Lectures related to Wave Equation: Euler-Paissan-Doubana

Fourier Analysis: Series and Divergence Theorem

Covers Fourier analysis, series convergence, divergence theorem, and vector analysis.

Summary using nabla symbol

Covers the concept of nabla symbol, vector scalar, divergence, and cross product in 3D.

Conformity and Compliancy in Geometry

Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.

Understanding Normal Vectors in Calculus

Delves into normal vectors in calculus, clarifying their role in integrals and parameterization of edges.

Scalar Product: Geometric Properties

Covers the definition and properties of the scalar product, including geometric interpretations and algebraic properties.

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Tangent Plane to Implicit Functions

Explores the tangent plane to implicit functions and its graphical representation in relation to defined variables.

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Mechanics: Introduction and Calculus

Introduces mechanics, differential and vector calculus, and historical perspectives from Aristotle to Newton.

Tangent Plane to Implicit Function

Explores the tangent plane to implicit functions, emphasizing equations and graphical representations.

Dynamics: Scalar Product and Rate of Change

Introduces scalar product, parallelism of vectors, and rate of change of a product.

Divergence of Vector Fields

Explores divergence of vector fields, rotational definitions, and integral derivation applications.

Curve Integrals: Gauss/Green Theorem

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Paraboloidal Waves and Gaussian Beams

Covers paraboloidal waves, Gaussian beams, intensity, size, and laser pulse applications.

Linear Applications and Eigenvectors

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.

Vector Algebra: Scalar Product

Explores the scalar product of vectors, including properties and calculation methods.

Scalar Products in 2D and 3D Geometry

Explores the scalar product, vector lengths, angles, norms, and rotations in 2D and 3D spaces.

Electromagnetic Waves: Wave Equation and Maxwell's Equations

Explores the wave equation for electromagnetic waves, Maxwell's predictions, and the importance of polarization in defining wave properties.

Green Theorem Proof

Covers the proof of the Green theorem, showing how the integral of a vector field along a domain's boundary equals the integral of the curve within the domain.