MA1101 Functions of Several Variables


Objectives:

Functions of two and three variables:Regions in plane, level curves and level surfaces, limit, continuity, partial derivatives, directional derivatives and gradient, normal to level curves and tangents, extreme values, Lagrange multipliers, double integral and iterated integral, volume of solids of revolution, approximation of volume, triple integral, change of variables, multiple integrals in cylindrical and spherical coordinates.

Course Contents:

Vector calculus:Gradient, Divergence, Curl, Line integral, conservative fields, Green’s theorem, surface area of solids of revolution, surface area, surface integral, Triple integrals and Gauss Divergence theorem, Stokes’ theorem.

Text Books:

G.B. Thomas Jr., M.D. Weir and J.R. Hass, Thomas Calculus, Pearson Education, 2009..

Reference Books:

1. E. Kreyszig, Advanced Engineering Mathematics, 10th Ed., John Willey & Sons, 2010.

2. N. Piskunov, Differential and Integral Calculus Vol. 1-2, Mir Publishers, 1974.

3. G. Strang,Calculus, Wellesley-Cambridge Press, 2010.4. J.E. Marsden, A.J. Tromba, A. Weinstein, Basic Multivariable Calculus, Springer Verlag, 1993.