1. 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 1. Caychys 2. Moreras 3. Cauchys Integral 4. Cauchy Derivative estimate 5. Liouvilles 6. 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