2 HYPERBOLIC FUNCTIONS

... This chapter will introduce you to the hyperbolic functions which you may have noticed on your calculator with the abbreviation hyp. You will see some connections with trigonometric functions and will be able to find various integrals which cannot be found without the help of hyperbolic functions. T ...

... This chapter will introduce you to the hyperbolic functions which you may have noticed on your calculator with the abbreviation hyp. You will see some connections with trigonometric functions and will be able to find various integrals which cannot be found without the help of hyperbolic functions. T ...

ON THE DISTRIBUTION OF EXTREME VALUES

... Theorem 1.5 does not hold in the range k ≥ c(log T log2 T )σ for any c > 12 (B(σ))σ . Concerning other families of L-functions, P.D.T.A Elliott [4] has established the analogue of Bohr and Jessen’s result for the family of quadratic Dirichlet L-functions, at a fixed point s, with 1/2 < Re(s) ≤ 1. Fu ...

... Theorem 1.5 does not hold in the range k ≥ c(log T log2 T )σ for any c > 12 (B(σ))σ . Concerning other families of L-functions, P.D.T.A Elliott [4] has established the analogue of Bohr and Jessen’s result for the family of quadratic Dirichlet L-functions, at a fixed point s, with 1/2 < Re(s) ≤ 1. Fu ...

Elementary Number Theory - science.uu.nl project csg

... Peano-axioms for the natural numbers, deﬁne addition, multiplication and ordering on them and then deduce their elementary properties such as the commutative, associatative and distributive properties. However, because most students are very familiar with the usual rules of manipulation of integers, ...

... Peano-axioms for the natural numbers, deﬁne addition, multiplication and ordering on them and then deduce their elementary properties such as the commutative, associatative and distributive properties. However, because most students are very familiar with the usual rules of manipulation of integers, ...

Mathematical Reasoning: Writing and Proof

... Students are introduced to a method to organize their thought processes when attempting to construct a proof that uses a so-called know-show table. (See Section 1.2 and Section 3.1.) Students use this table to work backward from what it is they are trying to prove while at the same time working forw ...

... Students are introduced to a method to organize their thought processes when attempting to construct a proof that uses a so-called know-show table. (See Section 1.2 and Section 3.1.) Students use this table to work backward from what it is they are trying to prove while at the same time working forw ...

Microlocal Methods in Tensor Tomography

... If (M, g ) is simple, lens rigidity is equivalent to boundary rigidity. For general manifolds, the lens rigidity is the right question to study. It turns out that linearizing any of those two problems, we arrive at the problem of inverting If modulo potential tensors. Potential tensors linearize the ...

... If (M, g ) is simple, lens rigidity is equivalent to boundary rigidity. For general manifolds, the lens rigidity is the right question to study. It turns out that linearizing any of those two problems, we arrive at the problem of inverting If modulo potential tensors. Potential tensors linearize the ...

# 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.