Program of lectures
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- Vector calculus, scalar, cross and triple product, vector functions.
- 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.
- 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.
- Introduction to the field theory: gradient, potential, divergence rotation, Gauss-Ostrogradsky's and Stoke's theorem.
-------------------
- Vector calculus, scalar, cross and triple product, vector functions.
- 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.
- 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.
- Introduction to the field theory: gradient, potential, divergence rotation, Gauss-Ostrogradsky's and Stoke's theorem.