Calculus

Calculus is the mathematics of continuous change. It provides tools for understanding rates of change (differentiation) and accumulation (integration), which are fundamental to optimizing machine learning models and working with continuous probability distributions.

This section covers:

• Foundations: Basic concepts of Functions, Limits, and Continuity, the definition and interpretation of Derivatives, essential Differentiation Rules, and the crucial Chain Rule.
• Multivariable Calculus: Extending calculus to Functions of Multiple Variables, defining Partial Derivatives, the Gradient vector, and Directional Derivatives.
• Optimization: Using calculus to find Maxima and Minima, the core algorithm of Gradient Descent and its variants, and the important concept of Convexity.
• Advanced Topics: Introduction to the Hessian Matrix, the Jacobian Matrix, and Lagrange Multipliers for constrained optimization.
• Integrals: Understanding Definite and Indefinite Integrals (Antiderivatives), the Fundamental Theorem of Calculus, and their direct Applications in Probability theory for continuous variables.
• Matrix Calculus: Combining linear algebra and calculus to differentiate with respect to vectors and matrices, essential for ML model training.

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