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Last update: RNDr. František Mošna, Ph.D. (30.01.2023)
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Last update: RNDr. František Mošna, Ph.D. (30.01.2023)
The primary goal of the course is to acquaint students with the basic concepts, knowledge and connections of an infinitesimal number of functions of two variables, following similar courses on functions of one variable. The secondary goal is to check, repeat and consolidate knowledge from previous courses, especially from mathematical analysis, but also geometry (curves, surfaces) or algebra (vector spaces, linear, quadratic forms). |
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Last update: RNDr. František Mošna, Ph.D. (31.01.2023)
school teaching - a total of 14 h preparation for school teaching - a total of 20 h reading mathematical literature 36 h homework - 10 h expected total time load of students - 80 h |
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Last update: RNDr. František Mošna, Ph.D. (30.01.2023)
basic: ● František Mošna: Inženýrská matematika (ČZU Praha) ● Zuzana Došlá, Ondřej Došlý: Diferenciální počet více proměnných (přírodovědecká fakulta MU Brno) ● Josef Kalas, Jaromír Kuben: Integrální počet funkcí více proměnných (přírodovědecká fakulta MU Brno) ● Serge Lang: Calculus of Several Variables, Springer N. York 1987 others: ● Walter Rudin: Principles of Mathematical Analysis,McGraw-Hill 1976 |
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Last update: RNDr. František Mošna, Ph.D. (13.02.2023)
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Last update: RNDr. František Mošna, Ph.D. (30.01.2023)
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. |