Lectures related to Ordinary Differential Equations

Differential Equations: Solution Methods MOOC: Electrical engineering II

Explores the resolution of differential equations and the properties of exponential functions in electrical engineering.

Runge-Kutta Methods: Approximating Differential Equations

Covers the stages of the explicit Runge-Kutta method for approximating y(t) with detailed explanations.

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.

Differential Equations: Approximation Methods and Analysis

Covers methods for approximating solutions to differential equations and their real-world applications.

Canonical Transformations: Existence and Equations

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

Multistep methods

Covers multistep methods for solving differential equations, focusing on stability conditions and examples.

Advanced Analysis II: Variation of Constants Method

Covers the variation of constants method for solving first-order linear differential equations, detailing its steps and implications for general and particular solutions.

High Order Methods: Space Discretisation

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

Numerical Analysis: Stability in ODEs Log in to Mediaspace to watch this video

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

Direction Fields, Euler Methods, Differential Equations Log in to Mediaspace to watch this video

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

Numerical Methods: Euler and Crank-Nicolson Log in to Mediaspace to watch this video

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

Error Estimation in Numerical Methods Log in to Mediaspace to watch this video

Explores error estimation in numerical methods for solving ordinary differential equations, emphasizing the impact of errors on solution accuracy and stability.

Numerical Methods for ODEs: Crank-Nicolson, Heun, Euler, RK4 Log in to Mediaspace to watch this video

Explores numerical methods like Crank-Nicolson, Heun, Euler, and RK4 for solving ODEs, emphasizing error estimation and convergence.

Ordinary Differential Equations: Non-linear Analysis Log in to Mediaspace to watch this video

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

Numerical Integration: Euler Method Log in to Mediaspace to watch this video

Covers the progressive Euler method for numerical integration of ODEs, including Cauchy problems and Runge-Kutta methods.

Error Estimation in Numerical Methods Log in to Mediaspace to watch this video

Explores error estimation in numerical methods for solving differential equations, focusing on local truncation error, stability, and Lipschitz continuity.

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.

Introduction to Ordinary Differential Equations Log in to Mediaspace to watch this video

Introduces ordinary differential equations, their order, numerical solutions, and practical applications in various scientific fields.

Homogeneous Differential Equations Log in to Mediaspace to watch this video

Explores solving first-order homogeneous differential equations through variable changes and delves into the Bernoulli differential equation.

Differential Equations: General Solutions and Methods Log in to Mediaspace to watch this video

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