Page 79 - CatalogNEP-PS

*TUTORIAL (15 Hours (1 Hour per week))

SUGGESTED READINGS:

1. James Ward Brown and Ruel V. Churchill, Complex Variables and Applications, 8th Ed.,
McGraw – Hill International Edition, 2009.
2. Joseph Bak and Donald J. Newman, Complex analysis, 2nd Ed., Undergraduate Texts in
Mathematics, Springer-Verlag New York, Inc., New York, 1997.
3. Walter Ruddin, Real and Complex Analysis, McGraw-Hill International Editions, 3/e,
1987.
4. Ahifors.L. V., Complex Analysis., McGraw Hill, New York, 2/e,1983.
5. S.Ponnusamy : Foundations of Complex Analysis, Narosa Pub, `97.
6. Kasana H.S., Complex Variables: Theory and Applications, Prentice-Hall of India Pvt.
Ltd, 2ndedition, 2005.
7. Complex Analysis, Spectrum Publication, Jalandhar.

Math.324 Multivariate Calculus 3+1*

LEARNING OBJECTIVES:

The primary objective of this course is to introduce:
 The extension of the studies of single variable differential and integral calculus to
functions of two or more independent variables.
 The geometry and visualisation of curves and surfaces in two dimensions (plane) and
26. three dimensions (space).
 The techniques of integration to functions of two and three independent variables.
 The applications of multivariate calculus tools to physics, economics, optimization etc.

LEARNING OUTCOMES:

This course will enable the students to: S
 Learn the conceptual variations when advancing in calculus from one variable to
multivariable discussion.
 Understand the maximization and minimization of multivariable functions subject to the
given constraints on variables.
 Learn about inter-relationship amongst the line integral, double, and triple integral
formulations.
 Familiarize with Green's, Stokes' and Gauss divergence theorems, and learn applications.

THEORY (45 Hours)

UNIT – I: Calculus of Functions of Several Variables (18 Hours)

Basic concepts, Limits and continuity, Partial derivatives, Tangent planes, Total differential,
Differentiability, Chain rules, Directional derivatives and the gradient, Extrema of functions of
two variables, Method of Lagrange multipliers with one constraint.

UNIT – II: Double and Triple Integrals (15 Hours)
Double integration over rectangular and nonrectangular regions, Double integrals in polar
coordinates, Triple integrals over a parallelopiped and solid regions, Volume by triple integrals,
Triple integration in cylindrical and spherical coordinates, Change of variables in double and
triple integrals.

UNIT – III: Green's, Stokes' and Gauss Divergence Theorem (12 Hours)

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