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Syllabus Core-13 Metric Spaces and Complex Analysis ,Bsc 6th sem Mathematics Dibrugarh University CBCS

 Core-13 Metric Spaces and Complex Analysis ,Bsc 6th sem Mathematics  Dibrugarh University CBCS ,Syllabus

                                        C6.1 Metric Spaces and Complex Analysis

                                             Total Marks: 100, Theory: 80, IA: 20,

                                                    Credit: 5+1=6;

                                                        (L=5, P=0, T=1)

 Visit to Dibrugarh University officiall website for Syllabus-HERE

Objectives: After going through this course the students will be able to describe

various properties of metrics paces

complex number system, its differentiation and integration.

 

Unit-1                                                                                                                Marks: 20, Contact hrs:20

Metric spaces: definition and examples. Sequences in metric spaces, Cauchy sequences. Complete Metric Spaces.

Open and closed balls, neighbourhood, open set, interior of a set. Limit point of a set, closed set, diameter of a set,

Cantors theorem. Subspaces, dense sets, separable spaces.

 

Unit-2                                                                                                                      Marks: 15, Contact hrs:15

ontinuous mappings, sequential criterion and other characterizations of continuity. Uniform continuity.

Homeomorphism, Contraction mappings, compactness Banach Fixed point Theorem. Connectedness, connected              subsets of R.

 

Unit-3                                                                                                                 Marks: 15, Contact hrs: 20

Limits, Limits involving the point at infinity, continuity. Properties of complex numbers, regions in the complex

plane, functions of complex variable, mappings. Derivatives, differentiation formulas, Cauchy-Riemann equations,

sufficient conditions for differentiability.

 

Unit-4                                                                                                                Marks: 12, Contact hrs:15

Analytic functions, examples of analytic functions, exponential function, Logarithmic function, trigonometric  function, derivatives of functions, definite integrals of functions. Contours, Contour integrals and its examples,upper bounds for moduli of contour integrals. Cauchy- Goursat theorem, Cauchy integralformula

.

Unit-5 Marks: 10,                                                                                                                       Contact hrs:10

Liouvilles theorem and the fundamental theorem of algebra. Convergence of sequences and series, Taylor series   and its examples.

 

Unit-6 Marks:                                                                                           08, Contact hrs:10

Laurent series and its examples, absolute and uniform convergence of power series.

Text Books:

 

1. S. Kumaresan, Topology of Metric Spaces, 2nd Ed., Narosa Publishing House,2011.

2. G.F. Simmons, Introduction to Topology and Modern Analysis, McGraw-Hill,2004.

3. J. W. Brown and R. V. Churchill, Complex Variables and Applications, 8th Ed., McGraw Hill

International Edition,2009.

Reference Books:

1. S. Shirali and H. L. Vasudeva, Metric Spaces, Springer Verlag, London, 2006.

2. J. Bak and D. J. Newman, Complex Analysis, 2nd Ed., Undergraduate Texts in Mathematics, Springer-Verlag


       RECOMENDED YOUR TEXT BOOK IF ANY BUY            


New York, Inc., New York,1997.

              DOWONLOAD TO  SYLLABUS IN PDF MODE            

                                                CLICK ME

Core-13 Metric Spaces and Complex Analysis ,Bsc 6th sem Mathematics  Dibrugarh University CBCS


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