Lectures related to Mechanics of Helix Under Gravity

Numerical Analysis: Stability in ODEs

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

Material Point Model: Basics

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

Differential Equations: Speed Variation Analysis

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

Simulation: Control of Dynamic Systems

Explores simulation of common structures and control of dynamic systems through friction and elasticity constants.

Mechanics of Slender Structures: Elasticity & Buckling

Explores 3D elasticity, beam bending, and buckling phenomena in slender structures.

Linear Differential Equations

Explores solving linear differential equations and the principle of superposition with illustrative examples.

Ordinary Differential Equations: Non-linear Analysis

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

Direction Fields, Euler Methods, Differential Equations

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

Dynamic Systems: Springs and Forces

Explores springs under forces using differential equations and mechanics examples.

One Dimensional Harmonic Oscillator

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

Beam Buckling

Explores beam buckling, moment-curvature relation, and linear elasticity for understanding beam behavior under different loading conditions.

Linear Differential Equations

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

Differential Equations: General Solutions and Methods

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

Homogeneous Differential Equations

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

Elasticity: Constitutive Modelling in Geomechanics

Explores constitutive modelling in geomechanics, focusing on stress-strain behavior and the application of elastic models in analytical and numerical methods.

Canonical Transformations in Analytical Mechanics

Explores canonical transformations, conservation of quantities, and differential equations in analytical mechanics.

Addition of Springs: General Physical Exercises I

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

Vibrating Strings: Mathematical Analysis and Fourier Series

Provides an overview of the mathematical analysis of vibrating strings using Fourier series and Laplace transforms.

Multilinear Regression: Basics and Applications

Covers the basics of multilinear regression and its application in analyzing material properties.

Introduction to Ordinary Differential Equations

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