Analysis is the part of mathematics which uses operations involving infinity, such as limits, convergent infinite series, differentiation and integration. Much of analysis involves functions and function spaces and the study of solutions of many kinds of equations involving functions.
Traditionally, the modelling of real word phenomena uses analysis. Although nowadays many other parts of mathematics also contribute to modelling, the interaction between analysis and applications remains very strong, and continuously feeds the field of analysis with fresh ideas. Many new branches of analysis have started by combining analysis with some other part of mathematics. See for instance geometric analysis and dynamical systems, algebraic analysis and q-analysis, stochastic analysis and numerical analysis driven by the need for efficient computer algorithms.
At KdVI we specialise in complex analysis within pure analysis, and dynamical systems and numerical analysis within applied analysis.