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Abstract index notation
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Related lectures (12)
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Mathematical Basics: Index Notation and Tensors
Covers index notation basics and introduces tensors and their transformations.
Fluid Dynamics Fundamentals
Covers deriving fluid dynamics equations, including mass conservation and stress-strain relationships, through differential analysis and key mathematical concepts.
Summation and Sequences: Notations and Formulas
Covers summation notation, product notation, geometric series, and important formulas.
Summation and Sequences: Notation and Formulas
Covers summation notation, product notation, and geometric series formulas.
Thermodynamics of Continuous Media
Covers historical thermodynamics, continuity equations, state functions, and Cartesian products in scalar and vectorial forms.
Symmetries and Conservation Laws
Covers symmetries and conservation laws in fluid dynamics, emphasizing the importance of maximizing symmetries in ideal fluid systems.
Tensor Transformations
Introduces tensor transformations, rotation matrices, and differential operators in mechanics.
Discrete Variables: Spatial Arrangement and Neighbourhood
Covers geometric properties, spatial arrangement, autocorrelation, and neighbourhood analysis in geographic information systems.
Algebraic Manipulations: Indices and Tensors in Continuum Mechanics
Provides an overview of algebraic manipulations involving indices and tensors in continuum mechanics.
Einstein Equations
Explores the Bianchi identity, Einstein tensor, and action principle for fields.
Plates II: Föppl-von Kármán Equations
Covers the framework for plates, bending and stretching energies, and Föppl-von Kármán Equations, exploring mean and Gaussian curvatures.
Symmetries in Mechanics and Wave Equations
Explores symmetries in Newtonian mechanics and wave equations, highlighting their significance in understanding physical laws.
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