Syllabus
Introductory part
• repetition - linear vector spaces, scalar, vector and external product (geometric meaning, determinants), lines - equations, parametrization according to distance, planes, functions
• convergence, neighborhood, distance of points (metric, norm - Euclidean, summation, maximum), points - interior, exterior, boundary, limit, isolated, sets - open, closed, bounded, convex, continuous, compact, area.
Differential calculus
• real function of two variables (R2->R), domain, contours, sections, limit (on a set, on a domain), continuity
• derivative in direction (Gâte's differential and derivative), partial derivative, total differential (Fréchet's derivative), mutual relations, gradient - geometric meaning
• derivatives of higher orders (interchangeability of mixed second derivatives), second differential, Taylor's theorem
• extrema - local, absolute, bound extremes (substitution method and Lagrange multipliers)
• search for tangent planes, tangents in direction, derivatives of implicitly specified functions
• coordinate transformation - polar, (cylindrical), spherical
Integral calculus
• multiple (double, triple) integral, calculation of content (circle), volume (sphere, cone), center of gravity (triangle, tetrahedron), moments, Fubini's theorem, substitution theorem - connection between determinant and volume, content
• curves in R2 (explicit, implicit, parametric expression), tangent, normal, length of curve (circle), divergence, (3rd component of rotation), curve integral, Green's theorem
• surfaces in R3, divergence, rotation, surface integral, Stokes, Gauss-Ostrogradsky theorem.
Annotation
Vector spaces, neighborhood of a point, convergence, functions of several variables, limits, continuity, derivative in direction, partial derivative, differential, tangent planes, normals, implicit function, curves, surfaces, coordinate transformation, multiple integral, substitution, Fubini's theorem, curvilinear and surface integral, use.