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Teories no lineals --- Dinàmica --- No linealitat (Matemàtica) --- Problemes no lineals --- Anàlisi funcional no lineal --- Anàlisi matemàtica --- Càlcul --- Física matemàtica --- Caos (Teoria de sistemes) --- Equacions diferencials no lineals --- Ones no lineals --- Oscil·lacions no lineals --- Sistemes no lineals --- Solitons --- Anàlisi de sistemes --- Cinètica --- Matemàtica --- Mecànica analítica --- Aerodinàmica --- Cinemàtica --- Dinàmica molecular --- Electrodinàmica --- Estabilitat --- Matèria --- Moviment --- Moviment rotatori --- Pertorbació (Matemàtica) --- Teoria quàntica --- Termodinàmica --- Estàtica --- Física --- Energia --- Mecànica --- Nonlinear theories. --- Dynamics. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics

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This book is aimed to undergraduate STEM majors and to researchers using ordinary differential equations. It covers a wide range of STEM-oriented differential equation problems that can be solved using computational power series methods. Many examples are illustrated with figures and each chapter ends with discovery/research questions most of which are accessible to undergraduate students, and almost all of which may be extended to graduate level research. Methodologies implemented may also be useful for researchers to solve their differential equations analytically or numerically. The textbook can be used as supplementary for undergraduate coursework, graduate research, and for independent study.

Differential equations. --- Sequences (Mathematics). --- Dynamics. --- Nonlinear theories. --- Algebraic fields. --- Polynomials. --- Differential Equations. --- Sequences, Series, Summability. --- Applied Dynamical Systems. --- Field Theory and Polynomials. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Algebra --- Algebraic number fields --- Algebraic numbers --- Fields, Algebraic --- Algebra, Abstract --- Algebraic number theory --- Rings (Algebra) --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Mathematical sequences --- Numerical sequences --- 517.91 Differential equations --- Differential equations --- Equacions diferencials --- Successions (Matemàtica) --- Dinàmica --- Teories no lineals --- No linealitat (Matemàtica) --- Problemes no lineals --- Anàlisi funcional no lineal --- Anàlisi matemàtica --- Càlcul --- Física matemàtica --- Caos (Teoria de sistemes) --- Equacions diferencials no lineals --- Ones no lineals --- Oscil·lacions no lineals --- Sistemes no lineals --- Solitons --- Anàlisi de sistemes --- Cinètica --- Matemàtica --- Mecànica analítica --- Aerodinàmica --- Cinemàtica --- Dinàmica molecular --- Electrodinàmica --- Estabilitat --- Matèria --- Moviment --- Moviment rotatori --- Pertorbació (Matemàtica) --- Teoria quàntica --- Termodinàmica --- Estàtica --- Física --- Energia --- Mecànica --- Seqüències (Matemàtica) --- Seqüències numèriques --- Successions numèriques --- Àlgebra --- Sèries (Matemàtica) --- Successions espectrals (Matemàtica) --- Sumabilitat --- Sumes exponencials --- Funcions de Bessel --- Àlgebra diferencial --- Càlcul integral --- Càlcul operacional --- Equacions d'evolució --- Equacions de camp d'Einstein --- Equacions de Lagrange --- Equacions de Pfaff --- Equacions diferencials algebraiques --- Equacions diferencials ordinàries --- Equacions en derivades parcials --- Funcions de Green --- Funcions de Lyapunov --- Problemes de contorn --- Problemes inversos (Equacions diferencials) --- Teoria d'estabilitat (Matemàtica) --- Transformació de Laplace --- Sequences (Mathematics)