The goal is to provide a deep understanding of ordinary differential equations and multivalued functions as well as a strong sense of how useful the subject can be and how one can apply it to work and future studies.
Introduction, examples, classification of ODEs; Existence, uniqueness and stability of solutions; Linear equations; separable equations; Modeling, linear vs. non-linear equations; Autonomous equations, exact equations; Introduction to second order linear ODE; Second order linear ODEs: Superposition, characteristic equation, the case of distinct real roots, Real roots and complex roots, Fundamental solutions and the Wronskian determinant, uniqueness of solutions, More on the characteristic equation: The case of repeated roots; nonhomogeneous equations.
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Applied Analysis and Fourier Theory, Filippakis Michael, ODE’s, Padelidis , Krabaritis, Hadjisavvas 2) Elementary Differential Equations and Boundary Value Problems, Boyce, DiPrima 3) ODE’s, Alikakos, Kalogeropoulos