Lectures related to Advanced-analysis-ii

Covers scalar linear higher order ODEs, focusing on properties of solutions and the superposition principle.

Linear Independence: Definition and Examples

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

Explains linear independence, basis, and matrix rank with examples and exercises.

Bernoulli Differential Equations: Historical Insights and Solutions

Discusses Bernoulli differential equations, their historical context, and methods for solving them, emphasizing the importance of linear algebra concepts in understanding these equations.

Transformations and Inversions: Laplace and Fourier

Discusses Laplace and Fourier transformations, focusing on their inversion formulas and applications in solving differential equations.

Linear Differential Equations: Methods and Solutions

Covers methods for solving first-order linear ordinary differential equations.

Generalization of Change of Basis Matrices

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Linear Equations and Vector Spaces

Explores solutions of linear equations, null spaces, subspaces, vector spaces, linear independence, bases, and dimensions.

Linear Algebra: Systems of Linear Equations

Introduces linear algebra concepts, focusing on solving systems of linear equations and their representations.

System of Linear 1st Order ODEs

Explores the system of linear first order ODEs and scalar linear ODEs with examples and solutions.

Vector Spaces Equivalence

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Linear Applications: Matrices and Spaces

Covers linear applications, matrices, and vector spaces, emphasizing the concept of linear independence.

Linear Algebra: Matrices and Vector Spaces

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Advanced analysis II: second order linear ODEs

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

Existence of y: Proofs and EDO Resolution

Covers the proof of the existence of y and the resolution of EDOs with practical examples.

Linear Independence and Bases

Covers linear independence, bases, and coordinate systems with examples and theorems.

Linear Independence and Bases in Vector Spaces

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

General Integrals: Notation and Equations

Covers the general concept of integrals, focusing on notation and equations.

Change of Basis: Matrices and Vector Spaces

Covers changing bases in vector spaces using matrices and the concept of dimension.

Vector Spaces in R2 and R3

Covers vector spaces in R2 and R3, including planes and lines.