt]

Originally posted by: silverpig
Lin alg and diff eq aren't really related. You can do them at the same time. Actually, the same goes for discrete math. They are so different that knowing lin alg won't help you with diff eq or discrete at all.

He speaks the truth. Obey the rule of prerequisits if there is an order to which you need to take your math courses. For instance, at my school we lumped vector calc in with linear algebra, and took one course titled Multivariable Calculus with Linear Algebra.

Linear Algebra and DiffEq are where you need to go next. In what order you take them is up to you, but I would take linear algebra first. Matrix math is fun stuff.

R

 

[Goosemaster]

Originally posted by: rgwalt

Originally posted by: silverpig
Lin alg and diff eq aren't really related. You can do them at the same time. Actually, the same goes for discrete math. They are so different that knowing lin alg won't help you with diff eq or discrete at all.

He speaks the truth. Obey the rule of prerequisits if there is an order to which you need to take your math courses. For instance, at my school we lumped vector calc in with linear algebra, and took one course titled Multivariable Calculus with Linear Algebra.

Linear Algebra and DiffEq are where you need to go next. In what order you take them is up to you, but I would take linear algebra first. Matrix math is fun stuff.

R

AS I said, I spoke to the univ I want to transfer to in the future. They informed me that Linear algebra was a freshman math while diff eq was a softmore math. In addition, Linear algebra is a prereq for diff eqn...

Don;t ask for specifics becuase I don't know.

Thanks for the info though

 

[Ionizer86]

From what I've seen, you should be able to go from Calc I (AP Calc AB) to any other class: Calc C/II, Calc D/III, Diff. Eq. etc because the Calc III doesn't build on Calc II, etc. However, the usual progression is through the calcs, then Diff. Eq, then Matrix Theory/Linear Algebra. In our school, Discrete Math is a separate course that's not part of the "normal progression."

 

[beer]

Originally posted by: Ionizer86
From what I've seen, you should be able to go from Calc I (AP Calc AB) to any other class: Calc C/II, Calc D/III, Diff. Eq. etc because the Calc III doesn't build on Calc II, etc. However, the usual progression is through the calcs, then Diff. Eq, then Matrix Theory/Linear Algebra. In our school, Discrete Math is a separate course that's not part of the "normal progression."

Uhh, no.

Calc AB = differentiation and integration
you CANNOT go straight to Diff Eq: Most of the non-elemtary methods for solving diffential equations call upon infinite series calculus, which is beyond Calc I (integro/differento)

Hell, the whole point of Fourier Series, which is absolutely critical in a study of PDEs, is rooted in series (hence the name). And to understand series, you need to understand sequence. At Texas, integro/differential is Calc I, sequence/series is calc 2, vector calc is calc 3, and then from that you can approach a survey course in ODE/PDE methods, or an etnire course in vector calculus.

There are entire methods to solving homogeneous and nonhomogenous ordinary differential equations that are rooted in infinite series sums. Without calc 2 you'd be dead in the water. I also strongly advise linear algebra before differential equations. A lot of differential equations call upon methods of linear algebra to solve, you can get by without it but it isn't fun.

The sheer misinformation that you guys are fed is just scary.

 

[Ionizer86]

Originally posted by: beer

Originally posted by: Ionizer86
From what I've seen, you should be able to go from Calc I (AP Calc AB) to any other class: Calc C/II, Calc D/III, Diff. Eq. etc because the Calc III doesn't build on Calc II, etc. However, the usual progression is through the calcs, then Diff. Eq, then Matrix Theory/Linear Algebra. In our school, Discrete Math is a separate course that's not part of the "normal progression."

Uhh, no.

Calc AB = differentiation and integration
you CANNOT go straight to Diff Eq: Most of the non-elemtary methods for solving diffential equations call upon infinite series calculus, which is beyond Calc I (integro/differento)

Hell, the whole point of Fourier Series, which is absolutely critical in a study of PDEs, is rooted in series (hence the name). And to understand series, you need to understand sequence. At Texas, integro/differential is Calc I, sequence/series is calc 2, vector calc is calc 3, and then from that you can approach a survey course in ODE/PDE methods, or an etnire course in vector calculus.

