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MATHEMATICAL MODELING AND ORDINARY DIFFERENTIAL EQUATIONS

MATHEMATICAL MODELINGANDORDINARY DIFFERENTIAL EQUATIONSI-Liang ChernDepartment of MathematicsNational Taiwan University2007, 2015 January 6, 20162 Contents1 First-Order Single DIFFERENTIAL is MATHEMATICAL MODELING ? .. and Equilibria .. population dynamics of single species .. to solve single first-order EQUATIONS .. first-order equation .. of variables .. special classes that are solvable .. Fields and Family of Curves .. Fields .. of curves and Orthogonal trajectories .. *Envelop.. *An example from thermodynamics existence of entropy .. and Uniqueness .. *Numerical Methods: First Order Difference EQUATIONS .. method .. difference equation .. Note ..392 Second Order Linear for linear oscillators .. spring-mass system .. circuit system .. to solve homogeneous EQUATIONS .. EQUATIONS (complex case).. equation (real case) .. to solve Inhomogeneous EQUATIONS .

MATHEMATICAL MODELING AND ORDINARY DIFFERENTIAL EQUATIONS I-Liang Chern Department of Mathematics National Taiwan University 2007, 2015 January 6, 2016

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