Ordinary Differential Equations: Definitions and Methods

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Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Explores ordinary differential equations, including general solutions, separate variables, order, linearity, and proof methods.

Explores propositions, proofs, and contraposition in mathematical theory, emphasizing logical rules and proof methods.

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

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

Discusses inductive propositions, their definitions, and applications in reasoning and evaluation techniques in Coq.

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

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

Covers the Runge-Kutta method for approximating solutions of differential equations.

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