# NOTE:

#### FOURIER SERIES

Fourier series - Euler’s formulae - Dirichlet’s conditions - Change of interval - Half range series – RMS value – Parseval’s identity – Computation of harmonics

SIAM's Playlist: Euler's Formula, RMS Value , Even and Odd Function , Parseval's Identity , Half range sine and cosine series , Computation of Harmonics

#### MATRICES

Eigenvalues and Eigenvectors - Properties of eigenvalues and eigenvectors – Cayley Hamilton theorem - Similarity of transformation - Orthogonal transformation and nature of quadratic form

Refer to Videos : 12 ,14,16, 18, 20

SIAM's Playlist: Introduction to Matrices ,Eigen Value and Eigen Vector , Cayley Hamilton Theorem(CHT),Diagonalisation , , Important Questions and Solutions,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

Refer to Videos : 1 - 12, 88 - 96

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.

Refer to Videos : 12

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.

Refer to Videos : Lec-24, Lec-25, 1 - 2, 1 - 8

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

Z-transform -transforms of standard functions - Inverse Z-transform: by partial fractions and convolution method

Refer to NOTES here

SIAM's Playlist: Z-transform Introduction, Properties of Z-transform, Problems on Z-transform, Inverse Z transform - Convolution Method and Partial Fraction Method

#### DIFFRENCE EQUATIONS

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

Refer to NOTES here

Refer to Videos : Difference Equation or Watch this, Fibonacci sequence, Particular integral by the method of undetermined coefficients, 23 - 24

SIAM's Playlist: Introduction, Difference Equation, CF and PI, Solution of Difference Equations-Z transform