Did anyone else feel this way when taking Calculus?

[Mangoes]

I'm now finishing up a semester of Calc 1 and I've got some doubts.

There were a lot of parts I liked about the class; I really enjoyed learning the logic behind differentiation and integration and I liked the applications I saw in class which you could do with differentiation (haven't quite gotten to applications of integration) but aside from that, a lot of the class has seemed like trigonometric manipulation and algebraic trickery more than anything.

I'm now learning about different methods of solving indefinite integrals and I just can't help but find it boring. From what I've seen, it's just learning the basic integration formulas and then just manipulating what you have to fit them. It feels like I'm being taught how to be a calculator more than anything.

Am I wrong in feeling this way? Did anyone else feel this way?
I realize I have a very limited scope of calculus, I just find the algebra in it so mind-numbing and I'm afraid that I just have more algebra to look forward to. To clarify, I haven't found the class particularly hard or anything, I'm just worried about how Calculus 2 and 3 will be like and if it'll be like Calc 1 where about 70% of the problems I've done are more or less mundane algebraic manipulation.

 

[Number Nine]

Calculus II (integral calculus) consists almost entirely of extremely tedious and difficult algebraic manipulation, which is, unfortunately, necessary in order to do integration. Calculus III (multivariable and vector calculus) is much better as far as the algebra goes, and is considerably more theoretical. You might try taking an introductory course in real analysis in the meantime, just to tide you over.

 

[DrewD]

It can be tedious, but math and the other sciences often are. The goal is to learn to like the tedious part because the pay off is worth it. If you are doing improper integrals you might do some side reading on Fourier Transform, Laplace Transforms, and the Gamma function. These all use the idea of improper integrals, but might be more challenging. You'll still have to do a lot of algebra though.

What's your major? Math, Physics, Engineering, Chem...? Depending on where you're going you might do some side reading in different topics.

 

[Robert1986]

I'm now finishing up a semester of Calc 1 and I've got some doubts.

There were a lot of parts I liked about the class; I really enjoyed learning the logic behind differentiation and integration and I liked the applications I saw in class which you could do with differentiation (haven't quite gotten to applications of integration) but aside from that, a lot of the class has seemed like trigonometric manipulation and algebraic trickery more than anything.

I'm now learning about different methods of solving indefinite integrals and I just can't help but find it boring. From what I've seen, it's just learning the basic integration formulas and then just manipulating what you have to fit them. It feels like I'm being taught how to be a calculator more than anything.

Am I wrong in feeling this way? Did anyone else feel this way?
I realize I have a very limited scope of calculus, I just find the algebra in it so mind-numbing and I'm afraid that I just have more algebra to look forward to. To clarify, I haven't found the class particularly hard or anything, I'm just worried about how Calculus 2 and 3 will be like and if it'll be like Calc 1 where about 70% of the problems I've done are more or less mundane algebraic manipulation.

Well, the problem is that most calculus classes aren't that good. You have mech. engineering people, ChemE people, biomedical engineering people, physics people, chem people, bio people, econ. people, math people, and this list goes on, who are all taking calculus because someone thinks they "need to know it". So, for some reason, in calculus classes, there is a HUGE emphasis on where you can use it. This is unlike every other class (that I have taken.) In Physics classes, 99% of the material is Physics with about 1% applications (and that is usually just incidental.) Same for the other classes. It is up to the engineers to teach other engineers the engineering stuff.


So, given finite resources, the theory takes a back seat sometimes to applications. (This isn't all that bad. It is good to know some applications for whatever career you might have.) In Calc II, you'll get to do series, which are very important in analysis, so you might have some fun there. And, you could probably work through something like Spivak now (though, it might be easier if you wait til after calc II.)

 

[Windowmaker]

Calculus is basically a few "simple" concepts that are applied to stuff you already should know, such as the trigonometric identities and algebra manipulation. I've tutored calc 1/2 for a year and realized most people have problems with trig and algebra. Things like the product rule, quotient rule, power rule and basic u-sub isn't that complicated but when you don't know algebra well, it can be very difficult. I'd brush up on trig and algebra before taking calc 2 because there's 10 times more trig in calc 2 than calc 2.

 

[micromass]

If you want a break from algebraic manipulations and want a real challenge, then pick up Spivaks Calculus. This is far more rigorous (but also harder) than the normal calculus texts. It is also a much more beautiful text. If you don't like computations, but instead are a fan of theory and the logic behind the subjects, then Spivak is the book for you!