Lectures related to Simplex: Implementation and Methods

Complex Numbers: Introduction and Operations

Introduces complex numbers and their forms, including Cartesian, polar, and exponential forms, and explains how to find the argument of a complex number.

Linear Equations and Matrices

Introduces linear equations, matrices, systems of equations, and solution sets for 2 or 3 unknowns.

Method of Undetermined Coefficients

Explores the method of undetermined coefficients for solving non-homogeneous linear differential equations with constant coefficients.

Systems of Linear Equations and Matrices MOOC: Warm-up for EPFL MOOC: Learning to study science and engineering MOOC: Linear Algebra (Part 1)

Covers the definition and solution of linear equations with real coefficients in 2D and 3D space.

Linear Homogeneous Equations

Covers second-order linear homogeneous differential equations and their solutions.

First Order Differential Equation MOOC: Warm-up for EPFL

Covers first-order differential equations, including linear equations and applications in physics.

Linear Differential Equations: Solutions and Wronskian

Covers linear differential equations, focusing on solutions, the Wronskian, and methods for solving non-homogeneous equations.

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Linear Equations and Matrices

Covers the fundamentals of linear equations, systems, solutions, and graphical representation.

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Linear Differential Equations: General Solutions

Covers linear differential equations of the first order and methods of demonstration.

Cauchy Problem Resolution: Differential Equations Overview

Covers the resolution of a Cauchy problem for a first-order linear differential equation, detailing the construction of its general solution and the determination of initial conditions.

Ordinary Differential Equations: Second Order

Covers the resolution of linear ordinary differential equations of the second order with constant coefficients and a source term.

Linear Equations: Least Squares Solution MOOC: Linear Algebra (Part 3)

Explains how to solve linear equations using the least squares method to minimize errors in the system.

Newton's Method: Convergence and Criteria Log in to Mediaspace to watch this video

Explores the Newton method for non-linear equations, discussing convergence criteria and stopping conditions.

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

Covers the definition of linear equations, systems, solutions, and representations in 2D and 3D.

Linear Equations: Introduction and Solutions Log in to Mediaspace to watch this video

Covers the introduction and solutions of linear equations, including methods for solving systems and determining the number of solutions.

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.

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.

General Solution of Inhomogeneous ED Log in to Mediaspace to watch this video

Covers the general solution of inhomogeneous differential equations and explores linear dependence, uniqueness theorems, and second-order equations.