Fourier series - Euler’s formulae - Dirichlet’s conditions - Change of interval - Half range series – RMS value – Parseval’s identity – Computation of harmonics
Eigenvalues and Eigenvectors - Properties of eigenvalues and eigenvectors – Cayley Hamilton theorem - Similarity of transformation - Orthogonal transformation and nature of quadratic form
SOLUTION OF ORDINARY DIFFERENTIAL EQUATION
Linear second-order ordinary differential equation with constant coefficients – Solutions of homogenous and non-homogenous equations - Method of undetermined coefficients – method of variation of parameters – Solutions of Cauchy-Euler and Cauchy-Legendre differential equations
SIAM's Playlist: Introduction and Homogeneous Differential Equations , Method of Undetermined Coefficients,Method of Variation of Parameters , Cauchy Euler and Cauchy Legendre Differential Equations (Part - 1), Cauchy Euler and Cauchy Legendre Differential Equations (Part - 2) , Application of Differential Equation in Electric Circuits , Application of Differential Equations in Spring Mass System
SOLUTION OF DIFFERENTIAL EQUATION THROUGH LAPLACE TRANSFORM AND MATRIX METHOD
Solution of differential equations through Laplace transform and matrix method: Solution of ODE’s, Nonhomogeneous terms involving Heaviside function, Impulse, function, Solving nonhomogeneous system using Laplace transform, Reduction of nth order differential equation to the first-order system, Solving nonhomogeneous system of first-order differential equations.
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SIAM's Playlist: Solution of Differential Equations - Introduction and Formulae, Solution of Differential Equations using Laplace Transform,Solution of Differential Equations with Unit Step Function,Solution of Differential Equations with Unit Impulse Function,Solving System of Differential Equations using Matrix method - 1,Solving System of Differential Equations using Matrix Method - 2,Solving System of Differential Equations using Diagonalization Method,Reduction of ODEs from nth order to first order
STRUM LIOUVILLE'S PROBLEMS AND POWER SERIES SOLUTIONS
The Strum-Liouville’s Problem - Orthogonality of Eigenfunctions - Series solutions of differential equations about ordinary and regular singular points - Legendre differential equation - Bessel’s differential equation.
SIAM's Playlist: Introduction, Strum-Liouville's problem, Reduction in SLP part -1 and part-2, Power Series and problems, Legendre Differential Equation, Frobenius Equation and problems part 1 and 2, Bessel's Differential Equation
Z-transform -transforms of standard functions - Inverse Z-transform: by partial fractions and convolution method
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Difference equation - First and second-order difference equations with constant coefficients- Fibonacci sequence - Solution of difference equations - Complementary function -Particular integral by the method of undetermined coefficients - Solution of simple difference equations using Z-transform
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