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Related lectures (30)
Vector Calculus: Green's Theorem
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Explores Green's theorem, vector field curl, Ampère's law, and magnetic field modeling.
Surface Integrals: Vector Fields
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Explains the surface integral for vector fields and demonstrates its calculation process through examples.
Vectors and Tensors: Derivatives and Transformations
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Explores gradient, divergence, and integral theorems in vector calculus.
Shells I: Mechanics of Slender Structures
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Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.
Turbulence: Numerical Flow Simulation
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Explores turbulence characteristics, simulation methods, and modeling challenges, providing guidelines for choosing and validating turbulence models.
Laplacian in Polar and Spherical Coordinates: Derivatives
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Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.
Divergence and Stokes' Theorems
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Introduces the divergence and Stokes' theorems, comparing surface and volume integrals, and explains parameterization of surfaces and boundaries.
Surface Integrals: Implicit Surfaces
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Covers implicit surfaces, parametric descriptions, regular parametrization, normal vectors, and orientable surfaces.
Geometric Surfaces: Paraboloids and Hyperboloids in Architecture
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Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.
Generalisation to Generalised Integrals
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Covers the generalisation to generalised integrals and convergence criteria.
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