Spring 2024 - MATH E-23C - Integrability and Sum of Integrals using Darboux Sums - Jimmy Q. Tran
Published 2024-07-04
This proof demonstrates that the sum of two integrable functions f and g on the interval [a, b] is also integrable, and that the integral of the sum equals the sum of the integrals. Using Darboux sums, the proof shows that the sum of the upper sums and the sum of the lower sums of f and g are integrable, which leads to the conclusion that the integral of f + g from a to b equals the integral of f from a to b plus the integral of g from a to b. This is part of the Mathematics for Computation and Data Science course (MATH E-23c) in the Spring 2024 term at Harvard. The course covers discrete mathematics, real analysis, linear algebra, and integral calculus, with applications in computer science, probability, statistics, and data science, and includes an introduction to R programming.
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