How difficult is Calculus I?

[Ken g6]

Calc I is a weird mix of two concepts. The first concept, limits, are fairly easy to understand, but hard to work with. They are conceptually the basis of the rest of calculus, but you don't really need to know anything about them for the rest of Calc I. Or probably II for that matter. Unless they introduce L'hopital's rule, which is just a nice, simple application of the second concept to the first.

The second concept, derivatives, is the real basis of calculus. Things you need to understand:

• A graphed straight line has a slope. Rise over run. Easy so far. Slope is also known as "rate of change" when the X axis represents time.
• A graphed "smooth" curve of any sort has a slope at every point if you zoom in on it infinitely. (This is where limits conceptually come in.) This is also known as "instantaneous slope" or "slope of the tangent line". Jagged lines don't have slopes at their pointy bits; this will be a test question!
• A graphed curve represents a function. (You learned about those, right?) This function can be represented in algebraic form. (See also "curve fitting" if you don't believe me, but this won't be covered in Calc I.)
• Imagine finding the instantaneous slope at every point of a graphed function. (You don't have to do it; just think about it.) You can also imagine doing just a few points to approximate the goal, if I've given you too many infinities.
• Now imagine taking those slope numbers and plotting each slope number on a new graph. Plot each point at the same position on the X axis as on the original function, but on the Y axis at the slope number from the original function. You now have a new function that represents the slope of the original function at every point. This function is called the "derivative" of the original function.
• It so happens that there exist rules that will allow you to transform the algebraic form of the original function into the algebraic form of its derivative. Here they are. Memorize those, and when to apply them, and you'll be good to go. The rest is just practicing with them.

 

[Noo]

Is calc I difficult or possible without taking the prerequisite (pre-calc 1&2)?

E.G. taking intermediate accounting II without: managerial accounting, financial accounting, and intermediate accounting I is like impossible.

 

[Ken g6]

Did you understand the concepts I listed? Calc I without algebra is impossible. Whether pre-calc is necessary depends on what they taught you in algebra, I think.

 

[fstime]

Is calc I difficult or possible without taking the prerequisite (pre-calc 1&2)?

E.G. taking intermediate accounting II without: managerial accounting, financial accounting, and intermediate accounting I is like impossible.

Yes, you need to take advanced algebra/pre-calculus or things will be much more difficult.

 

[Brian Stirling]

That depends on how strong your algebra and trig is. Not how good you think you are at algebra and trig, but how good you really are. If there is even any doubt, then you should take a course or 2 of pre-calc aka algebra and trig.



You should probably ask the university that. I can't answer questions about their admission policy.

I'll add to what Disappoint said...


Yeah, if you were/are strong in Algebra then Calculus isn't, or shouldn't be, much of a problem. 90% of Calculus is being good at Algebra as you have to message equations to simplify before or after performing the actual Calculus. It's also useful to be good at word problems as you often have to construct equations that define a problem, perform Algebra on it, then Calc.

If I remember correctly, and it's been about 30 years, Calculus 101 or whatever first semester Calculus is called where you are, doesn't get into much of the Trig equations for Calculus though you may use Trig to setup an equation. I found it hard to memorize the Calculus Trig functions but still aced most my tests.

The long and short of it is if you were good at Math up through Algebra then Calc 1 should be no sweat...


Brian

 

[Chaotic42]

Get this book

Seriously, it's an excellent study guide and will help simplify some of the concepts. I recommend it to anyone who is taking Calculus. They have a second book covering Calculus 3 and 4 if you ever take those.

 

[DrPizza]

• It so happens that there exist rules that will allow you to transform the algebraic form of the original function into the algebraic form of its derivative. Here they are. Memorize those, and when to apply them, and you'll be good to go. The rest is just practicing with them.

It's not really necessary to memorize all of the rules; though it comes in handy when working backwards (anti-derivatives, aka, integrals) in calc II.

For example, if you need the derivative (with respect to x) of arcsin(g(x)), you can simply let y = arcsin (g(x)), then rewrite it as sin y = g(x), then cos y dy/dx = g'(x), dy/dx = g'(x)/cos y, and finally, by drawing a little sketch of a right triangle, since sin y = g(x), put y in for one of the acute angles, and the opposite side is g(x), the hypotenuse is 1, and the adjacent side can be found from the pythagorean theorem = sqrt (1- (g(x))^2 ) Thus, dy/dx = g'(x) / sqrt[1-(g(x))^2]. If students encounter problems of this type frequently enough, they wind up inadvertently memorizing the formulas anyways. If not, then I'd simply recommend memorizing the derivative of arctan, due to the integral of dx/(1+x^2). Then again, you can simply do a tricky trig substitution, allowing x to be equal to tan theta, the numerator becomes secant squared theta dtheta, the denominator after a trig identity is also secant squared theta, and you have the integral of dtheta, which is theta, which is arctan(x); 15 extra seconds if you don't want to memorize.

