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Complex Number for Subject GRE Maths AGRE

Dive into the world of complex numbers with this detailed resource by Satyadhar Joshi. This guide covers essential topics including polar and exponential forms, roots, logarithms, powers, trigonometric functions, and hyperbolic functions. Delve into analytical functions, derivatives, and the Cauchy-Riemann equations. Understand complex line integrals, Taylor series, and the residue theorem, alongside reviews of earlier concepts relevant to GRE math and IIT JEE. Ideal for students aiming to excel in engineering mathematics.

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Complex Number for Subject GRE Maths AGRE

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  1. Complex Number for Subject GRE Maths AGRE By Satyadhar Joshi

  2. Content • Polar and Exp • Roots • Log • Powers • Trigno • Hyberbolic • Function • Derivative • Cauchy Riemann • Analytical Function • Complex line integrals • Taylor series • Singularities, Poles and Laurent Series • Residue Theorem

  3. Review of Earlier concepts • 50% Syllabus of IIT JEE Maths • The Engineering Maths covers it all

  4. Cauchy Riemann Equations • Easy questions on this area

  5. Analytical Functions • Differntiable at any point z in the complex plane

  6. Complex line integrals • Change of function to t

  7. All imp theories of analytical functions • 6 theorems exist • Caychy’s • Morera’s • Cauchy’s Integral • Cauchy Derivative estimate • Liouville’s • The Maximum Principle

  8. Singularities, Poles, and Laurent Series • Punctured open disk • Singularity

  9. Residual theorem • Laurents Theorem • Clo0sed Integral

  10. Review of some theorems Real numbers • Lebesgue Measure • Lebesgue Measurable Functions • Lebesgue integral function

  11. References • Cracking the Subject GRE Math Exam by Princeton

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