194 Views

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

133 Views

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

117 Views

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

111 Views

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

89 Views

Homogeneous linear equations with constant coefficients.

113 Views

Method of undetermined coefficients-superposition approach.

106 Views

Undetermined coefficient: Annihilator operator approach.

89 Views

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

91 Views

Variation of parameters method for higher-order equations.

102 Views

Applications of second order differential equation.

63 Views

Differential equations with variable coefficients, Cauchy- Euler equation.

92 Views

Cauchy-Euler equation: Alternative method of solution.

104 Views

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

101 Views

Power series solution of a differential equation.

104 Views

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

69 Views

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

79 Views

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

103 Views

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

86 Views

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

99 Views

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

103 Views

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

70 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.

70 Views

The Eigenvalue problem, Eigenvalues and Eigenvectors.

102 Views

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

88 Views

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

93 Views

Homogeneous linear systems, Eigenvalues and Eigenvectors.

92 Views

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