MA 103  Mathematics I                                                                                                                   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. Tangent planes and normals. Maxima, minima, saddle points. Lagrange multipliers. Exact differentials.

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

Texts/References

• G.B. Thomas, and R.L. Finney, Calculus and Analytic Geometry, 6th Ad., Addison-Wesley/ Narosa, 1985.

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