Mathematical Analysis MAT2201

Course content:
Complex functions. Derivatives.
Geometric properties of complex functions.
Ordinary differential equations of first order.
Theorems on existence and uniqueness of solutions.
Integrable equations of first order.
Equations of higher orders reducible to equations of first order. Linear equations of higher order.
Linear equations with constant coefficients.
Systems of linear differential equations. Fundamental matrix and its properties.
Systems of linear differential equations with constant coefficients.
Nonhomogeneous systems of linear equations.
Laplace transform.
Applications of Laplace transform.
Partial differential equations of first order.
Equations of elliptic type.
Equations of parabolic and hiperbolic type.

Learning outcomes:
knowledge of elementary complex functions,
ability of solving differential equations,
ability of computing Laplace transforms,
knowledge of equations of mathematical physics.