Number series: Definitions, geoemtric series and armonic ones; convergence tests for positive series: comparison test, root test, ratio test, limit comparison. Absolute convergence test and Leibniz test.
Power series: Total convergence, properties of the limit function, power series and Taylor series, examples.
Differential calculus for functions of several variables: critical points, maximum and minimum points,
Hessian matrix, Taylor formula, Lagrange multipliers.
Ordinary Differential equations: Cauchy problem;
equations of first order, linear and with separable variables; linear equations of second order with constant coefficients.
Curves and integration on curves; parametric equations and cartesian ones; tangent vector, lenght of a curve.Examples.
Multiple integrals: basic definitions, integation on normal domains; use of polar cohordinates.
Exlusive Topics of the Course Matematical Analysis II:
Differential forms and vector fields: closed and exact differential forms. Work of a vector field; gradient vector fields.
differential geometry of surfaces: basic definitions, tangent plane; divergence theorem and Stokes theorem.
Examples.
Exlusive Topics of the Course Matematic II:
Probability theory: combinatoric: permutation, permutation with repetition, k-permutation of n elements, combinations (with and without repetition).
Axiomatic definition of probabiity.
Conditional probability, Bayes rule, total probability law.
Random variables: discrete and continuous, density of a probability distribution; expected value, average,
first and second momentum; the variance; central limit theorem.
Examples: Normal distribution, exponential distribution, Poisson distribution, binomial distribution, Gaussian distribution, Uniform distribution
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