Calculus is a language to capture the essence of motion and transformation. From the orbits of celestial bodies to the learning curves of machine learning models, it measures the infinitesimal to grasp the infinite. ![[DALLE3_Calculus.png]] ## Concept Tree ### Basic 1. **Limits and Continuity** - Definition of a limit - Continuity at a point - Infinite limits and limits at infinity 2. **Derivatives** - Definition and basic rules - Product and quotient rules - Chain rule 3. **Integrals** - Indefinite integrals - Basic integration techniques - Fundamental Theorem of Calculus ### Advanced 1. **Applications of Derivatives** - Optimization - Related rates - Newton's method 2. **Definite and Indefinite Integrals** - Integration by substitution - Integration by parts - Partial fractions 3. **Sequences and Series** - Convergence and divergence - Power series - Taylor and Maclaurin series ### Mastery 1. **Multivariable Calculus** - Partial derivatives - Multiple integrals - Vector calculus 2. **Differential Equations** - First-order differential equations - Second-order linear differential equations - Systems of differential equations 3. **Connections to Machine Learning** - Gradient descent - Optimization in neural networks - Understanding backpropagation