Real and Complex Analysis (Code09050601)
S.No.  Content of the topics  Learning Objectives  Teaching Guidelines  Methodology  Time (Hours) 
1 
· Jacobians, Beta and Gama functions.
· Double and Triple integrals. · Dirichlets integrals, · Change of order of integration in double integrals.

Student will be able to understand the Jacobians, Double and Triple integrals,  Lecture should be effective so that student will be able to grasp the topics easily  Assignments/ Seminars/ Class tests/ Presentations 
15 
2 
· Fourier exceptional of piecewise monotonic functions.
· Properties of Fourier Coefficient, · Dirichlets conditions, Parseval’s identity for Fourier series. · Fourier series for odd and even functions. · Half range series, change of intervals. 
Student will be able to understand the Fourier Series  Lecture should be effective so that student will be able to grasp the topics easily  Assignments/ Seminars/ Class tests/ Presentations 
15 
3 
· Extended Complex plane.
· Stereographic projection of complex numbers. · Continuity and differentiability of complex functions. · Analytic functions, Cauchy –Riemann equations. · Harmonic functions. 
Student will be able to understand the Extended Complex plane  Lecture should be effective so that student will be able to grasp the topics easily  Assignments/ Seminars/ Class tests/ Presentations 
15 
4 
· Mapping by elementary functions,
· Translation. rotation, Magnification and Inversion. · Conformal mappings · Mobius transformations · Fixed points, Cross ratio, inverse Point and critical mappings 
Student will be able to understand the Mapping by elementary functions  Lecture should be effective so that student will be able to grasp the topics easily  Assignments/ Seminars/ Class tests/ Presentations 
15 