| Introduction to Ordinary differential equations (ODEs). Mathematical models based on ODEs.
| ODEs of order one in the explicit form: separable ODEs, homogeneous ODEs, linear ODEs, Bernoulli’s ODEs, Riccati’s ODEs.
| ODEs of order one in the implicit form: Clairaut’s ODEs, Lagrange’s ODEs.
| Linear ODEs of higher order with constant coefficients: homogeneous, non-homogeneous; the method of variation of constants.
| Positive and linear functionals. The Riemann-Stieltjes integral. Primitives.
| Improper integrals.
| Integrals depending on parameters.
| Special functions.
| Paths. The line integral with respect to the length. The line integral with respect to the coordinates. Differential forms. Exact differential forms. Path-independence of line integrals. Geometric and physical applications of line integrals.
| The double integral. The Green-Riemann Formula.
| The surface integral with respect to the area. The surface integral with respect to the coordinates. The Stokes Theorem. Geometric and physical applications of surface integrals.
| The triple integral. The Gauss-Ostrogradsky Theorem.
