Transcription of Matrix Methods for Linear Systems of Differential Equations
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Matrix Methods for Linear Systems of Differential Equations
Matrix Methods for Linear Systems of Differential EquationsWe now present an application of Matrix Methods to Linear Systems of Differential Equations . We shallfollow the development given in Chapter 9 ofFundamentals of Differential Equations and BoundaryValue Problemsby Nagle, Saff, Snider, third of MatricesIf we allow the entriesaij t in ann nmatrixA t to be functions of the variablet,thenA t is amatrix function of t. Similarly if the entriesxi t of a vectorx t are functions oft,thenx t is avectorfunction of t. A matrixA t is said to becontinuous at t0if eachaij t is continuous t isdifferentiable at t0if eachaij t is differentiable att0and we writedAdt t0 A t0 aij t0 n nAlso abA t dt abaij t dtn nWe have the following differentiation formulas for matricesddt CA CdAdt,Ca constant matrixddt A B dAdt dB
Matrix Methods for Linear Systems of Differential Equations We now present an application of matrix methods to linear systems of differential equations.
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