Is it possible to comprehend Calculus II-III with just graphical illustrations?

[Elite Engineer]

I took calculus I back in college, but never needed to take calc. II or III. I'm a little interested in learning II and III, just for general knowledge and boredom, but I don't

want to spend in-depth analysis with the actual math questions and such. Since I have general knowledge of calculus, is it possible to get a general idea of how

calc. II and III operates with just graphical examples?

 

 

~EE

[Bignose]

EE, almost surely not. What most typical books/courses consider calculus II could just as well be called 'integration techniques'. There really isn't much in the way of learning this via pictures. Calculus III extends I and II into multiple variables, and while there are some pictorial elements here, like a lot of other math, this is many, many times better to learn by doing than just seeing.

Edited March 8, 2017 by Bignose

[wtf]

I don't see why not. I could explain integration and infinite series in pictures. Integration's adding up little rectangles under a curve, and series are just little building blocks on top of the number line that add up to a finite number. In fact infinite series are actually just a special case of integration, that's the trick.

 

What are Calc II and III by the way, everyone has different defs. Are you including second year calc? Multivariable calc, DiffEq, and linear algebra?

 

All of the concepts are simple, it's the detail work that's hard and that provides real understanding. But I don't need to study relativity to imagine a bowling ball on a rubber sheet, and even though that's not gravity, it's an analogy that's close enough for the general public. You could definitely do calculus in stories and pictures. You wouldn't be ready to be an engineer, but you'd be a more educated layman. You'd know the difference between the deficit and the debt. It's the relationship between the derivative and the integral. The way the annual deficit accumulates into the national debt is the fundamental theorem of calculus. If people understood that they'd stop letting the government bs them about the federal budget.

Edited March 9, 2017 by wtf

[Bignose]

I could explain integration and infinite series in pictures.

Sure, the concept of integration as area under a curve is a picture, but show me a picture that explains trignometric integration? I'm not saying that there isn't one, I'm just rather curious if there is one... Typically, integration (as demonstrated by summing up lots of little rectangles) is done in Calc I. That's why I called Calc II integration techniques. Because it starts to detail different ways of getting that sum, not the concept of the sum itself.

 

And I'll be really impressed if you can draw me a picture explaining the divergence theorem in 4-D. (The divergence theorem being a very important topic covered in calc III).

 

I dont disagree that there are lots of possible pictures, but not pictures that explain some of the important topics in the classes. Some things are formulas and need to be worked with as such to get even a hint of what they are good for.