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MATHEMATICAL MODELING AND ORDINARY …

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 .. of underdetermined coefficients.

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

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