Differential calculus : Functions, composition of two functions and inverse of a function, limit, continuity, derivative, chain rule, derivatives of implicit functions and of functions defined parametrically. Rolle’s Theorem and Lagrange’s Mean Value theorem (statement only). Their geometric interpretation and elementary application. L’Hospital’s rule (statement only) and applications. Second order derivative।
Formulation and solution of differential equations of the forms,
(1) [tex]{{dy} \over {dx}} = f(x)g(y)[/tex]
(2) [tex]{{dy} \over {dx}} = f\left( {{y \over x}} \right)[/tex]
(3) [tex]{{dy} \over {dx}} = {{ax + by} \over {cx + ey}}[/tex]
(4) [tex]{{dy} \over {dx}} = {{({a_1}x + {b_1}y + {c_1})} \over {{a_2}x + {b_2}y + {c_2}}}[/tex] [tex]({{{a_1}} \over {{a_2}}} = {{{b_1}} \over {{b_2}}})[/tex]
(5) [tex]{{dy} \over {dx}} + P(x)y = Q(x)[/tex]
(6) [tex]{{{d^2}y} \over {{d^2}x}} + {P_1}{{dy} \over {dx}} + {P_2}y = 0[/tex]
(7) [tex]{{{d^2}y} \over {{d^2}x}} = f(x)[/tex]
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