Titlebook: Differential Equations and Data Analysis; Aleksei Beltukov Textbook 2025 The Editor(s) (if applicable) and The Author(s), under exclusive

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We show how probabilistic reasoning leads to ODE that describe radioactive decay, absorption of light, mutarotation of glucose, and similar memoryless processes. All ODE are linear with constant coefficients which further vindicates our decision to prioritize them.

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The Dream: A Future Powered by Plutoniumn it is applied to complex numbers and matrices. To avoid that confusion in later chapters, we show how the exponential function is properly defined by its Taylor series expansion and how that definition naturally extends its domain to complex and matrix inputs.

compel

Schaltungen mit mehreren Aktuatorenstructure is codified in the structure theorem which, together with the principle of superposition, provides a blueprint for constructing general solutions of linear ODE; no such blueprint exists for nonlinear ODE. As a concrete illustration of linearity in action, we study an RC-circuit driven firs

cornucopia

Fehlersuche in pneumatischen Systemen ODE with constant coefficients. All such ODE can be converted to matrix-vector form. We first show how to exponentiate matrices using eigendecomposition: this settles questions about homogeneous ODE and complimentary functions. We then introduce the method of undetermined coefficients for construct

Fermentation

Ambulant erworbene Pneumonie: Erreger,, where it is practically synonymous with digital signal processing (DSP). After reviewing orthogonal expansions, we show that DFT is one, and that it is also a way of approximating functions with sums of real harmonics or, equivalently, complex exponentials. The role of DFT in data analysis is illu