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Math Help - Taking Calculus 1 - 3

  1. #1
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    Taking Calculus 1 - 3

    I am currently a pre-calculus student planning to take the calculus series 1-3 and then differential equations.

    Most of my friends who have taken differential equations tell me that calculus 3 is not needed to be success in a differential equations course.

    Is this true?

    Also, what is the difference between calculus 1, 2 and 3?

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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by magentarita View Post
    I am currently a pre-calculus student planning to take the calculus series 1-3 and then differential equations.

    Most of my friends who have taken differential equations tell me that calculus 3 is not needed to be success in a differential equations course.

    Is this true?

    Also, what is the difference between calculus 1, 2 and 3?
    it is possible to survive diff eqs without calc 3, but it is better for you if you do calc 3 first or at least during. it will make your class a whole lot easier. also, there may be some things in diff eqs that you need the background from calc 3 to do. certain things with series for instance. most schools require you do cal3 as a pre-requisite or co-requisite to diff eqs anyway

    calculus 1 is mostly about rates of change, limits, differentiation and applications of differentiation, and maybe a little integration depending on your school. it is of course, in single variable

    calculus 2 is mostly about integration and applications of integration. again, in single variable.

    calculus 3 is all of the above, except you do it in multivariable. that is, you are working in 3 dimensions or more. you would also do some things about series


    you can find more information about these in the course bulletin for your school
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  3. #3
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    good

    Good reply.

    Thanks

    P.S. Go to my post in the Trigonometry section about Rational Trigonometry.

    What exactly is Rational Trigonometry?

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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by magentarita View Post
    I am currently a pre-calculus student planning to take the calculus series 1-3 and then differential equations.

    Most of my friends who have taken differential equations tell me that calculus 3 is not needed to be success in a differential equations course.

    Is this true?

    Also, what is the difference between calculus 1, 2 and 3?
    Calculus I tends to be the hardest of the calculus sequence. This is because you learn all the fundamentals (Limits, Differentiation, and Integration).

    Calculus II is more about the applications of integrals (volumes, surface area, work, etc.) and infinite series [most Calculus II classes tend to talk about polar calculus at the end...and possibly conic sections as well].

    Calculus III is the application of calculus I and II to 3-space [also known as the third dimension]. In my opinion, this was the easiest of the calculus sequence. You apply limits, differentiation, and integration to 3-space. Also, the calculus of vector valued functions, and introductory vector calculus [where you learn about line integrals, surface integrals, and famous theorems like Green's, Divergence, and Stoke's] is taught.

    At the college I attended, Calculus III was a prereq for Differential Equations, but I don't see why. I think you just need calculus II.

    Differential Equations (which I ), is about solving...erm...differential equations. These are important in the applied maths.

    You learn about first and second order DEs [and various techniques of solving them], applications of DEs, Systems of DEs, Matrix methods in solving DEs, and then the Laplace Transform and how its applied to solving DEs. Depending on how far you may go in the class, you may also touch on topics like Power Series Solutions, Boundary Value Problems, Fourier Series, and Sturm-Lioville Problems.

    I hope this gives you an idea of what to expect!

    --Chris

    EDIT: Man!! You're too quick for me Jhevon...I was too busy thinking about snicker bars...erm...haha
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  5. #5
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    Quote Originally Posted by magentarita View Post
    I am currently a pre-calculus student planning to take the calculus series 1-3 and then differential equations.

    Most of my friends who have taken differential equations tell me that calculus 3 is not needed to be success in a differential equations course.

    Is this true?

    Also, what is the difference between calculus 1, 2 and 3?
    You should be fine, but I'll give you a bit of warning. You are going to have a very rough time in Differential equations if you don't know derivatives from Calculus I and everything regarding integrals (Calculus I and II) like the back of your hand. Differential equations rely heavily on integrals to solve, and you'll be employing techniques of integration (you'll learn that in Calculus II) to solve them.

