260 Views

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

179 Views

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

166 Views

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

163 Views

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

142 Views

Homogeneous linear equations with constant coefficients.

144 Views

Method of undetermined coefficients-superposition approach.

160 Views

Undetermined coefficient: Annihilator operator approach.

124 Views

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

133 Views

Variation of parameters method for higher-order equations.

152 Views

Applications of second order differential equation.

111 Views

Differential equations with variable coefficients, Cauchy- Euler equation.

144 Views

Cauchy-Euler equation: Alternative method of solution.

153 Views

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

126 Views

Power series solution of a differential equation.

136 Views

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

116 Views

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

123 Views

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

148 Views

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

122 Views

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

138 Views

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

136 Views

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

123 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.

133 Views

The Eigenvalue problem, Eigenvalues and Eigenvectors.

144 Views

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

150 Views

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

172 Views

Homogeneous linear systems, Eigenvalues and Eigenvectors.

168 Views

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