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Lecture
Differentiability: Partial Derivatives and Hessiennes
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Differential Calculus: Introduction and Summary
Introduces and summarizes differential calculus, covering continuous functions, limits, differentiability, and tangent planes.
Differentiability and Composition
Covers differentiability, composition of functions, partial derivatives, Jacobian matrix, and polar coordinates.
Derivatives and Continuity in Multivariable Functions
Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.
Tangent to Graph of a Function
Explores finding the equation of the tangent line to a function's graph at a point.
Partial Derivatives and Differential Equations
Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.
Functions with Values in R^m
Explores functions with values in R^m, gradients, derivatives, and the Jacobian matrix in multiple dimensions.
Directional Derivatives
Explores directional derivatives, their calculation, examples, and cases of lack of continuity.
Partial Derivatives: Derivability
Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.
Partial Derivatives and Functions
Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.
Differentiability of Functions in Two Variables
Covers differentiability of functions in two variables and the conditions for a function to be differentiable.