Sequences of real numbers, Monotone sequence, Convergence, Absolute and conditional convergence, Infinite series, Convergence tests, Addition and multiplication of series. Power series, Radius of convergence, Taylor and Maclaurin series and their applications, Taylor polynomials and Taylor's formula, The binomial theorem and binomial series. Matrices and linear transformations, Matrix operations, Solutions of linear systems by matrices, Rank and inverse, eigenvalues and eigenvectors, canonical forms, Jordan form, generalized inverse of a matrix. Complex numbers and their properties, complex numbers as vectors, The complex plane, Complex algebra, Functions of a complex variable.