Linear Differential Equations

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Related lectures (45)

Differential Equations: Speed Variation Analysis Log in to Mediaspace to watch this video

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

One Dimensional Harmonic Oscillator Log in to Mediaspace to watch this video

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.

Homogeneous Solutions: Linear Independence Log in to Mediaspace to watch this video

Explores finding particular solutions for homogeneous differential equations, emphasizing linear independence and variation of constants.

Advanced analysis II: second order linear ODEs Log in to Mediaspace to watch this video

Explores second-order linear ODEs, solutions uniqueness, and linear independence.

Fluid Friction Forces Log in to Mediaspace to watch this video

Explores fluid friction forces, including laminar and turbulent flow, viscosity, and terminal velocity calculation.

Solutions of Homogeneous Linear Differential Equations Log in to Mediaspace to watch this video

Covers the solutions of homogeneous linear differential equations and how to find linearly independent solutions.

Semi-groups of Contractions Log in to Mediaspace to watch this video

Explores semi-groups of contractions, discussing uniqueness theorems, maximum principles, and the infinitesimal generator.

Untitled Log in to Mediaspace to watch this video

Linear Applications: Matrices and Transformations Log in to Mediaspace to watch this video

Covers linear applications, matrices, transformations, and the principle of superposition.

Linear Algebra: Introduction and Systems of Equations Log in to Mediaspace to watch this video

Covers the basics of linear algebra and systems of equations with exercises and IT tools for support.

Linear Equations: Solving Systems and Matrices Log in to Mediaspace to watch this video

Covers solving linear equations, focusing on systems with zero, one, or infinite solutions, and introduces matrices as a powerful tool for efficient solution.

Elliptic Partial Differential Equations Log in to Mediaspace to watch this video

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

Cramer's Rule and Matrix Inverse Log in to Mediaspace to watch this video

Explores Cramer's Rule for solving linear equations and calculating matrix inverses.

Orthogonal Families and Projections Log in to Mediaspace to watch this video

Introduces orthogonal families, orthonormal bases, and projections in linear algebra.

Matrix Rank and Linear Systems Log in to Mediaspace to watch this video

Explores matrix rank, subspaces, and their role in solving linear systems of equations.

Numerical Integration: Trapezoidal Rule Log in to Mediaspace to watch this video

Covers numerical integration methods, focusing on the trapezoidal rule and iterative processes.

Linear Transformations: Kernels and Images Log in to Mediaspace to watch this video

Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.

Numerical Analysis: Nonlinear Equations Log in to Mediaspace to watch this video

Explores the numerical analysis of nonlinear equations, focusing on convergence criteria and methods like bisection and fixed-point iteration.

Linear Algebra: Matrix Operations Log in to Mediaspace to watch this video

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

Linear Applications: Injectivity and Surjectivity Log in to Mediaspace to watch this video

Explores injective and surjective linear applications, map composition, and matrix relationships in vector spaces.

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