Applications of Differential and Difference Equations (MAT2002)
Credits : 4
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