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# NOTE:

YouTube channel for the course :

Books Needed:

MODULE 1

#### FOURIER SERIES

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

Notes

Refer to Videos : 1 - 3

SIAM's Notes

MODULE 2

#### 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

Notes

SIAM's Notes

MODULE 3

#### 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

Notes

SIAM's Notes

MODULE 4

#### 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

Notes

SIAM's Notes

MODULE 5

#### 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.

Notes

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

SIAM's Notes

MODULE 6

#### Z-TRANSFORM

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

Refer to NOTES here

Refer to Videos : 1 - 5

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

SIAM's Notes

MODULE 7

#### 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

SIAM's Notes

MODULE 8