Ibrahim Merabet
National Higher School of Mathematics
Analysis II
ENSTSA
About This Course
This course introduces key concepts in real analysis, essential for mathematics, physics, and engineering. Students study continuity, change, and accumulation through elementary functions, integration, and differential equations.
The curriculum covers trigonometric and inverse functions, Taylor series, antiderivatives, and integration techniques. It then develops the theory of the Riemann integral, rational fraction decomposition, and linear differential equations.
Balancing theory and computation, the course trains students to model dynamic phenomena and solve complex problems. Analysis II strengthens abstract reasoning and problem‑solving skills for advanced academic success.
Objectives
This course builds mastery in real analysis through two main axes: elementary functions and integral calculus. Students study continuity, limits, differentiability, and the behavior of exponential, logarithmic, trigonometric, and hyperbolic functions with their inverses. Emphasis is placed on functional identities and geometric insight to solve equations.
In parallel, learners gain fluency in evaluating indefinite integrals using integration by parts, substitution, partial fractions, and advanced trigonometric techniques. By the end, students can construct proofs with derivatives, manipulate inverse identities, and apply analytical tools to complex integrals, developing rigorous reasoning for advanced study in mathematics, physics, and engineering.
Requirements
Students should have a solid foundation in real numbers (intervals, inequalities, absolute values, bounds, completeness of ℝ) and core differential calculus (limits, ε–δ continuity, differentiation rules). Familiarity with polynomial, rational, exponential, logarithmic, and trigonometric functions and their identities is expected, along with fluency in algebraic manipulation and partial fraction decomposition.
Course Staff