DIFFERENTIAL EQUATION AND ANALYSIS

Exact Differential equations. Linear differential Equation. Equation reducible to linear form. First order and higher degree equations solvable for x, y and p. Clairaut's differential equations. Orthogonal trajectories.

UNIT II

Linear differential equation with constant coefficient. Operator method to find the particular integral. Linear differential equation of second order. Method of Variation of parameter.

UNIT III

Sequences. Theorem on limit of sequences. Bounded and Monotonic Sequences. Cauchy Sequences. Cauchy's convergence criterion.

UNIT IV

Series of non-negative terms. Comparison test, Cauchy's integral test, Ratio test. Alternating Series, Leibnitz's Theorem, Absolute and conditional convergence. Series of arbitrary terms.