519 Views

Definition of a differential equation, Classification of differential equations, Solution of a differential equation, Existence and uniqueness of solutions.

292 Views

Applications of first order differential equations : Orthogonal trajectories, Population dynamics.

308 Views

Radioactive decay, Newton's law of cooling, Carbon dating.

284 Views

Higher order linear differential equations, Linear differential equation, Non-homogeneous differential equation, Associated homogeneous differential equation.

264 Views

Homogeneous linear equations with constant coefficients.

249 Views

Method of undetermined coefficients-superposition approach.

265 Views

Undetermined coefficient: Annihilator operator approach.

222 Views

Variation of parameters: First order equation, Second order equation.

268 Views

Variation of parameters method for higher-order equations.

261 Views

Applications of second order differential equation.

255 Views

Differential equations with variable coefficients, Cauchy- Euler equation.

281 Views

Cauchy-Euler equation: Alternative method of solution.

238 Views

Power series, Convergence and Divergence, Ratio test, Absolute convergence, Arithmetic of power series.

229 Views

Power series solution of a differential equation.

227 Views

Analytic function, Ordinary and singular point, Polynomial coefficients, Non-polynomial coefficients.

218 Views

Solution about singular points, Regular and Irregular singular points, Frobenius’ theorem, Method of Frobenius-Cases 1: Roots not differing by an integer.

242 Views

Method of Frobenius-Cases II and III: Roots differing by a positive integer and Equal indicial roots.

297 Views

Bessel’s differential equation, Series solution of bessel’s differential equation, Bessel’s function of the first Kind.

219 Views

Legendre’s differential equation, Legendre’s polynomials, Rodrigues formula for legendre’s polynomials, Legendre’s polynomials are orthogonal, Normality condition for legendre’ polynomials.

270 Views

Systems of linear differential equations, Simultaneous differential equations, Systematic elimination: Operator method.

242 Views

Systems of linear first-order equation, The Nth-Order System, Systems reduced to normal form, Degenerate systems.

230 Views

Introduction to Matrices: Matrix, Order of matrix, Square matrix, Equality of matrix, Column matrix, Multiple of matrices, Addition, Difference, Multiplication of Matrices, Zero matrix, Associative, Distributive Laws, Determinant of a matrix.

245 Views

The Eigenvalue problem, Eigenvalues and Eigenvectors.

266 Views

Matrices and systems of linear first-order equations, Initial–value problem.

247 Views

Matrices and systems of linear first-Order equations (continued), Theorem: Existence of a fundamental set, Non-homogeneous systems, Particular integral.

322 Views

Homogeneous linear systems, Eigenvalues and Eigenvectors.

299 Views

Real and repeated eigenvalues, Eigenvalue of multiplicity m,Two and Three.