Lectures related to Bezier Curves II

Covers the basics of Bezier curves and introduces Bernstein polynomials.

Explores the fundamentals and applications of Bezier curves, focusing on their construction, properties, and practical uses in design and modeling.

Covers the basics of parametric curves, including straight lines, quadratic curves, Bézier curves, and cubic curves.

On Convex Optimization covers course organization, mathematical optimization problems, solution concepts, and optimization methods.

Explores the definition and derivability of functions in differential calculus, emphasizing differentiability at specific points.

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

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.

Covers the concepts of convexity and concavity in functions with examples.

Explores the optimization and penalization of natural cubic splines, including roughness penalties and Bayesian inference.

Explains partial derivatives, Hessienne matrix, and their properties.

Explores derivability, continuity, and composite functions with illustrative examples.

Explores geometric modeling using splines and freeform deformation for creating smooth surfaces and deformable objects in 3D space.

Explores exact linearization techniques for transforming non-linear systems into linear ones, emphasizing system stability.

Introduces the gradient concept and the Theorem of Mean Value for functions in several variables.

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Explores partial derivatives and derivability of functions, emphasizing geometric interpretations and avoiding common pitfalls.

Explains gradient descent for optimization and how to find the direction towards the solution by minimizing distances.

Explains the Jacobian matrix and derivative of composite functions with examples.

Explores involutes and Bezier curves, essential in computer-aided design.