Credit Structure: 2 0 2 6

Review of the prerequisites such as limits of sequences and functions, continuity, uniform continuity and differentiability. Rolle's theorem, mean value theorems and Taylor's theorem. Newton's method for approximate solution. Riemann integral and the fundamental theorem of integral calculus. Approximate integration. Applications to length, area, volume, surface area of revolution. Moments, centres of mass and gravity.

Review of vectors. Cylinders and quadric surfaces. Vector functions of one variable and their derivatives.

Partial derivatives. Chain rule. Gradient, directional derivative.

Repeated and multiple integrals with applications to volume, surface area, moments of inertia etc.

**Texts / References**

T.M. Apostol, Calculus, Vol. I, 2nd ed., Wiley Eastern, 1980.

G.B. Thomas and R.L. Finney, Calculus and Analytic Geometry, 9^{th} ed.,
ISE reprint, Addison-Wesley, 1998.