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Curriculum | Real and Complex Analysis (Code-09050601)

Real and Complex Analysis (Code-09050601)

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 Co-efficient,

·         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

Admission Open- 2018