Lectures related to Leonhard Euler

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

Euler Method: Understanding Higher Order Runge-Kutta Schemes

Explains the Euler method and higher-order Runge-Kutta schemes for solving differential equations.

Runge-Kutta Methods: Approximating Differential Equations

Covers the stages of the explicit Runge-Kutta method for approximating y(t) with detailed explanations.

Covers the theory of digital signal processing, including sampling, transformation methods, digitization, and PID controllers.

Buckling of Straight Beams

Explores the buckling phenomenon in straight beams due to material breakage or buckling stress being exceeded.

Euler and Moivre Formulas

Covers Euler and Moivre formulas, addition formulas, properties of exponentials, and generalizing sine and cosine definitions to complex numbers.

Dynamics of Steady Euler Flows: New Results

Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.

Set Union: Basics and Properties

Introduces set union, its properties, and examples with Euler course contest participants.

Complex Numbers: Operations and Properties

Explores complex numbers, including modulus, conjugation, and Euler formula.

Relative Movements and Gyroscopic Effects

Covers relative speed, Euler angles, and gyroscopic effects in rotating frames.

Euler and Moivre Formulas: Complex Numbers Analysis

Covers the Euler and Moivre formulas for complex numbers analysis.

Zero-stability and absolute-stability

Explores zero-stability and absolute-stability in numerical methods, including Forward Euler, Backward Euler, Crank-Nicolson, and Heun's methods.

Beam Bending: Deflection and Applications in Nanotechnology

Explores beam deflection theory, applications in nanotechnology, and AFM as a versatile tool for nanoscale biology.

Advanced Analysis II: Solving Separable Differential Equations

Covers the theory and methods for solving separable differential equations, focusing on existence, uniqueness, and the construction of solutions through integration.

Complex Systems: Critical Phenomena

Explores critical phenomena in complex systems, including stochastic objects, percolation, and combinatorial optimization.

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Heat Equation: Modeling and Numerical Methods

Covers the heat equation, its physical interpretation, and numerical methods for solving it.

Euler Product and Perron's Formula

Explores the Euler product theorem and Perron's formula in number theory and complex analysis.

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Numerical Methods: Boundary Value Problems

Explores numerical methods for boundary value problems, including heat diffusion and fluid flow, using finite difference methods.