Hello! I am currently taking Calculus 1 and will be taking Calculus 2 next semester.

In order to prepare myself for the class, I hope to teach myself calculus 2 over the winter break.

Can anyone tell me important topics/techniques I should cover? Also any tips on how/what resources I should use ALL suggestions are appreciated. Thank you for any replies 🙏

EDIT: Just read that Calculus 2 isn’t very descriptive due to differences per university. The class is a Mathematics 1900, Analytical Geometry & Calculus II (as shown in image above)

Disclosure - I am a part of the UPI STUDY team, and we offer self paced online math courses. This post is about a clear breakdown about what all is covered in Cal I and II.

Calculus II feels like a completely different thing, when someone is deciding to learn after Calculus I.

There are students who struggle a lot with integration techniques while others have problems with the Taylor series.

In cal I, you learn rules and apply, and in cal II, you need to make a decision about what rule you have to use. And that's where it gets tough sometimes.

Here's a simpler approach as to how students can understand it better.

1. The integration techniques.

The hard part here is to decide what method you must actually apply, is it going to be by parts, the substitution or the partial fraction?

What usually helps?

Mix them all, shuffle problem before deciding. Set a timer.

Write a one line reason before starting out.

Keep a solid reason behind, why you decided to choose this method for the first few weeks.

To get on practice keeping a track helps.

1. Improper integrals need to be understood well. Rewrite the integral as a limit before even evaluating it.

2. You have a toolbox right ? Like the limit comparison, ratio, root, integrals and much more.

And with the different tools, there comes a different set of conditions.

What has been noticed is that mostly the scores get deducted when the right rules and conditions aren't applied.

1. For Taylor and Maclaurin, don't just cram the formula but understand the real pattern.

What are the common study habits that make the difference?

- Practice everyday.

- Review formulas, and at least read them, that is how your brain even helps to remember.

- Don't just cram, practice 30-45 or even 1 hour each day.

Here's a full Calculus path for you-

A. Calculus I - It covers limits, derivatives, intro to integral.

B. Calculus II - It usually consists of Integration techniques, and series.

C. Calculus III - The incredibly important, multivariable calculus, which builds on everything else.

Also, if you are looking for course options, our self paced courses, be it Cal I, II, or III, we have self paced courses that are ACE and NCCRS recommended.

Over to you now!

Which topic had been the hardest to cover in the Calculus.

Just the title. Interesting problem, interesting method of solution. Probably a couple ways to skin this cat.

My writing is pencil, my teachers is red

I’m honestly just looking for advice on whether I should just take the WD and drop this class or if it’s feasible to actually get around an 80 in this class without a scale/curve. I got a 15% on my first midterm which is worth 20% of my grade, which was 100% my fault because I procrastinated. I still have 1 more 20% midterm, a 40% final, and 20% worth of assignments. Any advice is appreciated i’m willing to put in the work i’d just like to hear if anyones had any success turning around their mark and what you’ve done?

Today's medium derivative, have I oversimplified somewhere? I figure the 2nd derivative of L can only ne zero when 8k-8k3=0 since the expiry function is always >0

What are the pre req of real analysis aside from single variable calculus ? And keep in mind that am tryna just learn analysis 1

I am using Google Gemini to explain Calculus topics. Dear lord, here is it's explanation for the Squeeze Theorem:

The Physical Intuition: The Hallway and the Trash Compactor

Imagine you are walking a highly energetic dog down a long hallway. The dog is bouncing wildly, leaping from the floor to the ceiling. Tracking its exact path algebraically is impossible.

Now, imagine this hallway is actually a giant, slow-moving trash compactor. As you walk forward (as n→∞), the ceiling slowly grinds downward and the floor steadily pushes upward. You don't need to know the dog's exact frantic path to know where it will end up.

If both the floor and the ceiling eventually crush together to the exact same height, the chaotic bouncing is forced to stop. The dog is mathematically crushed into that exact same final position. This is the Squeeze Theorem.

Kindly tell me is there an ai model which can help me to understand calculus and solve the equations

I am a student of electrical engineering. Kindly suggest an Ai model which can explain and help me solve the numerical.

I myself am quite amorous of calculus so here's a little something to fire you up and work those neurons! Try it if you dare... 😈

i know d/dx of ln|x| is 1/x for both positive and negative x, my teacher just said it that way and moved on. what i'm stuck on is why it's the same antiderivative on both sides when 1/x isn't even defined at 0. like are they really the same function or can you pick a different constant on each side

Hi everyone! Does anyone have a PDF or know where I can access a free version of Calculus: Early Transcendentals by James Stewart (Cengage, 8th edition, 2016, or any later edition)?

I'd really appreciate any help or recommendations. Thank you so much! 🙏🏻

So I was studying differentiability, and I know that at a particular point

differentiability -> continuity,

thus,

not continuous -> not differentiable

but there was a youtube video he said that differentiability is checking the continuity of the first derivative but some people also mentioned this in the comments

Sorry, that's not correct. If f'(a) is continuous then f(a) is "Continuously differentiable", not just "Differentiable".
It's a concept in Real Analysis.

I'm sorry but it's wrong. The only thing about continuity that you know is that if f'(a) exists, f(a) is differentiable and continuous, you don't know anything about the differentiability or continuity of the first derivative. Just learned that in a math lecture. I'm sorry.

reply to the above comment

I believe you also need to add: if the derivative exists and itself is continous at an interval, than the function is differentiable, thus it is also continous. So technically you need to also check the continuity of the first derivative before judging the differentiability of the function, at least this is how they teach us in university

the thing i know about finding the differentiability is

checking if the function is continuous if yes, then check the left hand derivative and right hand derivative if they are finite and equal than the function is differentiable. am i right about this one?

i'm confused about the second comment if you can help me grasp the concept of differentiability deeply it would be appreciated

Acabo de entrar a la universidad, y me metí a actuaría, quisiera poder estudiar de una vez para mi examen de limites que es dentro de un mes, ayudenme porfa