Lectures related to Āryabhaṭa's sine table

Covers the Fourier series and interactions between sine and cosine functions.

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Covers the Z-transform, region of convergence, and examples of signals with multiple poles and finite-duration signals.

Explores the Fourier Trick for time-dependent diffusion problems in a Cartesian system.

Explores transposable elements in the genome and the use of microsatellites for DNA fingerprinting.

Explores the theory and applications of Fourier series, including convergence properties and piecewise-defined functions.

Covers the Laplace transform, region of convergence, impulse response, and multiple poles.

Covers the concept of uniform convergence of Fourier series and Dirichlet's theorem application.

Covers Laplace transform rules, examples, signal transformation, and process control.

Explores odd and even functions in Fourier series applications, including half-range series and cosine/sine series.

Explores the use of complex exponentials to simplify trigonometry and algebra in digital systems.

Explores Fourier series coefficients, periodicity, and series relations.

Covers properties of logarithms, derivatives, exponentials, and sine-cosine functions.

Covers the definition of sine and cosine functions, their graphs, and notable points.

Explores the properties and limits of trigonometric functions, emphasizing even nature and function parity.

Covers the integration of functions and Fourier series with examples and exercises.

Covers the concept of trigonometric functions and their applications in geometry.

Introduces Taylor series, covering their basics and applications in approximating functions and calculating limits.

Covers the fundamental theorem of calculus, immediate integration, and properties of derivatives, with examples of integration by substitution.

Introduces Taylor polynomials for approximating functions around a point, showcasing their importance in accurately representing functions.