I think the teacher can also make a huge difference (or other resources). For example, you're going to have to know the quotient rule: denominator times the derivative of the numerator, minus the numerator times the derivative of the denominator, all over the denominator squared. But, it's easier to memorize this: ho d hi, minus hi di ho, all over ho ho. Hi, obviously, represents the high part (the numerator), and ho is the bottom part. The most common mistake is that people will start it as "hi d ho minus ho d hi" - but it's easy to remember which way it goes; just remember, always keep the hoes out. <points toward the sides, class chuckles, and no one ever misses the quotient rule>

 

[Apathetic]

Here's how you pass calculus:

1) Make sure you attend EVERY class.
2) Take good notes.
3) Keep up with your homework.
4) If you have questions about a homework problem, ASK about it.

If you do this, you'll have a decent chance of passing. If you don't, it will crush you.

Dave

 

[Pr0d1gy]

I didn't find it to be very difficult at all. I think if you have a strong base of algebra and geometry to build off of it is basically the logical next step. Think of it as advanced trigonometry. I would highly recommend you try to teach it to yourself for a bit before you go to your first class if you can. Having some base to work from when you take your classes can make a huge difference in a high level math class.

DrPizza made a valuable post, the first lesson of the first day in my Calc101 class was derivatives. You learn the equation and how to implement it to solve the problem. That is where you should start if you want to get ahead of the class.

Congratulations on working your way into a major university. You have the right attitude, and you will do well in life if you continue on the path you are on.

 

[edro]

I remember Calc 1 and 2 being hard, but I didn't do much studying outside of class and homework... also, I was 18yo.
I think it would be much easier now, especially if I supplemented my text book with online videos. I didn't do this in college. I just read the book, attended lectures and did home work.

I felt college was just about keeping your head above water and absorbing enough for the next test. I probably should have taken those difficult classes twice, but didn't care when I was that young.

 

[manly]

It's all relative. I originally skipped pre-calc, and Calculus I kicked my butt for a few weeks until I was relegated back to pre-calc.

Now if you're Korean or Chinese, it's probably a breeze at age 12.

 

[AznAnarchy99]

This might help you.

https://www.coursera.org/course/precalculus

 

[SithSolo1]

My math career started on a steady decline with Algebra II and ended with a train wreck at Calc I. Alg II scraped by, Alg III/Trig two tries, Pre-calc two tries, Calc I teacher said there was no shame in withdrawing after the first test results came back.

Kinda a bummer since I rather enjoy physics but without calc you're pretty much sunk.

 

[Brian Stirling]

When taking Calculus 201, or whatever the second semester was called, the professor stopped during lecture and started laughing for no obvious reason and it took him a couple minutes to pull himself together. What was it that set him off ... apparently someone, almost certainly a student, had scribbled on the window frame "help me" and he lost it. Math can be like that and Math majors/professors are probably the specialty closest to crossing the line into insanity. Many of them are savants...


Brian

 

[AznAnarchy99]

My math career started on a steady decline with Algebra II and ended with a train wreck at Calc I. Alg II scraped by, Alg III/Trig two tries, Pre-calc two tries, Calc I teacher said there was no shame in withdrawing after the first test results came back.

Kinda a bummer since I rather enjoy physics but without calc you're pretty much sunk.

Mine too except I quit at Calc I. Started sucking at Algebra II sophmore year of high school. Struggled with pre-calc in junior year. Took AP Calc AB senior year, did bad but somehow passed the AP test. Wanted to do comp sci/engineering so I had to take the base Calc class again. Bombed it even after going to tutoring and studying my ass off. Said screw it in the end.

 

[shortylickens]

Its not as difficult as a spoiled blonde American wife.

 

[Buckeye269]

I just finished calc 1 and 2 at my university. Calc 1 wasn't bad as I took it in high school, but make sure you understand everything fully. If you think you need help on a concept, look it up. Use the book's examples but most importantly, use the internet. Khan's academy is a huge life saver. Youtube is as well since some professors from other universities and high schools will post some of their lectures and examples. Calc 2 on the other hand was the hardest class I have taken thus far. It went from simple calc to mind blowing stuff I still don't understand. I agree with someone in this thread with their thought that you only need to know what will be on the next test. My class made exams worth more than 70% of my final grade. Finally, you don't need to to awesome, just better or equal to the class average. They can't fail the whole class.

 

[bononos]

Is calc I difficult or possible without taking the prerequisite (pre-calc 1&2)?

E.G. taking intermediate accounting II without: managerial accounting, financial accounting, and intermediate accounting I is like impossible.

You could catch on on pre-calc on your own if you still remember it. Get a pre-calc book and do the exercises to see where you are at.
Calc1 is like what Pizza said, its really the foothills of a mountain. If you are mediocre at calc1, subsequent calc courses will be too much. You're squeezing a hundred years of discovery by the brightest minds in human history in months.

 

[bononos]

Mine too except I quit at Calc I. Started sucking at Algebra II sophmore year of high school. Struggled with pre-calc in junior year. Took AP Calc AB senior year, did bad but somehow passed the AP test. Wanted to do comp sci/engineering so I had to take the base Calc class again. Bombed it even after going to tutoring and studying my ass off. Said screw it in the end.

An Asian bombing at calc? impossible.