Lectures related to TNB Frame: Frenet-Serret Formulas

Covers the representation of plane curves and the nature of obtained curves.

Covers polar and spherical coordinate systems, position vectors, equations of motion, and Frenet frame concepts.

Curves: Parameterized Curves and Tangent Vectors

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

Differential Geometry: Parametric Curves & Surfaces

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

Curve Integrals of Vector Fields

Explores curve integrals of vector fields, emphasizing energy considerations for motion against or with wind, and introduces unit tangent and unit normal vectors.

Interpolation and Calculus

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

Curves and Isometries

Explores curves, isometries, Bezier curves, and the Frenet coordinate system.

Mechanics of Kirchhoff Rods I

Covers the mechanics of slender structures, focusing on exact kinematics and equilibrium equations of rods.

Parametric Curves - Introduction

Introduces parametric curves and discusses tangent vectors and symmetry properties.

Curvilinear Integrals: Tangent Vectors and Oriented Arcs

Explains the tangent vectors and curvilinear integrals along oriented arcs.

Parametric Curves: Analysis and Applications

Covers the analysis of parametric curves and their tangent vectors, focusing on applications and geometric interpretations.

Understanding Positive and Negative Orientation in Curves

Explores positive and negative orientation in curves, emphasizing their impact on tangent and normal vectors.

Parametric Curves: Introduction

Covers parametric curves, including examples, symmetry, tangent vectors, and derivative signs.

Parametric Curves Study Elements

Covers the study of parametric curves and tangent vectors.

Comparing Tangent Vectors: Parallel Transport

Explores the definition, existence, and uniqueness of parallel transport of tangent vectors on manifolds.

Local Frames

Covers the concept of local frames, their construction, and limitations.

Tangent Vectors and Bézier Curves

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

Differential Geometry: Surfaces

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

Coordinate Systems: Polar, Cylindrical, Spherical

Covers position, velocity, and acceleration in polar, cylindrical, and spherical coordinate systems.

Surfaces in R^3: Curves and Regular Surfaces

Covers curves in R^2, regular surfaces in R^3, and geometric properties of edges.