Lectures related to Weak Solutions of Differential Equations

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

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.

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

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.

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

Explores Banach spaces and the uniqueness of solutions in differential equations, emphasizing continuity and local behavior.

Covers separable differential equations of order 1, defining separable equations and providing examples.

Covers solving linear inhomogeneous differential equations and finding their general solutions using the method of variation of constants.

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.

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

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Covers ordinary differential equations, their orders, examples, and applications in various fields.

Covers linear differential equations of higher order, defining them as linear if they can be rewritten in a specific form.

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

Explores implicit solutions for differential equations and their applications in different scenarios.

Covers the basics of linear algebra, including solving equations and understanding systems of linear equations graphically.

Covers the material point model, initial conditions, and Newton's laws in physics.

Covers basics on optimization, including norms, Lipschitz continuity, and convexity concepts.

Covers the model problem of elliptic PDEs with weak formulation and classical solutions.