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Week
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Topics
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Study Metarials
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1
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Definition of differential equation and classification of differential equations, first order differential equations, linear equations, separable equations
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2
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Exact differential equations and integrating factors, existence and uniqueness theorem Bernoulli equation, special integrating factors and transformations
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3
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Higher order linear homogeneous equations with constant coefficients, characteristic equation, fundamental solutions, linear independence and Wronskian
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4
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Complex roots and repeated roots, reduction of order
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5
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Higher order nonhomogeneous equations, method of undetermined coefficients
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6
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The method of variation of parameters, Cauchy-Euler equation
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7
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Physical models and applications
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8
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Series solutions near an ordinary point
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9
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Series solutions near a regular singular point, Frobenius method
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10
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Laplace transform
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11
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Convolution integral, solution of initial value problems
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12
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Systems of first order linear homogeneous differential equations with constant
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13
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Coefficients, fundamental matrices, complex and repeated eigenvalues
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14
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Nonhomogeneous systems of linear differential equations
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