There are entire methods to solving homogeneous and nonhomogenous ordinary differential equations that are rooted in infinite series sums. Without calc 2 you'd be dead in the water. I also strongly advise linear algebra before differential equations. A lot of differential equations call upon methods of linear algebra to solve, you can get by without it but it isn't fun.

The sheer misinformation that you guys are fed is just scary.

I've taken Calc BC, Calc 3, Linear Algebra, and Diff Eq. When you have semester long classes, they don't usually cover too much. Like yes, we had sequences and series based diff eq's where we'd have equations that look like Sigma(AnX^n), but they were quite basic and easy to understand without going into mad crazy stuff in Calc C like Taylor and MacLauren polynomials. Those things flew over my head, but the sequences and series in Diff. Eq were easy.

And yes, our Diff Eq class was held before the Matrix theory class by the same prof. We didn't go super deep, so we were ok with having Diff Eq first. We did learn about eigenvalues and eigenvectors in Diff Eq before going into the subject in Matrix Theory again though 🙂

I'm saying that if you can differentiate and integrate basic stuff, you'll pretty much be ok in any math class from then on. If you asked me to do some calc with polynomials, sines, cosines, and natural logs right now, I'd be ok. But if you asked me to find some area of surface of rotation or do some massive Taylor series, I'd suck really bad. But still, I got A's in both Diff Eq and Matrix Theory. Most teachers teach the new concepts without trying to toss in really crazy derivatives and integrals from previous classes.

 

[beer]

Originally posted by: Ionizer86
I've taken Calc BC, Calc 3, Linear Algebra, and Diff Eq. When you have semester long classes, they don't usually cover too much. Like yes, we had sequences and series based diff eq's where we'd have equations that look like Sigma(AnX^n), but they were quite basic and easy to understand without going into mad crazy stuff in Calc C like Taylor and MacLauren polynomials. Those things flew over my head, but the sequences and series in Diff. Eq were easy.

And yes, our Diff Eq class was held before the Matrix theory class by the same prof. We didn't go super deep, so we were ok with having Diff Eq first. We did learn about eigenvalues and eigenvectors in Diff Eq before going into the subject in Matrix Theory again though 🙂

I'm saying that if you can differentiate and integrate basic stuff, you'll pretty much be ok in any math class from then on. If you asked me to do some calc with polynomials, sines, cosines, and natural logs right now, I'd be ok. But if you asked me to find some area of surface of rotation or do some massive Taylor series, I'd suck really bad. But still, I got A's in both Diff Eq and Matrix Theory. Most teachers teach the new concepts without trying to toss in really crazy derivatives and integrals from previous classes.

Your class must have been much simpler than mine. I don't think anyone could have passed the application (much less the proofs) section of the class wihout a firm understand of power series (amongst other things), which is clearly calc 2 material.

It also seems evident that your course didn't go into PDEs, which requires a foothold in series too.

 

[MovingTarget]

Calc 1 == basics of differentiation/integration (concepts such as limits of reiman summs/areas/etc)
Calc 2 == advanced integration/differentiation and applications (volumes of solids of revolution, advanced integration techniques
Calc 3 == Multivariable calculus, Series, and intro to Vector calculus
Vector Calculus == extension of Calculus 3 focusing on divergence, curl, laplacian operators, Green's Thm, flow/flux, etc.
Differential equations == advanced multivariable calculus. This focuses on how to solve specific types of differential equations including homogenous, nonhomogeneous, linear, nonlinear, and first/second/nth order equations. This is what I reccommend you take next. It is the most advanced of all these courses. Very interesting.

 

[CombatChuk]

At my school (CU, University of Colorado) Calculus broke down like this

Calc I differentiation, implicit differentiation, and touched integrals with antiderivatives
Calc II Integration, volumes, and Series and Sequences, basic differential equations
Calc III Multivariable, and vector.

Then there are classes of differential equations and linear algebra and numerical analysis.

BTW im a EE student

 

[Goosemaster]

I am in line for a nice tutoring job, so hopefully I will have some extra $$ soon. here it was I will do.

