🔎Condensed Notes
🧪Understanding Vectors and Their Operations🧪Applications and Visualization of Cross Product Orthogonality🧪Vectors are Independent of Basis, Components Transform via Rotation Matrices🧪The Kronecker Delta and Permutation Symbol are Essential Tools for Vector Algebra and Geometric Inte🧪Fields as Functions Mapping Space to Physical Quantities🧪Integral Theorems: Connecting Derivatives to Boundaries🧪Vector Calculus in General and Orthogonal Coordinate Systems🔎Scalar and Vector Potentials: Decomposing Vector Fields and Their Properties🔎The Outer Product and Tensor Transformations🔎Operations and Properties of Tensors🔎The Metric Tensor Covariant Derivatives and Tensor Densities🔎Tensors in Cartesian Coordinates and Their Integration🔎Applications of Tensors in Solid Mechanics Electromagnetism and Classical Mechanics🔎From Extensive Properties to the Continuity Equation🔎Derivation of the Diffusion and Heat Equations from the Continuity Principle🔎The Wave Equation-Derivation and Physical Applications and Wave Speed Determination🔎Boundary and Initial Conditions for Partial Differential Equations-Types and Uniqueness and Stationa🔎Fluid Momentum and the Continuity Equation-Derivation of the Cauchy and Navier-Stokes Equations
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