Operators on normed spaces
... In this chapter we investigate continuous functions from one normed space to another. The class of all such functions is so large that any attempt to understand their properties will fail, so we will focus on those continuous functions that interact with the vector space structure in a meaningful wa ...
... In this chapter we investigate continuous functions from one normed space to another. The class of all such functions is so large that any attempt to understand their properties will fail, so we will focus on those continuous functions that interact with the vector space structure in a meaningful wa ...
Constructions with Compass and Straightedge
... then use the fact that 54 = 641 − 24 . If you follow these steps you should be able to write 232 + 1 as 641 × some number. Extensive computer calculations over the past 50 years have shown that F 5 through F32 are all composite. At this time no one knows whether F33 is prime or composite, but the ...
... then use the fact that 54 = 641 − 24 . If you follow these steps you should be able to write 232 + 1 as 641 × some number. Extensive computer calculations over the past 50 years have shown that F 5 through F32 are all composite. At this time no one knows whether F33 is prime or composite, but the ...
Approximate Fixed Point Theorems
... (iv) functional analysis, variational calculus, theory of integro—differential equations, etc. (Ref. 8). However, for many practical situations, the conditions in the fixed point theorems are too strong, so there is then no guarantee that a fixed point exists. On the other hand, often in such situati ...
... (iv) functional analysis, variational calculus, theory of integro—differential equations, etc. (Ref. 8). However, for many practical situations, the conditions in the fixed point theorems are too strong, so there is then no guarantee that a fixed point exists. On the other hand, often in such situati ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.