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Complex Number for Subject GRE Maths AGRE. By Satyadhar Joshi. 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.
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Complex Number for Subject GRE Maths AGRE By Satyadhar Joshi
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
Review of Earlier concepts • 50% Syllabus of IIT JEE Maths • The Engineering Maths covers it all
Cauchy Riemann Equations • Easy questions on this area
Analytical Functions • Differntiable at any point z in the complex plane
Complex line integrals • Change of function to t
All imp theories of analytical functions • 6 theorems exist • Caychy’s • Morera’s • Cauchy’s Integral • Cauchy Derivative estimate • Liouville’s • The Maximum Principle
Singularities, Poles, and Laurent Series • Punctured open disk • Singularity
Residual theorem • Laurents Theorem • Clo0sed Integral
Review of some theorems Real numbers • Lebesgue Measure • Lebesgue Measurable Functions • Lebesgue integral function
References • Cracking the Subject GRE Math Exam by Princeton
