697 Views

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

417 Views

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

413 Views

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

398 Views

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

390 Views

Homogeneous linear equations with constant coefficients.

357 Views

Method of undetermined coefficients-superposition approach.

399 Views

Undetermined coefficient: Annihilator operator approach.

331 Views

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

367 Views

Variation of parameters method for higher-order equations.

361 Views

Applications of second order differential equation.

465 Views

Differential equations with variable coefficients, Cauchy- Euler equation.

394 Views

Cauchy-Euler equation: Alternative method of solution.

341 Views

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

345 Views

Power series solution of a differential equation.

333 Views

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

320 Views

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

355 Views

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

435 Views

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

307 Views

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

380 Views

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

324 Views

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

314 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.

340 Views

The Eigenvalue problem, Eigenvalues and Eigenvectors.

355 Views

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

351 Views

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

436 Views

Homogeneous linear systems, Eigenvalues and Eigenvectors.

406 Views

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