Classification of discontinuities

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Covers piecewise continuous functions, their properties, classification based on continuity, and integral types, including improper integrals.

Explores integrals on unbounded domains, addressing challenges with discontinuities and providing examples for illustration.

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Covers the criteria for failure in geotechnical engineering and the determination of ultimate loads through static and kinematic approaches.

Covers continuous functions, derivability, and global properties in differential calculus.

Explores topology concepts and edge detection in computer vision, highlighting the significance of contours and gradients in image analysis.

Explores Fourier series properties and examples, showcasing their application to continuous and discontinuous functions.

Explores the concept of whether a strictly increasing function is always injective.

Covers the calculation of Taylor polynomials and error bounds for function approximation.

Covers limits and derivatives in multivariable functions, focusing on continuity, partial derivatives, and the gradient.

Explores Magnetohydrodynamic equilibrium and stability, ideal MHD solutions, 'hairy ball' theorem, and boundary conditions.

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