Lectures related to Ordinary Differential Equations

Exponential of a Matrix

Explores the exponential of a matrix, properties, Frobenius norm, nilpotent matrices, commutativity, and system solutions.

Explicit Stabilised Methods: Applications to Bayesian Inverse Problems

Explores explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems, covering optimization, sampling, and numerical experiments.

Eigenvalues and Optimization: Numerical Analysis Techniques

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Matrix of Cofactors and Inverse Matrix Formula

Covers the concept of the matrix of cofactors and a formula to calculate the inverse of a matrix.

Numerical Analysis: Stability in ODEs

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

Inverse Monotonicity: Stability and Convergence

Explores inverse monotonicity in numerical methods for differential equations, emphasizing stability and convergence criteria.

Linear Differential Equations Example

Focuses on a linear system of ordinary differential equations and stability analysis.

Forced Oscillator Discussion

Explores forced oscillator dynamics, resonance, waiting time for maximum amplitude, and differential equations.

Linear Algebra: Eigenvalues and Eigenvectors

Explores eigenvalues, eigenvectors, diagonalization, and spectral theorem in linear algebra.

Ordinary Differential Equations: Non-linear Analysis

Covers non-linear ordinary differential equations, including separation, Cauchy problems, and stability conditions.

Systems of Differential Equations

Covers the solution of a 2x2 system of differential equations using matrix notation and explores stability methods and specific cases.

Signals & Systems I: Preliminary Concepts and Linear Systems

Covers preliminary concepts in signals and systems, including linear systems invariant in time and stability.

Linear Differential Equations: Solving Systems with Initial Conditions

Covers methods to solve linear differential equations in systems with initial conditions.

Inverse Power Method: Introduction to ODEs

Explores the inverse power method for ODEs and the significance of Lipschitz continuity.

Matrix Norms and Exponential Functions: Key Properties

Covers the definition and properties of matrix norms and the exponential of matrices.

Systems of n linear ODEs with constant coupling matrix A

Covers systems of n linear first-order ODEs with constant coupling matrix A and explores properties of solutions and the superposition principle.

Diagonalization Method: Application and Properties

Covers the method of diagonalization for determining if a non-square matrix A is diagonalizable.

Finite Differences and Finite Elements: Variational Formulation

Discusses finite differences and finite elements, focusing on variational formulation and numerical methods in engineering applications.

Differential Equations: Speed Variation Analysis

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