Calculus is essential in various branches of mathematics. This section is designed to take you from fundamental calculus concepts to the advanced techniques essential for optimization. Building on the foundation laid in Linear Algebra, we explore how calculus is applied to analyze and optimize complex systems. We begin with the classical notion of derivatives - ranging from scalar functions to those of vectors and matrices - and gradually introduce numerical methods. In doing so, we not only deepen your understanding of calculus but also provide the essential background and analytical foundations that lie behind Machine Learning (Section V).
Nature and data are rarely static. In the broader framework of this site, this section explores the continuous world, where we utilize the power of Calculus and Analysis to model change. We progress from the mechanics of Jacobians and Hessians to the deep theory of Measure and Lebesgue Integration, establishing the completeness (the absence of mathematical holes) required for robust computation. In the context of Computer Science, this is the study of efficiency and refinement. Whether we are navigating the loss landscape of a neural network through Gradient Descent or modeling the continuous density functions of Probability & Statistics (Section III), the concepts of limits and convergence are the essential engines that allow machines to "learn" and adapt to an analog reality.