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Precize Real Analysis 2 for MSc Mathematics – Panjab University by Dr. G.S. Sandhu, B.K. Aggarwal, and Mohinder Kumar is a comprehensive book covering Complex Analysis-II as per the Panjab University syllabus. It includes detailed chapters on Taylor & Laurent Series, Residue Theorem, Conformal Mappings, Analytic Continuation, Infinite Products, and Special Functions. Designed for MSc students and UGC NET aspirants, this book features theorem proofs, solved examples, and MCQs for exam preparation. Published by First World Publications, it ensures conceptual clarity and high marks in university exams. A must-buy for mastering advanced complex analysis.

Precize Real Analysis 2 for MSc Mathematics – Panjab University by Dr. G.S. Sandhu, B.K. Aggarwal, and Mohinder Kumar is a meticulously crafted textbook designed to cater to the syllabus of MSc Mathematics (Complex Analysis-II) at Panjab University. Published by First World Publications, this book serves as an indispensable resource for postgraduate students, researchers, and aspirants preparing for competitive exams like UGC NET.

Key Features of the Book

1. Unit-Wise Syllabus Coverage – The book is divided into four units, each addressing critical aspects of Complex Analysis as prescribed by Panjab University.

2. Detailed Theoretical Explanations – Concepts like Cauchy’s Residue Theorem, Argument Principle, Open Mapping Theorem, and Schwarz Reflection Principle are explained with mathematical rigor.

3. Solved Examples & Theorems – Each chapter includes step-by-step solutions to reinforce understanding.

4. MCQs for UGC NET Preparation – A dedicated section with Multiple Choice Questions helps students prepare for competitive exams.

5. Real Integrals via Contour Integration – Special emphasis on evaluating real integrals using complex analysis techniques, a crucial topic for exams.

6. Infinite Products & Special Functions – Detailed discussions on Gamma Function, Riemann Zeta Function, Weierstrass’s Elliptic Functions, and their properties.

7. Conformal Mappings & Bilinear Transformations – Applications in mathematical physics and engineering are covered.

8. Analytic Continuation & Monodromy Theorem – Advanced topics essential for higher studies in mathematics.

Who Should Buy This Book?

1. MSc Mathematics Students (Panjab University) – Perfect for semester exams.

2. UGC NET/JRF Aspirants – MCQs and advanced concepts included.

3. Research Scholars – Reference for higher studies in complex analysis.

4. Mathematics Enthusiasts – Deep dive into analytic functions and their applications.

Conclusion

Precize Real Analysis 2 for MSc Mathematics is a must-have textbook for students pursuing MSc Mathematics at Panjab University. With clear explanations, solved examples, and exam-focused content, this book ensures a strong conceptual foundation and high scores in examinations. Whether you are preparing for university exams or competitive tests, this book serves as an ideal companion for mastering Complex Analysis-II.

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0. Preliminaries

1. Taylor and Laurent Series

2. Maximum Modulus Principle and Schwarz’s Lemma

3. Classification of Singularities

4. Calculus of Residues

5. Evaluation of Certain Integrals

6. Conformal Mappings and Bilinear Transformations

7. Analytic Continuation

8. Convergence of Infinite Products

9. Entire Functions

MCQs For UGC NET

MATH 624S : Complex Analysis-II

Note: 1. The question paper will consist of 9 questions. Candidates will attempt total five questions.

2. Question No.1 is compulsory and will consist of short answer type questions covering the whole syllabus.

3. There will be four questions from each Unit and the candidates will be required to attempt two questions from each Unit.

4. All questions carry equal marks.

UNIT-I

Maximum Modulus principle, Schwarz’ Lemma, Taylor series and Laurent series. Singularities, Cauchy’s

residue theorem. Calculus of residues, bilinear transformations. Zeros and poles of meromorphic functions,

Rouche’s theorem, Argument Principle.

(Scope as in “Foundations of Complex Analysis” by Ponnusamy S., Chapter 6 (§6.1-§6.3), Chapter 4(§4.10-

§4.12), Chapter 7, Chapter 8, Chapter 9.)

UNIT-II

Definitions and examples of conformal mappings. Infinite products, Weierstrass theorem, Mittagleffer’s

theorem, Canonical product, Analytic Continuation through power series (basic ideas), Natural boundary, the

Gamma function and Riemann Zeta function.

(Scope as in “Foundations of Complex Analysis” by Ponnusamy S., Chapter 5, Chapter 10 (§10.1, §10.4),

Chapter 11.)