Course detail

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


Credit hours

In-class work
per week
Practice
per week
Credits
Duration
Total
15
5
5
3 weeks
75 hours

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

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

Content
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.

Bibliography
Anton, H. Cálculo: um novo horizonte. 6ª ed. Porto Alegre. Bookman. 2000. 1V.
Courant, Richard. Cálculo Diferencial e Integral. Porto: Lopes da Silva, 1982. 2V.
Dantas, C.B. Probabilidade: Um Curso Introdutório. Edusp - Editora da Universidade de São Paulo, São Paulo, 1997.
Figueiredo, V., Wetzler, H. G. Álgebra Linear. 3 ed. São Paulo: Harbra, 1984. 411p.
Heck, André. Introduction to MAPLE: Springer-Verlag. New York. 1993. 497p.
Hoffman, K. Álgebra Linear. 2.ed. Rio de Janeiro: Livros Técnicos e Científicos. 1979. 514p.
Holmes, M. H.; Ecker, J. G.; Boyce, W. E. Exploring Calculus with MAPLE: Addison-Wesley. 1993. 258p.
James, B.R. Probabilidade: Um curso em Nível Intermediário. Livros Técnicos e Científicos Editora S.A, Rio de Janeiro, 2009.
Johnson, R. Elementary Linear Álgebra. Boston: Prendle, Weber & Schmidt, 1971. 291 p.
Leithold, L. O Cálculo: com Geometria Analítica. 2 ed. São Paulo: Harbra, 1994. 2V
Meyer, P.L. Probabilidade: Aplicações à Estatística. 2ª ed. Livros Técnicos e Científicos Editora S.A Rio de Janeiro, 1983.
Mood. A M.; Graybill, F.A. e Boes, D.C. Introduction to the Theory of Statistics. 3ª ed. McGraw Hill Book Company, 1987.
Piskounov, N. S. Cálculo Diferencial e Integral. Porto: Lopes da Silva, 1982. 2v. Ross, S.A First Course in Probability. 6ª ed. Prentice Hall Inc. Londres, 2002.
Ross, Sheldon. Introduction to the Probability Models. 11th ed. London, 2014.
Ross, Sheldon. A first Course in Probability. 9th. ed. London, 2010.
Simmons, G. F. Cálculo com Geometria Analítica. São Paulo. McGraw-Hill. 1987.2V.
Swokowski, E. W. Cálculo com Geometria Analítica. 2 ed. São Paulo. Makron Books.1983. 2V.
HOFFMANN, L.D. Cálculo: Um curso moderno e suas aplicações. 10ª ed. Rio de Janeiro. LTC. 2012.
HUGHES-HALLETT, D.; GLEASON, A.M.; McCALLUM, W.G., et al. Cálculo. 5ª ed. Rio de Janeiro. LTC. 2011. 1v.
SIMMONS, G.F. Cálculo com geometria analítica. São Paulo: Pearson Makron Books, 2010. 2V.
Searle, S. R. (1982). Matrix Algebra Useful for Statistics. New York: Wiley.
Rencher, A.C.; Schaalje, G.B. Linear Models in Statistics. 2nd ed. New York: John Wiley & Sons (2008).
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