Linear Algebra is something I've been told to take first by the univ I want to go to. Might as well follow their directions.

however, I've been told that it is a rather easy class compared to Diff eqns.

What I will do is continue taking my Calc III class, which will finsh in about 7.5-8 wks.

@ wk 7 I will start taking Linear Algebra fro the second-week session of summer, finshing Calc III about 1.5-2 weeks into LA.

Then I will take Diff eqns in the fall as it seems to be pretty damn hard.


At least this is what I plan to do 😀 😉

Calc II was BITCH...5 credits= $$$$$$$$$

Calc III and above are all 4 credits, so they will definitely be easier on the wallet😀 if not hard on the noggin😉

 

[Chu]

Originally posted by: Goosemaster
I am in line for a nice tutoring job, so hopefully I will have some extra $$ soon. here it was I will do.

Linear Algebra is something I've been told to take first by the univ I want to go to. Might as well follow their directions.

however, I've been told that it is a rather easy class compared to Diff eqns.

What I will do is continue taking my Calc III class, which will finsh in about 7.5-8 wks.

@ wk 7 I will start taking Linear Algebra fro the second-week session of summer, finshing Calc III about 1.5-2 weeks into LA.

Then I will take Diff eqns in the fall as it seems to be pretty damn hard.


At least this is what I plan to do 😀 😉

Calc II was BITCH...5 credits= $$$$$$$$$

Calc III and above are all 4 credits, so they will definitely be easier on the wallet😀 if not hard on the noggin😉

There are two very different ways to teach Linear Algebra. The first way is the method you've probably been exposed to all your live, which is teaching Linear from problem solving perspective, i.e. 'this is how you convert to an orthoginal base'. The second way to teach Linear is as the transition from 'solving' math to 'exploration' math, i.e. focusing on theorms and progression of mathematical ideas instead of solving specific problems. Linear algebra is either trivial or difficult depending on which course you take. Also, a lot of people find Linear extreemly boring if they get stuck in the first, because its pretty much all arithmetic.

That being said, if your an engineer DifEq is infinetly more important to grasp, since you will use it all the time.

-Chu

P.S., btw, if you want to get more a feal for what linear is about, here is a link to the best intro Linear book I've seen, and even better its free.

 

[Goosemaster]

Originally posted by: Chu

Originally posted by: Goosemaster
I am in line for a nice tutoring job, so hopefully I will have some extra $$ soon. here it was I will do.

Linear Algebra is something I've been told to take first by the univ I want to go to. Might as well follow their directions.

however, I've been told that it is a rather easy class compared to Diff eqns.

What I will do is continue taking my Calc III class, which will finsh in about 7.5-8 wks.

@ wk 7 I will start taking Linear Algebra fro the second-week session of summer, finshing Calc III about 1.5-2 weeks into LA.

Then I will take Diff eqns in the fall as it seems to be pretty damn hard.


At least this is what I plan to do 😀 😉

Calc II was BITCH...5 credits= $$$$$$$$$

Calc III and above are all 4 credits, so they will definitely be easier on the wallet😀 if not hard on the noggin😉

There are two very different ways to teach Linear Algebra. The first way is the method you've probably been exposed to all your live, which is teaching Linear from problem solving perspective, i.e. 'this is how you convert to an orthoginal base'. The second way to teach Linear is as the transition from 'solving' math to 'exploration' math, i.e. focusing on theorms and progression of mathematical ideas instead of solving specific problems. Linear algebra is either trivial or difficult depending on which course you take. Also, a lot of people find Linear extreemly boring if they get stuck in the first, because its pretty much all arithmetic.

That being said, if your an engineer DifEq is infinetly more important to grasp, since you will use it all the time.

-Chu

P.S., btw, if you want to get more a feal for what linear is about, here is a link to the best intro Linear book I've seen, and even better its free.

wow..thanks. Like I said, I hope to take Diff eqns in the fall(16 week course). SInce it is more importatn, Ifeel I should devote mor etime to it. That and the fact that Linear algebra is a freshman course that i need to get of the way if I want to transfer.