    EDIT: To answer your second question.

    From what I've seen, Calculus I is different than it is here in Georgia than in the rest of the US. But I'll explain from my perpective.

    Calculus I: Covers Limits & continuity (the foundation of Calculus), derivatives, and applications of derivatives

    Calculus II: Integrals (area, u-subsitution, applications, techniques of integration, Fundamental Theorem of Calculus), infinite series, and polar coordinates

    Calculus III: Partial Derivatives, Multiple Integrals, and Vector Calculus
    Last edited by mathgeek777; August 31st 2008 at 05:56 PM. Reason: Answering Second question.
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    You know, i never did vector calculus in calc 3? you know, things like Green's theorem and Stoke's theorem, etc. i also never touched integration in calc 1. neither did i do polar coordinates in calc 2. among a lot of other topics! i did calc 1 and 2 at a liberal arts college

    It seems to be the general consensus that calc 2 was the hardest and calc 3 was the easiest. i disagree, i think calc 1 was the easiest, it was the closest to pre-calc, which i love, and your biggest problem was algebra. not the case with the other two calculus courses. for those guys, getting the concept and setting up the problem was the hardest. you wished that they would give you a straight forward problem with killer algebra. but half the time, you don't even know how to set up the problem so you can do it. this is generally not a problem in calc 1. it is pretty much straight forward. i found calc 3 was the hardest, but maybe it was my professor. (i usually don't blame my professors for anything, so you know how bad it is here)
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  7. #7
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    Quote Originally Posted by Jhevon View Post
    You know, i never did vector calculus in calc 3? you know, things like Green's theorem and Stoke's theorem, etc. i also never touched integration in calc 1. neither did i do polar coordinates in calc 2. among a lot of other topics! i did calc 1 and 2 at a liberal arts college

    It seems to be the general consensus that calc 2 was the hardest and calc 3 was the easiest. i disagree, i think calc 1 was the easiest, it was the closest to pre-calc, which i love, and your biggest problem was algebra. not the case with the other two calculus courses. for those guys, getting the concept and setting up the problem was the hardest. you wished that they would give you a straight forward problem with killer algebra. but half the time, you don't even know how to set up the problem so you can do it. this is generally not a problem in calc 1. it is pretty much straight forward. i found calc 3 was the hardest, but maybe it was my professor. (i usually don't blame my professors for anything, so you know how bad it is here)
    I also find Calc 1 to be easy since it is primarily algebra based. Once you get the derivative concepts in Calc 1 down, the only problem you have to worry about with solving integrals is figuring out what to substitute u for (as well as v when you enter parts), which I've heard can be quite a challenge. Calc 3 (at least the start of it) is just a reintroduction of Calc 1, but in a 3-dimension space, which isn't all that bad (at least if you got Calc 1 down. If you didn't, i would be seriously wondering how you got through Calc 2 with a high enough grade to move on)
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mathgeek777 View Post
    I also find Calc 1 to be easy since it is primarily algebra based. Once you get the derivative concepts in Calc 1 down, the only problem you have to worry about with solving integrals is figuring out what to substitute u for (as well as v when you enter parts), which I've heard can be quite a challenge. Calc 3 (at least the start of it) is just a reintroduction of Calc 1, but in a 3-dimension space, which isn't all that bad (at least if you got Calc 1 down. If you didn't, i would be seriously wondering how you got through Calc 2 with a high enough grade to move on)
    yeah, the first part of calc 3 was easy. things started going weird around multiple integrals. besides that, you needed a better memory. a lot of things were straight forward, but you had to remember a formula for it. the formulas were usually too hard to derive on the spot, which is what i depended on in calc 1 and 2. my memory is horrible! the only way i survive math is to remember a few basic things, and understand the concepts so that i am able to derive everything else i might need. so if something is hard to derive, i am in trouble. that seemed to happen a lot in calc 3.
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    Thank you all for the great information.
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