(Mathematics) Calculus & Geometry B.Sc 2nd Semester Bihar

Syllabus

Mathematics

MJC-02: Calculus and Geometry

Unit 1                                                                                                                           (Lectures: 12)

Successive differentiation and Leibnitz’s theorem, Maclaurin’s and Taylor’s series of Expansion, Tangent and Normal, Partial differentiation and Euler’s theorem, Total Differential, L’Hospital’s rule, Curvature, Asymptotes. Curve tracing in Cartesian coordinates and polar coordinates of standard curves.

Unit 2                                                                                                                           (Lectures: 12)

Integration of rational and irrational functions. Evaluation of definite integrals, Reduction formulae. Area, Length of plane curves and area bounded by plane curves. Volume and surface area of solid of revolution, Beta and Gamma Functions, Multiple Integrals.

Unit 3                                                                                                                           (Lectures: 10)

Transformation of rectangular axes, General equations of conics and its reduction to the normal form, Equation of the tangent and normal at a point of the Conics.

Unit 4                                                                                                                           (Lectures: 12)

Sphere, Cone, Cylinder, Central conicoid, Paraboloids, Plane section of conicoid, Generating lines, Tangent plane and normal to a conicoid.

Unit 5                                                                                                                           (Lectures: 14)

Scalar triple product and vector triple product, Product of four vectors, Introduction to vector functions, Operations with vector-valued functions, Differentiation and integration of vector functions, Gradient of a scalar and Divergence and Curl of a vector function in Cartesian coordinate.

MIC-02: Calculus and Geometry

Unit 1                                                                                                                           (Lectures: 08)

Successive differentiation and Leibnitz’s theorem, Maclaurin’s and Taylor’s series of Expansion, Partial differentiation and Euler’s theorem, Total Differential, L’Hospital’s rule, Tangent and Normal, Asymptotes. Curvature.

Unit 2                                                                                                                           (Lectures: 08)

Evaluation of definite integrals, Reduction formulae, Length of plane curve and area bounded by plane curves, Volumes and Surface area of solid revolution.

Unit 3                                                                                                                           (Lectures: 07)

Transformation of rectangular axes, General equations of Conic and its Reduction to the normal form, Equation of the tangent and normal at a point of the Conic.

Unit 4                                                                                                                           (Lectures: 07)

Sphere, Cone, Cylinder, Central conicoid. Paraboloids, Plane section of conicoid, Generating lines, Tangent plane and normal to a conicoid.