Calculus question?

Question

The chain rule and inverse chain rule, Integration by substitution, antiderivatives. I can't see a real life problem that you would have to use all this stuff to figure out. Textbooks are good at giving a bunch of numbers for you figure ou, but in real life would we need to do those procedures for? Does anyone have a real life engineering problem or what ever that you needed to do that?

Answer 1

You bet!
I had these questions posed to me and have asked them myself.
And there are basically two ways of looking at it:
1.If do not care then stop and forget about it.
2.If want to know why thing work the way they do you need these methods. An idiot can use equations derived by someone else. And there are no truly universal equations almost all of them require some custom work.

The applications are numerous; electrical, mechanical, chemical and civil engineering, theoretical physics, aerodynamics…I can go on but you got the point.

Calc I and II is just the foundation and Calc III sprinkles a little flavor. The real stuff is differential equation and later application of difference equations, finite element methods to real world problems using a computer.

But why go that far. The most classical problem is optimization of surface area and volume enclosed by that area. This is by the way is Calc I (min-max). Maximize area and minimize perimeter. http://www.analyzemath.com/calculus/Problems/optimize_area.html

Also look at the entire math curriculum you will study as exercises to develop both general math knowledge and training of your brain to handle and understand different methods. Frequently many branches come together to solve one real world problem.

Answer 2

Yes. Without getting into detail I had a problem involving a complex double integral last week (it involved electrochemical plating). To solve it I had to use several methods including integration by parts and trigonometric substitution. However, there are easier ways to determine DEFINATE integrals than by actually solving them. Finite difference approximations work very well, and can be done quickly in Excel or other spreadsheets. Calculus comes up a lot more than one would imagine.

Answer 3

I used advanced calculus the other day at work. The problem was to derive a confidence interval which can be used for hypothesis testing. Say you have a folded normal distribution and want to derive the CI. A part of the CI is the variance. To derive the variance one needs to Compute E(X^2) and E(X) of the function. To derive the variance one needs to solve the integral \int f(X) * x^2 dx.

Answer 4

Good question - I've got a degree in maths and occassionally calculus comes up in my actuarial exams and are quite good for helping me figure out how statistical distributions work that I use, but even then its still quite abstract.

In real life I don't see any use unless you're going into an academic career in mathematics or statistics or something along those lines.

Answer 5

Physical chemistry uses this type of calculus to find solutions to wave functions which describe the movement of electrons in atoms and molecules. This information is then used to develop all sorts of things like new materials, new drugs, and anthing else you can think of that uses chemistry.

Engineers also use these same type of equations to determine the resonant frequencies of bridges and buildings so they can build them so they don't have dangerous resonant frequencies. Without them you get cases where bridges can literally tear themselves apart due to resonance in high winds.

These are just a couple cases I am familiar with. I am sure there are others.

Answer 6

The chain rule alone comes up in partial differential equations all the time. In fact, it would be almost impossible to work with p.d.e.s without it.

duluth06che:
It's Definite and not Definate.

Answer 7

Don't be an electrical engineer then. Physics, circuit analysis, signals and systems analysis, and electromagnetics rely heavily on calculus, escpecially calculus of several variables and vector calculus. You also use it in other classes you wouldn't think you would like probabilistics.

Answer 8

Try looking through the list at http://www.calculus.net/ci2/search/?request=category&code=853&off=0&tag=9200438920658 or google/ search on yahoo for "calculus application engineering"

Answer 9

Sorry, I can't help you. I am only in Pre-Calculus. Check out http://www.algebra.com/ They offer free online tutoring on all different math subjects, including calculus.

Answer 10

forget this- hurry up and answer the marble question
and in now gonna be 5 points from level 2