Lectures related to Advanced-analysis-ii

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

Differential Equations: Speed Variation Analysis

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

Differential Equations: General Solutions and Methods

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

Material Point Model: Basics

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

Differential Equations: Initial Conditions and Solutions

Covers the solution of differential equations with initial conditions and limit analysis.

Advanced Analysis II: Second Order Linear Differential Equations

Covers second order linear differential equations, focusing on solution construction and the concept of linear independence among solutions.

Cauchy Problem: Existence and Uniqueness of Solutions

Covers the Cauchy problem, focusing on the existence and uniqueness of solutions to differential equations.

Canonical Transformations: Existence and Equations

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

Separable Differential Equations

Covers separable differential equations of order 1, defining separable equations and providing examples.

Advanced Analysis II: Differential Equations and Timers

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

Differential Equations: Introduction and Theoretical Results

Covers differential equations, including examples and unique solutions.

Vertical Metronome: Equilibrium and Stability

Explores equilibrium and stability of a vertical metronome system with springs.

Homogeneous Differential Equations

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

Linear Differential Equations

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

Numerical Analysis: Stability in ODEs

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

Differential Equations: Solution Methods

Explores the resolution of differential equations and the properties of exponential functions in electrical engineering.

Uniqueness of Solutions: Cauchy-Lipschitz Theorem

Covers the uniqueness of solutions in differential equations, focusing on the Cauchy-Lipschitz theorem and its implications for local and global solutions.

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Cauchy Problem: Existence and Uniqueness of Solutions

Covers the Cauchy problem, focusing on the existence and uniqueness of solutions to differential equations.

Cable Structures: Analysis and Equilibrium

Covers cable structures analysis, equilibrium, and comparison with arches, including examples and exam preparation.