Differential calculus of functions of many variables (Implicit functions, extrema of functions). Integral calculus (double, triple, line, surface integrals). The theorems of Green, Gauss and Stokes. Applications to geometry and physics.
- Teacher: Ιωάννης Γάσπαρης
ECTS : 5
Language : el
Learning Outcomes : Upon successful completion of the course, the student will be able to: • have understood the concepts of partial derivative and directional derivative. • be able to calculate partial derivatives of functions in implicit form. • be able to use the main differential operators. • be able to apply Differential Calculus methods to optimization problems. • have understood the concepts of double, triple, line, surface integral. • have understood the basic theorems of Vector Analysis. • be able to calculate the double/triple integral with appropriate selection of successive simple integrals. • be able to calculate the line integral of a vector field either directly, or by reducing it to a double integral via Green s theorem. • be able to calculate the surface integral either directly, or by reducing it to a triple integral via Gauss s theorem, or by reducing it to a line integral via Stokes theorem. • be able to correlate the above types of integrals with concepts of Physics. • be able to apply the above types of integrals to calculate values of physical quantities such as mass, moment of inertia, charge distribution, vector field flux. • understand the flexibility offered by the choice of the order of integration of variables and apply it to calculations of volumes of solids and areas of surfaces which are extremely difficult, if not impossible, through the traditional methods of Euclidean Geometry.