MATHS I

MA 111                                                                                  No.of hrs/week = 04

                                                                                                No.of credits  = 04

Successive differentiation, polar co-ordinates, polar curves, derivative of arc length, curvature, radius of curvature and evolutes.

Rolles theorem, mean value theorems - Lagrange's and Cauchy's mean value theorems, Taylor's theorem, Mclaurin's development, L'Hospital's Rule and indeterminate forms.

Infinite series, series with positive terms - test of convergence, comparison, D'Alemert's ratio test, Cauchy’s root test, Raabe's test, integral test, alternating series - Leibnitz's rule, power series, centre of convergence and radius of convergence, interval of convergence.

Reduction formula, curve tracing, application of integration to find the area of the plane regions, surface area, arc length, volume of revolution.

Analytical solid geometry - three dimensional coordinate system, direction cosines and its properties, planes, lines, spheres, section of sphere by planes, right circular cone and right circular cylinder.

REFERENCE:

1.Calculus and Analytical Geometry - IV Edn., George B.Thomas, Jr. (1992) Addison Wesley Publications.

2.Calculus & Analytical Geometry - George B.Thomas Jr & Ross L.Finney (1990), Addison Wesley Publications.