Applied Mathematics [ 6ΕΠ03 - Eighth Semester ]
Differential equations and introduction to complex analysis: Seperable differential equations. First order linear differential equations. Exact and non-exact equations. Integrating factor technique. Second order linear differential equations with constant coefficients. Method of variation of parameters. Method of undetermined coefficients. Euler equations. Systems of differential equations. Linear systems. Homogeneous / Nonhomogeneous linear systems. Euler’s method for systems. Complex numbers and complex functions. Analytic functions. The Cauchy-Riemann equations.
In this part of the course, students are introduced to multivariate data analysis and to the use of multivariate normal sampling theory. They learn how to treat multivariate data and how to estimate the mean vector, the variance-covariance matrix and the correlation matrix, as well as, how to create linear transformations of random variables and graphical representations of multidimensional data. Moreover, in this course students are taught to perform one- and two-sample tests in multivariate data sets, profile analysis, partial and multiple correlation and multivariate ANOVA, discriminant analysis, principal components, factor analysis, and cluster analysis. In this part of the course, students are introduced to the basics of stochastic processes. Specifically, after learning basic terms, students are introduced to simple Markov chains (discrete time); recurrence, transience, stationary distributions; Poisson processes (continuous time) and their simple simulations using examples from biology and genetics.