Why Choose Rsquared Mathematics?

At Rsquared Mathematics, we understand the significance of thorough preparation. Our platform offers:

• Extensive Topic Coverage: We cover every crucial topic in Complex Analysis, from Analytic Functions to the Schwarz Lemma.
• MCQ Format: Practice with Multiple Choice Questions that simulate the real exam environment.
• Detailed Solutions: Each question is accompanied by an in-depth solution to enhance your understanding.

Complex Analysis : CSIR NET JRF Syllabus

• Introduction and Geometrical Representation of Complex Numbers
  • Polar Forms of a Complex Number P(x,y)
  • Inverse Points with respect to a circle
  • Chordal Distance
  • Stereographic Projection and Point Set Topology
• Limit, Continuity and Differentiability
  • Topology in the Complex Plane
  • Limit of a function
  • Alternative Definition of limit of function
  • Limit of a function at z = ¥
  • Continuous functions
  • Uniform continuity
  • Differentiability
  • Cauchy-Riemann Equations
  • Polar Form of C-R Equations
  • Complex form of C-R Equation
  • Necessary condition for differentiability
  • Sufficient Condition of Differentiability
  • Assignment
• Singularities of Analytic Functions
  • Regular point and Analytic Functions
  • Singularity
  • Classifications of singular points
  • Entire functions
  • Result on Analyticity
  • Construction of Analytic function
• Complex Integration
  • Curves and Cauchy’s Integral Formula
  • Extension of Cauchy’s Integral formula to multiply connected Regions
  • Cauchy integral formula for the derivative of an Analytic function
  • Higher Order Derivatives
  • Morera’s Theorem
  • Analytic functions on simplyh connected domains
  • Cauchy’s inequality
  • Assignment
• Some Important Theorems and Their Applications
  • Liouville’s Theorem
  • Fundamental Theorem of Algebra in C
  • Gauss’s Theorem
  • Luca’s Theorem
  • Generalized Version of Liouville’s Theorem
• Power Series
  • Power Series
  • Result on the Radius of convergence
• Taylor and Laurent Expansion
  • Taylor Series Expansion
  • Laurent Series Expansion
  • Analysis of singularities through Laurent series
  • Picard’s little Theorem
  • Picard’s Great Theorem
• Some Special functions related to the Exponential
  • The exponential function
  • The logarithm function
  • The square Root function
• Meromorphic functions
  • Argument Theorem
  • Rouche’s Theorem
• Calculus of Residues
  • Residue at a finite point
  • Some result on poles
  • Residue at infinity
  • Cauchy residue theorem
  • Extended Residue formula
  • Assignment
• Conformal Mapping
  • Defination
  • Conformal Mapping/Conformality
  • Magnifications factor and scale factor
  • Linear fractional/Bilinear/Mobius Transformation
  • Matrix Interpretation of a Mobius transformation
  • Fixed points
  • Normal form or canonical form of a bilinear transform
  • Classification of bilinear transformation on the basis of normal form
  • Cross Ratio
  • Automorphisms of Disks and Half-plane
  • Automorphism of the unit disk
• Maximum and Minimum Modulus Principle and Schwarz Lemma
  • Mean value property
  • The open mapping theorem
  • maximum modulus principle
  • minimum modulus theorem
  • Schwarz pick lemma

Practice Makes Perfect

At Rsquared Mathematics, we believe in the power of practice. Our carefully curated MCQs are designed to test your knowledge and improve your problem-solving skills. Each question is followed by a detailed solution, ensuring you not only get the correct answer but also understand the underlying concepts.

Boost Your Exam Performance

Whether you’re preparing for the CSIR NET, IIT GATE, or any other competitive exam, our resources are tailored to meet your needs. Our extensive coverage of topics and comprehensive solutions will help you build a solid foundation in Complex Analysis and boost your confidence on exam day.

Explore More Resources

In addition to our extensive collection of practice questions on Complex Analysis, we offer a variety of articles to further aid your preparation. Check out our detailed guides on downloading the CSIR NET syllabus, solving previous year questions (PYQs) for CSIR NET, effective strategies on how to prepare for CSIR NET, and our recommendations for the best books for CSIR NET. These resources are designed to provide you with all the information and tools you need to succeed. Check out official website of NTA CSIR NET.

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Conclusion

Complex Analysis is a challenging but rewarding subject. With Rsquared Mathematics, you have the perfect guide to navigate through the complexities and excel in your exams. Start practicing today and take the first step towards mastering Complex Analysis for CSIR NET and other competitive exams.