1332 Views

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

950 Views

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

946 Views

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

1065 Views

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

969 Views

Homogeneous linear equations with constant coefficients.

882 Views

Method of undetermined coefficients-superposition approach.

1027 Views

Undetermined coefficient: Annihilator operator approach.

839 Views

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

954 Views

Variation of parameters method for higher-order equations.

930 Views

Applications of second order differential equation.

1109 Views

Differential equations with variable coefficients, Cauchy- Euler equation.

891 Views

Cauchy-Euler equation: Alternative method of solution.

953 Views

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

867 Views

Power series solution of a differential equation.

884 Views

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

819 Views

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

957 Views

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

1033 Views

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

838 Views

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

913 Views

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

810 Views

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

960 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.

830 Views

The Eigenvalue problem, Eigenvalues and Eigenvectors.

819 Views

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

1184 Views

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

936 Views

Homogeneous linear systems, Eigenvalues and Eigenvectors.

1333 Views

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