Mathematical analysis is the branch of mathematics that studies functions, spaces, and operators through quantitative methods of approximation and convergence. It grew out of calculus, especially the use of derivatives and integrals to study variable quantities, and in the 19th century its foundations were reformulated with greater rigor. Basic objects of study in mathematical analysis include the real numbers, functions, sequences, series, and limits. Analysis has remained closely connected with applications in the sciences, where it is used to study equations, approximate one object by another, and estimate the accuracy of such approximations.