Title Real and Complex Analysis (Code 09010601)

S.N |
Unit |
Content |
Learning Objective |
Teaching Guidelines |
Methodology |
Time (Hrs) |

1 | One | · Jacobians, Beta and Gama functions.
· Double and Triple integrals. · Dirichlets integrals, · Change of order of integration in double integrals. · Fourier expentionof piecewise monotonic functions. · Properties of Fourier Co-efficient, · Dirichlets conditions, Parseval’s identity for Fourier series. · Fourier series for odd and even functions. · Half range series,change of intervals. |
Study of Jacobians, Double and Triple integrals, and Fourier Series | Lecture should be so effective so that the students can grasp the topic easily | Lecture
Seminar Discussion Assignments Seminar Class Tests |
15 |

2 | Two | · Extended Complex plane.
· Stereographic projection of complex numbers. · Continuity and differentiability of complex functions. · Analytic functions, Cauchy –Riemann equations. · Harmonic functions. |
Study of Extended Complex plane | Lecture should be so effective so that the students can grasp the topic easily | Lecture
Seminar Discussion Assignments Seminar Class Tests |
15 |

3 | Three | · Mapping by elementary functions,
· Translation. rotation, Magnification and Inversion. · Conformal mappings · Mobius transformations · Fixed points, Cross ratio, inverse Point and critical mappings |
Study of Mapping by elementary functions | Lecture should be so effective so that the students can grasp the topic easily | Lecture
Seminar Discussion Assignments Seminar Class Tests |
15 |