3rd(maths…)

Maths 3^rd sem

Group A(differential calculus)

Unit I:-  limit, Cauchy’s criterion for existence of limit(without proof), problems on limits, continuity, problems on continuity, bounded function-l.u.b, g.i.b, properties of continuous and bounded function, Differentiability, problems on differentiability, relation between continuity and differentiability, Successive differentiation-standard cases, Leibnitz’s theorem and its application in simple cases,

Unit II:- Intermediate forms-0, ………………………………………………..

Application of L’s hospitals theorems, Rolle’s theorem, Lagranges and cauchy’s form of mean value theorem, statement and application of Taylor’s and Maclaurin’s theorem’s,  Taylor’s and Maclaurin’s series, expansions of functions ……………………………………, maxima and minima for function of one variable, necessary and suffuciant condition for maxima and minima.

Unit III:-  function of two or more variables-partial derivatives , Euler’s theorem(proof for two variables only and problems for two and three variable).

Tangents, normal:- Equation and properties of tangent and normal, sub-tangent and subnormal’s of Cartesian and polar curves, Geometrical problems, simple problems of two variable.

Group B:-(integral calculus)

Unit I:-  definition and properties of definite integrals, fundamental theorems, reduction formula.

Unit II:- significance of plane curves-Cartesian and polar curves, area bounded by plane curves- Cartesian and polar curves, volumes and surface area of solids of revolution about axes- Cartesian curves