Program of lectures
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1st Block: Vector calculus, scalar, cross and triple product, vector functions.
2nd Block: Differential calculus of functions of two or more real variables: domain, graph, limit and continuity. Partial derivatives, total differential, tangent plane and normal to a surface. Implicit function and its derivatives.
Extremes of functions, calculation via derivatives. Constrained extremes, Lagrange's method. Global extremes. Taylor's theorem.
3rd Block: Two-dimensional integrals on a rectangle and on a general domain. Calculations of two-dimensional integrals, applications in geometry and physics. Three-dimensional integrals, calculation and application. Line integral of the first and second kind, calculation methods. Applications of curved integrals, Green's theorem, independence of the integration path. Surface integrals and their calculation.
4th Block:- Introduction to the field theory: gradient, potential, divergence rotation, Gauss-Ostrogradsky's and Stoke's theorem.
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1st Block: Vector calculus, scalar, cross and triple product, vector functions.
2nd Block: Differential calculus of functions of two or more real variables: domain, graph, limit and continuity. Partial derivatives, total differential, tangent plane and normal to a surface. Implicit function and its derivatives.
Extremes of functions, calculation via derivatives. Constrained extremes, Lagrange's method. Global extremes. Taylor's theorem.
3rd Block: Two-dimensional integrals on a rectangle and on a general domain. Calculations of two-dimensional integrals, applications in geometry and physics. Three-dimensional integrals, calculation and application. Line integral of the first and second kind, calculation methods. Applications of curved integrals, Green's theorem, independence of the integration path. Surface integrals and their calculation.
4th Block:- Introduction to the field theory: gradient, potential, divergence rotation, Gauss-Ostrogradsky's and Stoke's theorem.