Biomechanics Modeling: Musculoskeletal System

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Partial Differential Equations in Biomechanics

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

Introduction to Partial Differential Equations

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Numerical Methods: Boundary Value Problems

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Introduction to ODEs: System of 1st Order ODEs

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Diffusion: Macroscopic View

Explores diffusion from a macroscopic perspective, emphasizing the derivation of the diffusion equation through mass conservation and fixed flux law.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and de-noising data.

Canonical Transformations: Existence and Equations

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

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.

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.

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.

One Dimensional Harmonic Oscillator Log in to Mediaspace to watch this video

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

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.

Two Phase Flow and Heat Transfer Log in to Mediaspace to watch this video

Covers the fundamentals of two-phase flow and heat transfer phenomena.

Fourier Analysis and PDEs Log in to Mediaspace to watch this video

Explores Fourier analysis, PDEs, historical context, heat equation, Laplace equation, and periodic boundary conditions.

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.

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.

Numerical Approximation of Partial Differential Equations Log in to Mediaspace to watch this video

Explores numerical methods for solving partial differential equations computationally, emphasizing their importance in predicting various phenomena.

Linear Differential Equations Log in to Mediaspace to watch this video

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

Multi-injection microreactors: Modeling and Heat Transfer Analysis Log in to Mediaspace to watch this video

Explores modeling and heat transfer in multi-injection microreactors, analyzing temperature, concentration, and reactor length.

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