What are the essential topics to learn in Calculus?

[Hydrargyrum]

Hey. I'm teaching (trying to) myself calculus before i go to college. The book i got from my trigonometry seems pretty repetitive, but I was wondering which topics i need to learn. So far, I've learned limits, derivatives, applications of derivatives (I wasted about a month on the chapter because it turns that the only application is finding maxs and mins and Newton's method), integration, and natural logs and exponents. The other chapter are applications of integration, integration techniques, series, analytic geometry, vectors, and multivariable calculus. So which parts should i try to learn?

 

[PowerIso]

Hehe there are more applications for derivatives, but you'll see that later on. Well, with all that, you seem to have a good head start. I would skip applications of integration, since arc length, work, center of mass, are all things you can learn later and skipping it will not hamper you too much.

A good chapter to work and spend a lot of time is on integration techniques. Just look at the homework section on the form and you'll see a lot of people asking for help. If you can introduce yourself to integration by parts, trig sub, improper integration, etc, before you learn it formally, that'll be awesome.

Knowing the infinite series test before hand will make going over the topics easier when you are introduced to them later. For a lot of people, the test are tedious and they have no idea which one to use. If you know about them before hand, you'll probably have a good idea when to use them and how.

I think vectors are important, but you want want to introduce some linear algebra into your skills before you tackle them. It's nice to know what a laplace expansion is before you have to use it! Of course multi variable calculus is important, specially line integration, green's theorem, and stroke's theorem.

I think most calculus 1 classes over what you cover already in their first semester. 2 semester is generally techniques of integration to analytic geometry and the last part is the third semester. (I had to do calc 1 and 2 in one semester =( )

 

[mjsd]

if you are learning calculus for the first time, multivariable calculus, analytic geometry, vector calculus and perhaps series may be omitted at this stage

 

[Hydrargyrum]

Thank you for your help.^^^^^ Why? Is those difficult? If so that's why I'm trying to teach myself. I'm trying to develop engineering problem-solving skills

 

[mjsd]

^^^^^ Why? Is those difficult? If so that's why I'm trying to teach myself. I'm trying to develop engineering problem-solving skills

those are what you usually learn after you have learned the basics. but if you are already good at the basics then, they would not be difficult at all

 

[PowerIso]

You mention that you are trying to develop engineering problem-solving skills. If you feel good about your basic derivative and integration skill, I think you can probably start an introduction to physics book.

 

[kentm]

If you are just trying to be prepared for you college courses, your first calculus course will probably go over what you've already learned:
Calculus I: Limits, Derivatives, Applications of Derivatives, Anti derivatives/Definite Integrals.

Calculus II: Applications of Integrals, Integration Techniques, Infinite Sums, Sequences and Series, convergence and error bounds, separable differential equations, parametric curves in the plane and polar coordinates.

Calculus III: Vector algebra and geometry, multi-variable calculus, partial and directional derivatives, gradient, chain rule, optimization, multiple and iterated integrals, Parametric curves and surfaces, vector fields, divergence and curl, line and surface integrals, Green's, Stokes' and divergence theorems.

That stuffs basically out of the course outlines from my school.

 

[Hydrargyrum]

You mention that you are trying to develop engineering problem-solving skills. If you feel good about your basic derivative and integration skill, I think you can probably start an introduction to physics book.

i'm taking physics now but it's not calculus based

 

[Hydrargyrum]

those are what you usually learn after you have learned the basics. but if you are already good at the basics then, they would not be difficult at all

i looked at the vector and multivariable sections and they look about as hard these Differential Equations I've been hearing about

 

[Vid]

http://en.wikipedia.org/wiki/List_of_calculus_topics

 

[seichan]

What calculus do you want to take when you get to college? Sounds like you'll be fine to skip Calc 1. Calc 1 only gets up to integration.

 

[Hydrargyrum]

I guess calculus 2