Differential calculus is used to find rates of change in the grade of a slope or a curve. Mathematicians typically use a combination of integral and differential calculus in solving their problems. Let's look at an example. Imagine that you need to push a box up a hill on a smooth, ...
I don't want to sound egotistical here, I don't think that I am beyond the knee of this curve and I don't know anyone who is. I do know some people that were. I think, for example, that anyone will agree that Isaac Newton would be well on the top of this curve. When you th...
Math Calculus Continuous functions What does a smooth embedding mean?Question:What does a smooth embedding mean?Functions in MathA function in mathematics is defined as the relation between two sets, these sets have corresponding values where every element or value for one of the set is ...
I think there is some ambiguity in the use of the word 'curve'. To me, a 'curve' in a manifold M is a smooth map γ:I→M (where I is some interval in R containg 0). You seem to be using 'curve' as the image of such a map, right? Feb 13, 2011 #8 HallsofIvy Scien...
So we need curvature, defined in Calculus, and is a function of position on the curve, which can be summarized as k(t)=|\gamma^{''}(t)|, where k(t) is the curvature of a plane curve \gamma. It also means the length of the acceleration vector, when \gamma is given a unit-...
If f and g are differentiable functions of one variable, prove that \int _{C}f(x)dx+g(y)dy = 0 for every piecewise-smooth simple closed curve C. Consider the following function: f(x)=\left\{\begin{matrix} x^2sin\frac...
Mathematically, the p-value is calculated using integral calculus from the area under the probability distribution curve for all values of statistics that are at least as far from the reference value as the observed value is, relative to the total area under the probability distribution curve. Sta...
Curve Analyzed using calculus. Understanding the curve's slope at different points required differential calculus. 4 Arc Something shaped like a curve or arch The vivid arc of a rainbow. Curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line...
Apart from the fact that it is convex, it has a symmetry center, and has a smooth boundary except for two points (there the surface is conical). The centric symmetry follows immediately from the fact that pic-tures /(r) = Imax/2 + af(r) (/ arbitrary) lead to observations that lie...
In calculus, we learn to integrate functions to find the area under a curve. 1 Incorporate To cause to form into a legal corporation Incorporate a business. Integrate Combine (one thing) with another to form a whole A fully equipped laboratory is being integrated into the development Transport...