Department of Mathematics

https://www.univ-soukahras.dz/en/dept/math

Lecturer	Abdelwaheb ARDJOUNI
Information	Bachelor - Socle Commun Mathématiques et mathématiques appliquées L2 Department of Mathematics Website : https://www.univ-soukahras.dz/en/module/1199 Semester : S3 Unit : UEF312 Credit : 7 Coefficient: 4
Content	Chapter 1: Numerical Series Real or complex series Algebraic structure of the set of convergent series Cauchy criterion Series with positive terms Comparison theorems Riemann series d\'Alembert\'s rule Cauchy\'s rule Cauchy-Maclaurin rule for the integral Bertrand series Series with terms of any sign Leibniz series Alternating series Rule for convergence of alternating series Rules for convergence of series with terms of any sign Dirichlet\'s rule Abel\'s rule Additional properties of convergent series Grouping of terms Product of series Chapter 2: Sequences and Series of Functions Sequences of functions Convergence Graphical interpretation of uniform convergence Cauchy criterion for uniform convergence Properties of uniformly convergent sequences of functions Series of functions Simple convergence Uniform convergence Properties of uniformly convergent series of functions Chapter 3: Entire Series Real entire series Cauchy-Hadamard rule d\'Alembert\'s rule Properties of real entire series Taylor series Complex entire series Normal convergence Weierstrass\' rule Properties of complex entire series Sums and products of entire series Chapter 4: Fourier Series Trigonometric series Fourier coefficients Fourier series of even or odd functions Rules for convergence Some applications of Fourier series Complex form of the Fourier series Parseval\'s formula Chapter 5: Improper (Generalized) Integrals General convergence criteria Cauchy\'s rule Absolute and semi-convergence Dirichlet\'s rule Abel\'s rule Relations between convergence of integrals and convergence of series Cauchy principal value Generalized integral of an unbounded function Change of variable in an improper integral Generalized integral and series Mean value formulas Second mean value theorem Practical methods for calculating certain generalized integrals Chapter 6: Functions Defined by an Integral Continuity Differentiability Integral depending on a parameter located both at the bounds and inside the integral Uniform convergence Uniform convergence of generalized integrals Criteria for uniform convergence of generalized integrals Weierstrass\' rule Dirichlet\'s rule Abel\'s rule Properties of a function defined by a generalized integral Passage to the limit in the generalized integral Integration with respect to the parameter Unbounded function defined by a generalized integral Euler\'s Γ (Gamma) function Euler\'s β (Beta) function
Evaluation	Exam: 60% Directed activities: 40% Evaluation method: Mini-quiz: 12 points Participation: 04 points Discipline: 04 points