[Guille]

Originally Posted by AntonioLao Matrices is just a mathematical tool of arranging numbers suitable for doing transformations. It does not matter whether the numbers are real or complex. Matrices are used whenever certain transformations are the objects of finding various solutions. Complex analysis is just the applications of the calculus to complex numbers which I believed started by Cauchy.

I lack of calculus knowledge. I can deal with very little of it. When I read "Th road to reality" I believe I will understand calculus. Then I'll be able to start with complex analysis.

[AntonioLao]

Calculus deals only with two basic concept 1. derivatives and 2. antiderivatives.
The branch of calculus that deals with derivatives is called differential calculus. The other is integral calculus which deals with antiderivatives.

Derivatives are infinitesimal ratios or slopes of change of the dependent variables and the independent variables.

Antiderivatives are infinitesimal areas of the products between the dependent and independent variables.

Multivariate calculus deals with partial differentiations of partial derivatives and multiple integrals of antiderivatives which include volumes and multidimensional arc lengths, areas and volumes.

[Guille]

Originally Posted by AntonioLao Calculus deals only with two basic concept 1. derivatives and 2. antiderivatives. The branch of calculus that deals with derivatives is called differential calculus. The other is integral calculus which deals with antiderivatives. Derivatives are infinitesimal ratios or slopes of change of the dependent variables and the independent variables. Antiderivatives are infinitesimal areas of the products between the dependent and independent variables. Multivariate calculus deals with partial differentiations of partial derivatives and multiple integrals of antiderivatives which include volumes and multidimensional arc lengths, areas and volumes.

Up to what I know, all antiderivatives are integrals. Or are there antiderivatives which are not integrals?

[AntonioLao]

According to the fundamental theorem of calculus differentiation and integration are inverse operations of each other. http://en.wikipedia.org/wiki/Fundame...em_of_calculus

[Guille]

Originally Posted by AntonioLao According to the fundamental theorem of calculus differentiation and integration are inverse operations of each other. http://en.wikipedia.org/wiki/Fundame...em_of_calculus

Yes, I know.

But is there any kind of antiderivative which is not an integral?

[AntonioLao]

Originally Posted by GUILLE But is there any kind of antiderivative which is not an integral?

For every integral there is an antiderivative. But for multiple integrals there are multiple antiderivatives.

[Guille]

Originally Posted by AntonioLao For every integral there is an antiderivative. But for multiple integrals there are multiple antiderivatives.

Then, what is the actual difference between antiderivatives and integrals?

Aren't they exactly equal?

[AntonioLao]

Originally Posted by GUILLE what is the actual difference between antiderivatives and integrals?

antiderivative is a function. Integral is a sum.

[Guille]

Originally Posted by AntonioLao antiderivative is a function. Integral is a sum.

antiderivative is what kind of function? integral is what kind of sum?

Is there an equation with antidervative in a side, and integral in the other?

I think it would help to see what is the difference.

[AntonioLao]

Originally Posted by GUILLE Is there an equation with antidervative in a side, and integral in the other?

Given the antiderivative or probability distribution function F(t), and the probability density function f(t) then F(t)=∫f(t)dt, which says that F(t) is the integral of f(t) running along differential time dt.