Can Calculus Be Mastered Without a Strong Foundation in Geometry?

[thushanthan]

Hi everyone,

I am taking Calculus - I in my college. Do I need to be very good at Geometry? What topics from Geometry I need to do Calculus well?. Thank you!

 

[n1person]

Well, there are a few different ways to view "geometry."

The most crucial idea of calculus is the function, and the best way to visualize this is through a graph. If you have an good idea of what a graph is and what a slope is you should do pretty well.

If you are wondering about stuff like area formulas, proofs, and finding angles, it generally isn't that important for a first year calculus course. As long as you know the area of a rectangle given height and width you can do pretty well!

Overall, good algebra skills are more important than good geometry skills in a intro calculus course.

 

[thushanthan]

Thank you

 

[darkside00]

yeah, but once in several variable calculus, you need to be good a visualization (graphs) of functions to solve double integrals over certain planes/areas I found

 

[thushanthan]

Thank you Darkside!

Currently I am learning Single Variable Calculus only.

 

[darkside00]

your right, one step at a time

 

[thushanthan]

But I have no idea why it is called as Single Variable & Multi Variable ?

In Cal - I we use something like y=x²+20x+100; It involves two variables X and Y. Then why

we call it as Single Variable? One of my friend told that in Multi variable I will be learning to do Calculus with

Vectors and Matrices. Also I have to plot graphs in 3 Dimension. Is it true? Can anyone explain this to me ??

Thanks in advance.

 

[darkside00]

Single basically means two dimensions. You will be differentiating and integrating with respect to one variable, say x. Multivariable is 3 dimensions, and you will be dirrentiating/integrating with respect to x, y, z. Vector calculus does come in when your dealing with 3 dimensions as in the real world . Although a vector can be only 1 or two dimensions

 

[thushanthan]

Thank you

 

[kiwakwok]

In single variable calculus course, you differentiate or integrate functions with only one variable. For example, f(x) = x² + ax + b
If you plot a graph of y = f(x), you will have a 2 dimensional plot.

In multivariable calculus course, you will deal with functions with more than one variables. For example, f(x, y) = x²/a² + y²/b²
If you plot a graph of z = f(x, y), you will have a 3 dimensional plot.

P.S. I am just a beginner in Calculus (and also Physics Forum ).

 

[LCKurtz]

P.S. I am just a beginner in Calculus (and also Physics Forum ).

Hi Kiwakwok. Welcome to the forums. You will find it to be a friendly and helpful place.

 

[n1person]

Indeed! Welcome!

 

[thushanthan]

Thank you Kiwakwok

Even though I am not good in Math, I like Calculus. It unifies all the topics in Math from Geometry to Trigonometry and it helps us to study about functions at the deepest level

 

[The Chaz]

But I have no idea why it is called as Single Variable & Multi Variable ?

In Cal - I we use something like y=x²+20x+100; It involves two variables X and Y. Then why

we call it as Single Variable? One of my friend told that in Multi variable I will be learning to do Calculus with

Vectors and Matrices. Also I have to plot graphs in 3 Dimension. Is it true? Can anyone explain this to me ??

Thanks in advance.

Let's consider the function you suggested: f(x) =x²+20x+100.
We call this function "single-variable" because it DEPENDS one one variable. You've probably heard "x" and "y" referred to as the "dependent" and "independent" variables (respectively).

You are actually already familiar with multivariable functions (functions that DEPEND on
more than one variable). Think about a restaurant that sells burgers, chips, and drinks. We can call these variables b, c, and d. The amount of income/revenue for the restaurant depends on how many burgers, chips, and drinks they sell. If the prices are $4, $1, and $2, an appropriate function for r (the revenue) would be:
r(b,c,d) = 4b + 1c + 2d.

Here's what you AREN'T used to:
In the xy plane, you can graph the parabola that we started with. The x-coordinates come from the DOMAIN, and the Y-coordinates come from the RANGE.

You can still graph a function like g(x,y) (=z). The x AND y coordinates come from the domain, while the z-coordinate comes from the RANGE.

With more than 2 independent variables, it's actually IMPOSSIBLE to graph the domain and range. There are these things called level curves and slope fields and all sorts of fancy-pants stuff, but we can cross that bridge when we get to it.

As for your other questions:
Vectors can have one, two, or MORE dimensions. The matrix component of many multivariable courses is minimal. You could spend a half hour learning about the dimensions of matrices, matrix multiplication, and determinants, and that might get you through.

 

[thushanthan]

Thank you. In my Linear Algebra course, I learned about matrices, determinants and vectors, but only the

basics. Not connected with Calculus.

 

[g_edgar]

Sometimes in calculus (areas, volumes) you will need to use similar triangles and such things from geometry.

 

[The Chaz]

Sometimes in calculus (areas, volumes) you will need to use similar triangles and such things from geometry.

Definitely. You'll see "geometry" show up in some rather contrived ways, but the best relationship between calculus and geometry is seeing where the geometry formulas come from! WHY is the volume of a sphere 4/3piRsquared (too lazy...)? Well, once you learn spherical coordinates, triple integrals, and the Jacobian determinant, ALL of this knowledge will be YOURS!

But seriously, you get to see some pretty cool stuff. What's more important will be algebra - solving equations, polynomial long division, etc.