Lectures related to Introduction to ODEs: System of 1st Order ODEs

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

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

Explores the concept of separation of variables in quantum mechanics and its application in solving differential equations.

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

Explores the one-dimensional harmonic oscillator, equilibrium positions, and forced oscillators with external forces.

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

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

Explores biomechanical modeling of the musculoskeletal system using differential equations and finite element modeling.

Explores the use of PDEs and ODEs in biomechanics, including the Lotka-Volterra model.

Covers the material point model, initial conditions, and Newton's laws in physics.

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

Explores power series solutions in quantum mechanics for differential equations and energy quantization.

Explores Jacobi identity, gauge invariance, and conservation laws in quantum mechanics and classical physics.

Explores the Hamiltonian formalism, conservation laws, preserved quantities, and differential equations in classical physics.

Explores springs under forces using differential equations and mechanics examples.

Discusses advanced analysis concepts, focusing on differential equations and timers in microcontrollers.

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

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

Explores projectile motion with friction effects and dynamics of polar expeditions.

Explores linear differential equations, including higher-order linear homogeneous equations and equations with constant coefficients.