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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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Classification of differential equations: Open solution, closed solution, initial value problems, existence and uniqueness of solution
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2
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First order ordinary differential equations: Separable differential equations, exact differential equations
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3
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Integral factor and reducible equations, first order linear differential equations, Bernoulli differential equations
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4
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First order homogeneous equations, special transformations. Riccati equation, applications of first order differential equations
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5
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Theory of higher order homogeneous linear differential equations, linear dependence and independence, nonhomogeneous linear differential equations
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6
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Reduction of order. Homogeneous linear equations with constant coefficients
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7
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Solution of non-homogeneous differential equations: Indefinite coefficients method, method of changing parameters
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8
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Cauchy Euler differential equations, Laplace transforms: Definition and properties of Laplace transform
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9
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Inverse Laplace transforms. Solution of initial value problems by Laplace transform method
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10
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Series solutions of differential equations: Power series solutions: Solution around ordinary point
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11
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Systems of linear differential equations: Differential operators, operator method and Laplace transform method
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12
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Fourier series for periodic functions
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13
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Fourier cosine and sine series-I
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14
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Fourier cosine and sine series-II
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