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Lecture
Derivatives and Chain Rule
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Differentiability and Partial Derivatives
Explores differentiability in two variables and the chain rule for compositions.
Differential Calculus: Definition and Derivability
Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.
Derivative Chain Rule
Covers the derivative of the composition of two functions and the chain rule theorem.
Differentiation and Coordinate Changes in Multivariable Functions
Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.
Differentiability and Composition
Covers differentiability, composition of functions, partial derivatives, Jacobian matrix, and polar coordinates.
Derivability and Composition of Functions
Explores derivability and function composition with examples.
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Explores linear applications, derivatives, Jacobian matrix, composition of functions, and matrix products.
Differential Calculation: Trigonometric Derivatives
Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.
Power Functions: Properties and Derivatives
Covers properties of logarithms, power functions, and their derivatives, with examples illustrating key concepts.
Laplacian in Polar and Spherical Coordinates: Derivatives
Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.
