Lectures related to Differential-algebraic system of equations

Power Systems Dynamics: Stability and Behavior

Explores transient stability in power systems, covering synchronous machine synchronism after disturbances, voltage stability, and power flow calculations.

Numerical Methods for ODEs: Crank-Nicolson, Heun, Euler, RK4

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

Second Order Differential Equations: Solving Examples and Conditions

Focuses on solving second order differential equations with examples and conditions, including Fourier series and Sturm-Liouville theory.

Ordinary Differential Equations: Non-linear Analysis

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

Advanced Numerical Analysis: Space Discretization

Explores advanced space discretization techniques in numerical analysis for solving differential systems efficiently and accurately.

Non-inertial Reference Frames & Constraints

Covers forces in non-inertial reference frames, constraints, and the use of pulleys and ropes.

Gaussian Elimination Method

Covers the Gaussian elimination method for solving linear equations using row operations and equivalent matrices.

Linear Algebra: Systems of Equations

Explores solving systems of equations using matrices and determinants.

Green-Riemann Formulas

Covers the Green-Riemann formulas and their applications in evaluating integrals and solving differential equations.

Addition of Springs: General Physical Exercises I

Covers the addition of springs in series and parallel, exploring equivalent movements.

Reflection and Rotation Composition

Explores reflection and rotation composition in analytical geometry, including finding centers and solving fixed point systems.

Linear Algebra: Operations and Applications

Explores operations and applications of linear algebra in solving equations and transformations.

Linear Algebra: Systems of Equations and Vector Operations

Explores systems of equations, vector operations, and geometric interpretations in linear algebra.

Quantities of Movement and Energy

Explores quantities of movement, impulse, work, energy, and momentum, including Newton's laws and technical equation solutions.

Linear Algebra: Cramer's Rule

Covers Cramer's Rule for solving linear equations using determinants.

Eigenspaces: Definitions and Examples

Introduces eigenspaces in linear algebra through definitions and practical examples of determining eigenspaces for matrices.

Fixed Point Methods

Explores fixed point methods for function solutions and non-linear systems.

Systems of Linear Equations and Matrices

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

Linear Functions and Systems of Equations

Explores linear functions, systems of equations, and geometric interpretations of solutions.

System of Linear 1st Order ODEs

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