Introductory Mathematical Analysis for Quantitative Finance

Daniele Ritelli is associate professor of mathematical analysis at the Department of Statistical Sciences of the University of Bologna, in Italy. He teaches ordinary and partial differential equations and special functions in various three-year and magister degree courses in statistics and finance. His research interests concern special functions, ordinary differential equations and pure and applied mathematics. Giulia Spaletta is associate professor of numerical analysis at the Department of Statistical Sciences of the University of Bologna, in Italy. She lectures in various three-year and master degree courses in computer science, statistics and economics. Her research interests include numerical error analysis in linear algebra and differential equations and numerical modeling in biomedical engineering.

Euclidean space. Sequences and series of functions. Multidimensional differential calculus. Ordinary differential equations of first order: methods for explicit solutions. Linear differential equations of second order. Prologue to Measure theory. Lebesgue integral. Radon-Nikodym theorem. Multiple integrals. Gamma and Beta functions. Fourier ransform on the real line. Parabolic equations.