Differentiable Functions: Derivatives and Approximations

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Related lectures (48)

Derivatives and Continuity in Multivariable Functions Log in to Mediaspace to watch this video

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Differentiability of Functions of Several Variables Log in to Mediaspace to watch this video

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Taylor Polynomials: Calculating Limits and Derivatives Log in to Mediaspace to watch this video

Covers the calculation of Taylor polynomials and their applications in limits and derivatives of functions from R² to R.

Taylor Development: Higher Derivatives Log in to Mediaspace to watch this video

Covers the calculation of Taylor polynomials, higher derivatives, and Taylor series using examples.

Derivatives: Definition and Examples Log in to Mediaspace to watch this video

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

Differentiable Functions and Lagrange Multipliers Log in to Mediaspace to watch this video

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Higher Derivatives, Taylor Introduction Log in to Mediaspace to watch this video

Introduces higher derivatives and the Taylor development, illustrating examples and discussing the uniqueness of the Taylor polynomial.

The Increment Theorem: Understanding Derivatives Log in to Mediaspace to watch this video

Explores the increment theorem and derivatives in calculus, focusing on polygonal valleys and curve traces.

Implicit functions theorem Log in to Mediaspace to watch this video

Explores the implicit functions theorem, showcasing examples of implicit differentiation and function definition.

Functions: Multivariable Functions and Exact Differentials Log in to Mediaspace to watch this video

Explores functions as a function of time and space, differentiation of multivariable functions, exact differentials, and gradients.

Differentiability and Tangent Planes Log in to Mediaspace to watch this video

Covers differentiability in multivariable functions, focusing on tangent planes and their properties.

Functions of Class C^p Log in to Mediaspace to watch this video

Explores functions of class C^p, emphasizing continuity and differentiability properties.

Computing Derivatives: Derivatives and Algebraic Operations Log in to Mediaspace to watch this video

Covers the computation of derivatives and the properties of differentiable functions.

Taylor Polynomials: Orders 1 and 2 Log in to Mediaspace to watch this video

Explores Taylor polynomials of orders 1 and 2 for linear function approximation around a point.

Differentiability Analysis Log in to Mediaspace to watch this video

Explores differentiability, partial derivatives, Schwarz's theorem, and function continuity in mathematical analysis.

Optimization Techniques: Local and Global Extrema Log in to Mediaspace to watch this video

Discusses optimization techniques, focusing on local and global extrema in functions.

Partial Derivatives and Gradient Log in to Mediaspace to watch this video

Covers the definitions and properties of partial derivatives and gradients in mathematical contexts.

Advanced Analysis II: Multi-Index and Taylor Formula Log in to Mediaspace to watch this video

Explores multi-index, Taylor formula, partial derivatives, and remainders estimation in Taylor series.

Analytical Real Functions Log in to Mediaspace to watch this video

Explores analytical real functions, focusing on series expansion and properties of u(x) in different neighborhoods.

Differentiation and Coordinate Changes in Multivariable Functions Log in to Mediaspace to watch this video

Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.

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