Contents
What is the purpose of integration and differentiation?
Differentiation is used to break down the function into parts, and integration is used to unite those parts to form the original function. Geometrically the differentiation and integration formula is used to find the slope of a curve, and the area of the curve respectively.
What is the relationship between differentiation and integration?
Differentiation is used to calculate the gradient of a curve. It is used to find out the instant rates of change from one point to another. Integration is used to calculate the area under or between the curves.
How can integration be seen as the reverse of differentiation?
Integration can be seen as differentiation in reverse; that is we start with a given function f(x), and ask which functions, F(x), would have f(x) as their derivative.
Is there literature on reverse mode automatic differentiation?
There’s not that much literature on the topic out there and existing implementation (like the one in TensorFlow) are hard to understand without knowing the theory behind it. Thus I’d be very thankful if somebody could show in detail what we pass in, how we process it and what we take out of computational graph.
How to make the process of automatic differentiation automatic?
So far we have shown how the derivative can be calculated for a specific function like our example. To make the process fully automatic, we prescribe a set of rules for translating a program that evaluates an expression (like Program A) into a program that evaluates its derivatives (like Program B).
What do you call the reverse of differentiating?
This process, the reverse of differentiating, is called integrating; for it consists in finding the value of the whole quantity y when you are given only an expression for dy or for dy dx. Hitherto we have as much as possible kept dy and dx together as a differential coefficient: henceforth we shall more often have to separate them.