This paper is a reprint of the original work by A. P. Calderón published by the Brazilian Mathematical Society (SBM) in 1980. The original paper had no abstract, so this reprint is published without one. The paper discusses an inverse boundary value problem, where the goal is to determine the conductivity function γ of a domain D based on boundary measurements. The problem is formulated using the differential operator L_γ(w) = ∇·(γ∇w) and the quadratic form Q_γ(φ). The paper shows that the linearized problem has an affirmative answer, meaning that the derivative of the mapping Φ: γ → Q_γ is injective. However, the original mapping Φ is not necessarily injective. The paper also provides a method to approximate γ when it is close to a constant. The method involves using Fourier transforms and convolution to estimate γ from the measured data. The paper concludes that if γ is sufficiently close to a constant, it can be approximately determined from the measurements with an error much smaller than the L^∞ norm of the difference between γ and the constant. The paper also references other works on similar inverse problems.This paper is a reprint of the original work by A. P. Calderón published by the Brazilian Mathematical Society (SBM) in 1980. The original paper had no abstract, so this reprint is published without one. The paper discusses an inverse boundary value problem, where the goal is to determine the conductivity function γ of a domain D based on boundary measurements. The problem is formulated using the differential operator L_γ(w) = ∇·(γ∇w) and the quadratic form Q_γ(φ). The paper shows that the linearized problem has an affirmative answer, meaning that the derivative of the mapping Φ: γ → Q_γ is injective. However, the original mapping Φ is not necessarily injective. The paper also provides a method to approximate γ when it is close to a constant. The method involves using Fourier transforms and convolution to estimate γ from the measured data. The paper concludes that if γ is sufficiently close to a constant, it can be approximately determined from the measurements with an error much smaller than the L^∞ norm of the difference between γ and the constant. The paper also references other works on similar inverse problems.