Non-analytic Smooth FunctionsExplores non-analytic smooth functions, their properties, and applications in differential geometry and partitioning unity.
Real Analytic FunctionsExplores real analytic functions, discussing their convergence and neighborhood properties in different contexts.
Optimization on ManifoldsCovers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.
Nth DerivativeExplores obtaining n-th derivatives through a recursive process and the regularity of functions defined by power series.
Analytical Real FunctionsExplores analytical real functions, focusing on series expansion and properties of u(x) in different neighborhoods.
Derivation Term by TermIntroduces the study of functions defined by power series and emphasizes the importance of separately considering boundary points.
