Pınar Ongan

The field of complex numbers, the extended complex plane and its topological properties, series of complex functions, M-test, power series, analytic functions, elementary functions and their mapping properties.

Vector calculus, functions of several variables, directional derivatives, gradient, vector-valued functions, divergence and curl, Taylor’s theorem, Lagrange multipliers, multiple integrals, change of variables, line integrals, Green’s theorem.

Vector spaces, linear transformations, rank and nullity, change of basis, canonical forms, Euclidien spaces, Gram-Schmidt orthogonalization method.

First-order differential equations, second-order linear equations, Wronskian, change of parameters, homogeneous and non-homogeneous equations, series solutions, Laplace transform, systems of first-order linear equations, boundary value problems, Fourier series.

Systems of linear equations, Gaussian elimination, matrix algebra determinants, inverse of a matrix, Cramer’s rule, rank and nullity, the eigenvalue problem, introduction to linear programming.

Introduction to basic problems, sums and recurrences, elementary number theory, properties of binomial coefficients, special numbers, discrete probability theory, generating functions.

Riemann integration, fundamental theorem of calculus, techniques and applications of integration, improper integrals, basic transcendental functions, infinite series, convergence tests, Taylor polynomials, power series.

Fundamental properties of real numbers, sequences and subsequences, Bolzano-Weierstrass theorem, limits of functions, continuity, intermediate and extreme value theorems, differentiation and its applications, mean value theorems.

Prepositional logic, quantification, methods of proof, sets, relations, functions, operations, equivalence relations, cardinality, introduction to algebraic structures.