The course aims to make students able to understand and assimilate the basic mathematical concepts such as sequences, matrices, determinants, complex numbers, derivatives, integrals.
Matrices and Determinants. Class table. Elementary transformations table. Matrix inversion. Linear systems. Characteristic equation table. Eigenvalues-eigenvectors. Similar matrices. Normal form of Jordan. Complex number. Equality of complex numbers. Operations set of complex numbers. Conjugate complex numbers. Measure complex number. Trigonometric, exponential and polar form complex number. Introduction to complex functions. Differentiation and integration of functions of one variable and applications. Definitions of functions, limits and continuity. Rules, differentiation and applications of graphs, limits, approximations and extrema of functions. Some vaguely integrals. Basic theorems. Integration techniques. Integration Applications in Engineering and electricity. Approaches definite integrals. Improper integrals: Definitions, Improper integrals of the first, the second type and mixed type, convergence criteria, convergence conditional. Depending on series. Series of real numbers: definitions, criteria of convergence, absolute convergence, conditional convergence. Alternating rows (positive and negative) terms, radius and interval of convergence. Differentiation and integration of power series. Taylor series and Mac-Laurin.