# Supplementary mathematics/Mathematics analysis

Analysis is a branch of mathematics . Analysis has existed as an independent branch of mathematics since Leonhard Euler (18th century). Since then it has been the mathematics of natural and engineering sciences .

Its basics were developed independently in the 17th century by Gottfried Wilhelm Leibniz and Isaac Newton as infinitesimal calculus . Calculus is the mathematical study of continuous change, just as geometry is the study of form and algebra is the study of the generalization of arithmetic operations.

Central concepts of analysis are those of the limit value , the sequence , the series and, in particular, the concept of the function . The investigation of real and complex functions with regard to continuity , differentiability and integrability is one of the main subjects of analysis. The two bodies are fundamental to the entire analysis (the field of real numbers ) and(the field of complex numbers ) together with their geometric, arithmetic , algebraic and topological properties.