Vibration of Diatomic Molecules

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Fourier Series: Approximation and Convergence

Introduces Fourier series, explaining their approximation properties and convergence, along with the Dirichlet theorem and coefficient computation.

Boundary Conditions and Basis Decomposition

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.

Fourier Series: Convergence and Coefficients

Explores Fourier series convergence and coefficient calculations through examples and derivations.

Fourier Series: Complex Case

Covers the calculation of Fourier coefficients for periodic complex signals and the concept of a complete orthonormal system.

Fourier Series and Equations

Covers Fourier series, periodic functions, and Fourier transforms.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Fourier Transform: Concepts and Applications

Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.

Trigonometric Polynomials: Periodicity and Fourier Coefficients

Explores trigonometric polynomials, periodicity, and Fourier coefficients in mathematical analysis.

Reciprocal Trigonometric Functions

Explores reciprocal trigonometric functions, hyperbolic functions, and area theorems.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.