During the seminar, mathematical problems will be solved that are directly related to the content of the XAMAT (Mathematics) course. 1. Basics of vector calculus in three-dimensional Euclidean space (3D coordinate system, distance of points in 3D, vectors basic concepts, linear dependence and complanarity of vectors, linear combination of vectors, basis of vector space, scalar, vector and mixed product of vectors) 2. Sequence and its limit (sequence, limit of sequence, computation of limit of sequences, monotonicity of sequences, convergence and sum of geometric series) 3. Function and its limit (function, function defined in parts, continuity and limit of function, one-sided limits, rules for calculating limits, calculations of type limits of functions) 4. Differential calculus of functions of one real variable (definition of derivative, theorems on derivatives of power, goniometric, logarithmic, exponential and cyclometric functions, derivatives of composite functions, differential of a function, L'Hospital's rule for calculating limits of functions, tangents and normals) 5. Function progression (monotony of a function, stationary points of a function, local and absolute extremes of a function, inflection points of a function, convexity and concavity of a function, asymptotes of the graph of a function, optimization problems) 6. Indefinite integral of functions of one real variable (primitive functions and indefinite integral, methods of integration - direct, substitution and per partes) 7. The definite integral and its applications (methods of calculating definite integrals, calculating the area under the graph of a function) 8. First order differential equations (initial problem, separation of variables method, growth and decay models, logistic model) 9. Differential and integral calculus Translated with DeepL.com (free version)
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