About This Course

A key component of higher mathematics education is the Analysis II course, which is intended for first-year undergraduate students (L1) in Science and Technology (ST). To bridge the gap between single-variable analysis and the study of more complex systems, this program aims to improve students' proficiency in integral and differential calculus. Ordinary Differential Equations (ODEs) are covered in the first section of this course, teaching students first-order equations—such as those involving separable variables, homogeneous and Bernoulli's equation—followed by second-order and higher-order equations with a special focus on linear equations with constant coefficients.

The second part of the course introduces Functions of Several Variables, exploring limits, continuity, and differential calculus after defining topological foundations in R^n. A major emphasis is placed on differentiable optimization in R^2, where students learn to use Taylor's formula and the Hessian matrix to identify and characterize critical points (minima, maxima, and saddle points). Upon completion, students will be able to classify complex mathematical problems, calculate gradients and total differentials, and design rigorous mathematical models representing physical realities.