Intuitive Approach to Derivatives

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Parametric Curves and Derivatives

Explores parametric curves, derivatives, equivalence of paths, and local behavior of functions.

Advanced Physics I: Trajectory and Velocity

Explores trajectory, velocity, and acceleration in advanced physics, emphasizing rectilinear motion and the importance of instantaneous velocity.

Derivatives: Definition and Examples

Covers the definition of derivatives and provides examples of differentiable functions.

Partial Derivatives: Definitions and Applications

Explores the definitions and applications of partial derivatives in functions of several variables, emphasizing the importance of specifying the choice of variables.

Extrema and Lagrange Multipliers

Explores Lagrange multipliers for finding extrema under constraints and various proof methods.

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

Directional Derivative: Definitions and Examples

Covers the definition of directional derivative and provides illustrative examples.

Brownian Motion: Historical Background and Mathematical Construction

Explores the historical context and mathematical aspects of Brownian motion, including Einstein's model and experimental verification.

Introduction to Derivatives

Introduces derivatives, forward contracts, options, and their financial uses.