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Lecture
Generalized Finite Increments
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Derivatives: Definition and Examples
Covers the definition of derivatives and provides examples of differentiable functions.
Derivatives and Tangent Planes
Covers derivatives, differentiability, and tangent planes for functions of one and two variables.
Differentiability of Functions in Two Variables
Covers differentiability of functions in two variables and the conditions for a function to be differentiable.
Derivatives and Continuity
Explores derivatives, reciprocal functions, and continuity of functions with examples and formulas.
Derivability and Chain Rule
Covers the demonstration of the chain rule and the theorem of Rolle.
Partial Derivatives and Functions
Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.
Differentiability in Analysis
Explores differentiability in analysis, discussing conditions for functions to be differentiable and continuous.
Directional Derivatives
Explores directional derivatives, their calculation, examples, and cases of lack of continuity.