Course detail

LCE5701 - Differential and Integral Calculus, Matrices and Notions of Probability

Credit hours

In-class work
per week
per week
3 weeks
75 hours

Cesar Goncalves de Lima
Idemauro Antonio Rodrigues de Lara
Renata Alcarde Sermarini

To review the basic knowledge of Differential and Integral Calculus, probabilities and matrices algebra.

Function of a real variable. Limits, continuity, derived, maximum and minimum. Undefined integration and defined. Integration techniques. Undetermined and integrals unfit. Functions of several variables. Limits, continuity, partial derived, derived signals. Extremes of functions of several variables. The Lagrange multipliers. Series of Maclaurin and Taylor. Multiple integrals. Sample space. Events: algebra and sigma-algebra. Definition of probabilities: frequentista and axiomatic definition. Theorems basic. Elements of Combinatories. Conditional probability and Stochastic Independence. Random variables: distribution functions, random vectors, independence of random variables. Distributions of Discrete random variables. Distribuitions of Continuous random variables. Mathematical Expectation: Definition and properties. Variance, Covariance and correlation coefficient. Moments. Distributions and Conditional Expectation. Matrices: Definition, repeated rescues basic. Systems of linear equations. Determinant and inverse matrix. Determination of the rank. Spectral decomposition. The vectorial space: dependence and independence, basis.

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