Course No

M306

Credit

4

Syllabus

Differentiability of functions from an open subset of R n to R m and properties, chain rule, partial and directional derivatives, Continuously differentiable functions, Inverse function theorem, Implicit function theorem, Interchange of order of differentiation, Taylor’s series, Extrema of a function, Extremum problems with constraints, Lagrange multiplier method with applications, Integration of functions of several variables, Change of variable ormula (without proof) with examples of applications of the formula, spherical coordinates, Stokes theorem (without proof), Deriving Green’s theorem, Gauss theorem and Classical Stokes theorem.

Text Books

- W. Fleming, “Functions of Several Variables”, Undergraduate Texts in Mathematics. Springer-Verlag, 1977.
- T. M. Apostol, “Calculus Vol. II”, Wiley-India edition, 2009.

Reference Books

- W. Kaplan, “Advanced Calculus”, Addison-Wesley Publishing Company, 1984.
- T. M. Apostol, “Mathematical Analysis”, Narosa Publishing House, 2013.