43 citations · 51 across the 5 of their papers we have counts for
8 papers
The Exponential Matrix: an explicit formula by an elementary method
Oswaldo Rio Branco de Oliveira
We show an explicit formula, with a quite easy deduction, for the exponential matrix of a real square matrix of order . The elementary method developed requ…
The Implicit Function Theorem for maps that are only differentiable: an elementary proof
Oswaldo R. B. de Oliveira
This article shows a very elementary and straightforward proof of the Implicit Function Theorem for differentiable maps defined on a finite-dimensional Euclidean space. Th…
A Complex Primitive th Root Of Unity: A Very Elementary Approach
Oswaldo Rio Branco de Oliveira
This paper presents a primitive th root of unity in . The approach is very elementary and avoids the following: the complex exponential function, trigonometry, and gr…
The Implicit Function Theorem when the matrix is only continuous at the base point
Oswaldo R. B. de Oliveira
This article presents an elementary proof of the Implicit Function Theorem for differentiable maps F(x,y), defined on a finite-dimensional Euclidean space, with $\frac{\partial F}{…
The Implicit and the Inverse Function theorems: easy proofs
Oswaldo Rio Branco de Oliveira
This article presents simple and easy proofs of the Implicit Function Theorem and the Inverse Function Theorem, in this order, both of them on a finite-dimensional Euclidean space,…
An Alternative Method for the Undetermined Coefficients and the Annihilator Methods
Oswaldo Rio Branco de Oliveira
This paper exhibits a very simple formula for a particular solution of a linear ordinary differential equation with constant real coefficients, P(d/dt)x = f, f a function given by…