CHER-2115( Calculus-III)

Calculus III:

1. Vector-valued functions of a single variable: Limits, derivatives and integrals of vector valued functions.

2. Tangent lines to graphs of vector-valued functions . Arc length from vector view point. Arc length parametrization.

3. Curvature of plane and space curves: Curvature from intrinsic equations, Cartesian equations and parametric equations. Radius of curvature. Centre of curvature,

4. Partial Differentiation: Functions of several variables. Graphs of functions of two variables. Limits and continuity. Partial derivatives. Differentiability, linearization and differentials. The Chain rule. Partial derivatives with constrained variables. Directional derivatives; gradient vectors and tangent planes.

5. Extrema of functions of several variables, Lagrange multipliers. Taylor’s formula.