Lectures related to Advanced Analysis II: Isoclines Method

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Explores direction fields, Euler methods, and differential equations through practical exercises and stability analysis.

Discusses the Cauchy problem for ODEs with initial conditions and the importance of homeomorphism and Lipschitz continuity.

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Discusses advanced analysis concepts, focusing on differential equations and timers in microcontrollers.

Covers Euler and Crank-Nicolson methods for solving differential equations.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers the analysis of speed variation using differential equations and small time intervals.

Covers the correction of an exam from 2018, focusing on Taylor polynomials and Jacobian matrices.

Covers solutions of differential equations with initial conditions and boundedness concepts.

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Covers high order methods for space discretisation in linear differential systems.

Covers continuity, limits, and different approaches to approaching points in various coordinate systems.

Explores solutions of differential equations and properties of functions.

Covers the solution of differential equations with initial conditions and limit analysis.

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.