MA5370 MULTIVARIABLE CALCULUS


Course Details

Differential Calculus: Functions of several variables, Open sets, Limits and continuity, Derivatives of a scalar field with respect to a vector, Directional derivatives, Partial derivatives, Total derivative, Gradient of a scalar field, Level sets and tangent planes, Derivatives of vector fields, Chain rules for derivatives, Derivatives of functions defined implicitly, Higher order derivatives, Taylor’s theorem.
Applications of Differential Calculus: Maxima, Minima, Saddle points, Stationary points, Lagrange's multipliers, Inverse function theorem, Implicit function theorem.
Line Integrals: Paths and line integrals, Fundamental theorems of calculus for line integrals, Vector fields and gradients.
Multiple Integrals: Double and triple integrals, Iterated integrals, Change of variables formula, Applications to area and volume, Green's theorem, Two-dimensional vector fields and gradients.
Surface Integrals: Parametric representation of a surface, Fundamental vector product and normal to a surface, Stokes' theorem, Curl and divergence of a vector field, Gauss' divergence theorem.

Course References:

Text Books:
1. T.M.Apostol, Calculus Vol. II, 2nd Ed., John Wiely & Sons, 2003. [Ch. 8, 9, 10, 11, 12.]
2. T.M.Apostol, Mathematical Analysis, 2nd Ed., Narosa Pub. House, 1997. [Sec. 13.2, 13.3, 13.4]
References:
1. D.V.Widder, Advanced Calculus, 2nd Ed., PHI Learning, 1987.
2. M.R.Spiegel, Vector Analysis, Schaum's Outline Series, Mc-Graw Hill, 1959.
3. H.M.Edwards, Advanced Calculus-A Differential Forms Approach, Birkhauser, 1994.