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Analysis II (2025-2026)

Semester : 02

Teaching Unit: Fundamental

Subject: Analysis 2

Credits: 6

Coefficient : 4

 Course Objective: 

This module aims to give students the different aspects of integral calculus: Riemann integral, different techniques for calculating primitives, introduction to the solution of differential equations.

Recommended Prior Knowledge: Analysis 1.

Chapter I: Indefinite Integrals

Indefinite Integral, Some Properties of the Indefinite Integral, Integration Methods, Variable Change Integration, Part Integration, Regular Expression Integration, Irrational Function Integration.

Chapter II: Definite Integrals

 Definite Integral, Properties of Definite Integrals, Integral Function of its Upper Bound, Newton-Leibniz Formula, Cauchy-Schwarz Inequality, Darboux Sums-Conditions of the Existence of the Integral, Properties of Darboux Sums, Integrability of Continuous and Monotonic Functions.

Chapter III: First-Order Differential Equations

General, Classification of First-Order Differential Equations, Equation with Separable Variables, Homogeneous Equations, Linear Equations, Bernoulli Method, Method of Variation of the Lagrange Constant, Bernoulli's Equation, Total Differential Equation, Riccati's Equation.

Chapter IV: Second-Order Differential Equations with Constant Coefficients

 Homogeneous second-order differential equations with constant coefficients, Non-homogeneous second-order differential equations with constant coefficients, Methods for solving second-order differential equations with constant coefficients.

 

Method of assessment: Examination (60%), continuous assessment (40%)

 

 Références

 

· J.-M. Monier, Analyse PCSI-PTSI, Dunod, Paris 2003.

· Y. Bougrov et S. Nikolski, Cours de Mathématiques Supérieures, Editions Mir, Moscou, 1983.

· N. Piskounov, Calcul différentiel et intégral, Tome 1, Editions Mir, Moscou, 1980.

· K. Allab, Eléments d'Analyse, OPU, Alger, 1984.

· B. Calvo, J. Doyen, A. Calvo, F. Boschet, Cours d'analyse, Librairie Armand Colin, Paris, 1976.

· J. Lelong-Ferrand et J. M. Arnaudiès, Cours de mathématiques, tome 2, Edition Dunod, 1978.