Lectures related to Tangent Lines and Approximation

Explores differentiability in functions and geometric interpretation of tangent planes.

Differentiable Functions: Definitions and Interpretation

Covers the definitions of differentiable and derivable functions and their geometric interpretation.

Explores finding the equation of the tangent line to a function's graph at a point.

Differential Geometry: Parametric Curves & Surfaces

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Derivability and Tangents

Covers derivability, tangents, Rolle's theorem, and linear approximation of functions.

Elliptical Arch Construction

Explores the construction of elliptical arches using a single ellipse arc.

Implicit Function Theorem

Covers the Implicit Function Theorem for functions of two variables and explores graphical representations and tangent lines.

Differential Geometry: Surfaces

Explores the differential geometry of parametric surfaces, covering tangent space, normal curvature, principal curvatures, and asymptotic curves.

Interpolation and Calculus

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

Tangent Vectors: Definition and Applications

Explores the definition and applications of tangent vectors in determining curve directions on surfaces.

Cones and Cylinders: Geometric Definitions

Explains the geometric definitions of cones and cylinders in space and their tangent properties.

Tangent Vectors and Bézier Curves

Explains tangent vectors of curves and the construction and applications of Bézier curves in computer graphics.

Tangent vectors without embedding space: Making tangent spaces linear

Explores making tangent spaces linear, defining tangent vectors without an embedding space and their operations, as well as the equivalence of different tangent space notions.

Geometry of Surfaces in R²

Explores the geometry of surfaces in R², including implicit descriptions, critical points, and regular surfaces.

Curves: Parameterized Curves and Tangent Vectors

Explores the definition of curves, parameterized curves, and tangent vectors in relation to open intervals and continuous functions.

Tangent spaces to submanifolds

Introduces tangent spaces to submanifolds and their properties in optimization on manifolds.

Differentiability and Tangent Planes in Multivariable Functions

Explains differentiability in multivariable functions and the geometric interpretation of tangent planes.

Taylor Polynomials: Definition and Approximation

Covers Taylor polynomials for function approximation and their properties, with examples.

Supporting Hyperplanes

Explores supporting hyperplanes for approximating function graphs in higher dimensions through normal vectors and linear approximations.

Graph Algorithms II: Traversal and Paths

Explores graph traversal methods, spanning trees, and shortest paths using BFS and DFS.