Tangent spaces to submanifolds

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Page 3 of 4

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Interpolation and Calculus

Covers revisions on calculus, derivation rules, interpolation, and tangent vectors.

Orthogonality and Gram-Schmidt Process

Explores orthogonality, Gram-Schmidt process, dot products, and solution minimization in systems.

Parametric Curves: Descartes' Folium

Covers Descartes' Folium, a parametric curve with specific equations and properties, including domain boundaries and tangent vector analysis.

Length of Curves and Tangent Vectors

Covers the calculation of the length of curves and the properties of tangent vectors.

Generalization of Change of Basis Matrices

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Advanced Analysis II: Isoclines Method

Explores the Isoclines Method and solutions of differential equations with tangents.

Analysis Reminder: Open Sets and Denseness

Reviews open sets, denseness, real numbers, convergence, curves, continuity, and derivatives in analysis.