Best way to study C:E&M

About to finish self-studying Multivariable Calculus and I want to add C:E&M to my list. My deadline is early August, so I've got a month. Recommend textbooks and/or content creators.

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u/WillingnessTasty9628 — 11 days ago

Calculus 3 Progress Update

About a month ago, I asked if it'd be possible to finish Calculus 3 over the summer. Well, fast-forward to 6/24/2026, and I'm officially one Professor Leonard video away (+practice problems) from finishing.

In case anyone has similar plans, I had a rough experience at the start, as I found myself losing motivation from the absurdities of torsion and curvature. Entire pages of work for one problem was less than enthralling. But I pushed through, and starting from partial differentials, my excitement for the class has grown exponentially. The vector field calculations for the last unit have been particularly interesting as a highschool student intending to study physics.

I know there are comparisons between Calculus 2 and Calculus 3. Which one is more challenging? It's hard to say, especially since I took BC Calculus rather than a standard college course (still taught myself trigonometric substition, telescoping sums, etc). In my experience, the difficulty doesn't shift much. The formulas in Calculus 3 are much more complex, but the applications for them are sensible and you gather intuition quickly. It seems to me that Calculus 2 tests your depth of knowledge and ability to implement it, while Calculus 3 tests your comprehension of deeper concepts.

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u/WillingnessTasty9628 — 11 days ago

How to smurf AP Calculus BC

  1. Use double integrals for all polar area.
  2. Don't use the disk method. Instead, find a multivariable function for your solid of revolution and use a double integral. Note that y^2+z^2 is f(x)^2.
  3. For implicit derivatives, move the variables to the same side and use -Fx/Fy (partial of x over partial of y).
  4. Optimization? Find the gradient of a function and its constraint to solve for the legrange multiplier.
  5. Make sure all of your chain rule notation is expressed as a partial differential.
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u/WillingnessTasty9628 — 13 days ago

[ algebra 2 ] finding the radius of an inscribed semicircle

I solved it through an algebraic approach and obtained 10/3, but I'm not sure if it's correct.

First, I noticed that for any semicircle at a point y, theres only one x that would make it intersect exactly once with the line. So, since y is zero in this case, I set up the following equations

For the semicircle:
(x-(12-r))^2+(y)^2 = r^2
y = sqrt(r^2-(x-(12-r))^2

For the line:
y = 5/12x

When you set them equal, you get a quadratic equation. For there to be one solution, the discriminant must be zero, and you get an equation in terms of just r. Solving for r like this gets 10/3.

u/WillingnessTasty9628 — 2 months ago

who had these frqs

frq 1 had something about tons of wood being processed

frq 2 was polar and asked if there'd be a vertical tangent at point B

i forgot the others ones but there was arctan to infinity and stuff

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u/WillingnessTasty9628 — 2 months ago

I have two concerns with this post.

The first being an estimated time for self-studying Calc 3. Given that it took me a month to intake all of the units for Calc BC and have a solid understanding of them, how long would it take me to self-study Calc 3? I'll be able to dedicate my summer to it, so we're assuming multiple hours a day. And this isn't necessarily to master it, but to have a solid grasp of everything (I want to be able to study Physics 2 as well).

Second, what's the best resource for self-studying Calc 3? Cost isn't an issue, so I'd prefer anything that would present me with enough practice problems to cover the nuance of the subject. Khan Academy and Stewart are my only sources as of the moment.

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u/WillingnessTasty9628 — 2 months ago

I know that your school is notified if you score a flawless 108/108 on BC. Will you be recognized for AB if your overall score is less than 108, but your subscore is a perfect 54/54?

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u/WillingnessTasty9628 — 2 months ago