221 Views

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

154 Views

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

137 Views

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

135 Views

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

110 Views

Homogeneous linear equations with constant coefficients.

131 Views

Method of undetermined coefficients-superposition approach.

121 Views

Undetermined coefficient: Annihilator operator approach.

98 Views

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

105 Views

Variation of parameters method for higher-order equations.

115 Views

Applications of second order differential equation.

82 Views

Differential equations with variable coefficients, Cauchy- Euler equation.

119 Views

Cauchy-Euler equation: Alternative method of solution.

115 Views

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

123 Views

Power series solution of a differential equation.

115 Views

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

74 Views

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

100 Views

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

124 Views

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

102 Views

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

108 Views

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

115 Views

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

91 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.

83 Views

The Eigenvalue problem, Eigenvalues and Eigenvectors.

120 Views

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

100 Views

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

114 Views

Homogeneous linear systems, Eigenvalues and Eigenvectors.

107 Views

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