Hey Guys, Welcome to our website, where I discuss the M.S.C syllabus related to Complex analysis. This is mainly for WBSU, but similar to other universities also. This gives you an overall view of the M.sc course.
After that, I mention some useful books suggested by my professors, which will give you a guide in m.sc and various competitive exams.
In postgraduate mathematics, Complex Analysis appears in 1st semester in various colleges under WBSU. But the other college under WBSU may not follow the syllabus. Total marks of algebra for 1st semester is 50, during 6 months of 1st semester this 50 marks subdivided into internal three topics which are-
- Midterm exam: It will occur generally on the head of 3 months of 1st semester. This mod term consists of 5 marks. But teachers took 20 or 15 marks exam and make a percent out of 5. For example, if you get 10 out of 20 then you get 2.5 out of 5.
- Student Lecture/viva: It consists of 5 marks. Students choose a topic sweetly for them and make a presentation with the help of PowerPoint, python, MathType e.t.c on the computer and present in front of the teacher. The teacher can ask questions during the presentation.
- The final exam consists of 40 marks for 2 hours.
- Syllabus of WBSU:
Riemann’s sphere, the point at infinity, and the extended complex plane.
Functions of a complex variable, limit, and continuity. Analytic functions. Cauchy-Riemann equations. Complex integration, Cauchy’s fundamental theorem statement only) and its consequences. Cauchy’s integral formula.
Derivative of an analytic function. Morera’s theorem. Cauchy’s inequality. Liouville’s theorem. Fundamental theorem of classical algebra.
Uniformly convergent series of analytic functions. Power series. Taylor’s theorem. Laurent’s theorem.
Zeros of an analytic function. Singularities and their classification. Limit points of zeros and poles. Riemann’s theorem. Weierstrass-Casorati theorem. Theory of residues. Argument principle. Rouche’s theorem. Maximum
modulus theorem. Schwarz lemma. The behavior of a function at the point at infinity.
Contour integration. Conformal mapping. Bilinear transformation. The idea of analytic continuation. Multivalued functions-branch point. The idea of winding number.
- WBSU Previous Year Question Papers:
- Some Useful Books:
1) Complex Variable by Murray R.Spiegel,Seymour Lipschutz,John J.Schiller & Dennis Spellman (Schaums Outline series):
2) Complex Analysis by Serge Lang:
3) Functions of One Complex Variable by John B.Conway:
4) Complex Variable with Application by S.Ponnusamy and Herb Silverman:
5) Complex Variables by James Ward Brown & Ruel V.Churchill:
6) Function of Complex Variable by E.T. Copson:
https://drive.google.com/file/d/1JDADc74-a4c4_MzYl41HdcDBsm8v9AS1/view?usp=drivesdk
Visit,
for postgraduate free textbook pdf of various topics for the 2nd and 3rd semester respectively.
To view another page click on "Home" above. Thank you.
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- Syllabus of WBSU:
Riemann’s sphere, the point at infinity, and the extended complex plane.
Functions of a complex variable, limit, and continuity. Analytic functions. Cauchy-Riemann equations. Complex integration, Cauchy’s fundamental theorem statement only) and its consequences. Cauchy’s integral formula.
Derivative of an analytic function. Morera’s theorem. Cauchy’s inequality. Liouville’s theorem. Fundamental theorem of classical algebra.
Uniformly convergent series of analytic functions. Power series. Taylor’s theorem. Laurent’s theorem.
Zeros of an analytic function. Singularities and their classification. Limit points of zeros and poles. Riemann’s theorem. Weierstrass-Casorati theorem. Theory of residues. Argument principle. Rouche’s theorem. Maximum
modulus theorem. Schwarz lemma. The behavior of a function at the point at infinity.
Contour integration. Conformal mapping. Bilinear transformation. The idea of analytic continuation. Multivalued functions-branch point. The idea of winding number.
- WBSU Previous Year Question Papers:
- Some Useful Books:
1) Complex Variable by Murray R.Spiegel,Seymour Lipschutz,John J.Schiller & Dennis Spellman (Schaums Outline series):
2) Complex Analysis by Serge Lang:
3) Functions of One Complex Variable by John B.Conway:
4) Complex Variable with Application by S.Ponnusamy and Herb Silverman:
5) Complex Variables by James Ward Brown & Ruel V.Churchill:
6) Function of Complex Variable by E.T. Copson:
https://drive.google.com/file/d/1JDADc74-a4c4_MzYl41HdcDBsm8v9AS1/view?usp=drivesdk
Visit,
for postgraduate free textbook pdf of various topics for the 2nd and 3rd semester respectively.
To view another page click on "Home" above. Thank you.
