741 Views

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

450 Views

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

444 Views

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

431 Views

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

422 Views

Homogeneous linear equations with constant coefficients.

384 Views

Method of undetermined coefficients-superposition approach.

440 Views

Undetermined coefficient: Annihilator operator approach.

361 Views

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

397 Views

Variation of parameters method for higher-order equations.

391 Views

Applications of second order differential equation.

517 Views

Differential equations with variable coefficients, Cauchy- Euler equation.

428 Views

Cauchy-Euler equation: Alternative method of solution.

378 Views

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

376 Views

Power series solution of a differential equation.

364 Views

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

350 Views

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

387 Views

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

471 Views

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

341 Views

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

414 Views

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

357 Views

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

344 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.

369 Views

The Eigenvalue problem, Eigenvalues and Eigenvectors.

388 Views

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

383 Views

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

465 Views

Homogeneous linear systems, Eigenvalues and Eigenvectors.

441 Views

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