EM 212

On successful completion of the course, the students should be able to;

1. Sketch level curves and level surfaces of functions of two and three variables, and sketch their surfaces and solids.
2. Compute double and triple integrals of scalar functions over any given 2D and 3D regions.
3.  Compute gradient, divergence and curl of a given functionusing orthogonal. curvilinear coordinates and to solve related problems using cylindrical and spherical coordinates.
4. Evaluate line, surface and volume integrals of continuous scalar and vector fields over a given domain and apply integral theorems.

1. Functions of several variables : Sketching level curves and level surfaces of functions of two and three variables, sketching surfaces and volumes, limit, and continuity of functions of two and three variables;Tangent planes, gradient vector and directional derivative, scalar line integrals.
2. Double and Triple Integration : Definitions of double and triple integrals, double and triple integrals over rectangular domains,double and triple integrals over any general domains;cylindrical and spherical polar coordinates, Jacobian and its properties, applications of double and triple integrals(change of coordinates). 
3. Vector Fields and Vector Operators : Scalar fields and vector fields, gradient,divergence and curl and theirgeometrical and physical interpretations. 
4. Vector and complex line integra : Line integrals of vector valued functions and path independency of line integrals, simply connected domains and conservative vector fields, Cauchy-Riemann equations and line integrals of complex valued functions, complex line integrals over simply connected domains and Cauchy’s theorem.
5. Orthogonal curvilinear coordinates, Surface integrals and Integral Theorems : Greens Theorem on the plane ,surface integrals of scalar fields and vector fields;Stokes’ theorem and divergence theorem,area and volume elements in terms of orthogonal curvilinear coordinates;Surface integrals with orthogonal curvilinear coordinates ,applications of integral theorems in terms of orthogonal curvilinear coordinates.

1. James Stewart, Calculus,5thedition, (2006), Thomson Books/Cole. 
2. Watson Fulks ,Advanced Calculus an Introduction to Analysis,3rd Edition,(1978),John Wiley & SonsInc. 
3. E. B. Saff and A. D. Sinder ,Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics, 3rd edition,(2014), Pearson Education Ltd.