1547 Views

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

1096 Views

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

1092 Views

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

1350 Views

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

1110 Views

Homogeneous linear equations with constant coefficients.

1033 Views

Method of undetermined coefficients-superposition approach.

1163 Views

Undetermined coefficient: Annihilator operator approach.

975 Views

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

1212 Views

Variation of parameters method for higher-order equations.

1224 Views

Applications of second order differential equation.

1253 Views

Differential equations with variable coefficients, Cauchy- Euler equation.

1034 Views

Cauchy-Euler equation: Alternative method of solution.

1089 Views

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

1010 Views

Power series solution of a differential equation.

1020 Views

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

951 Views

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

1093 Views

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

1173 Views

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

1021 Views

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

1059 Views

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

948 Views

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

1120 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.

962 Views

The Eigenvalue problem, Eigenvalues and Eigenvectors.

967 Views

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

1522 Views

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

1060 Views

Homogeneous linear systems, Eigenvalues and Eigenvectors.

1780 Views

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