Email-id: nikhil.gupta34@gmail.com WhatsApp number: 63766-37094 In this video we will discuss 1. Introduction of analytic function @ 0:09 min. 2. Necessary condition for a function to be analytic(Derivation of c-r equation) @ 2:00 min. WATCH ALSO: **Sufficient Condition for a Function to be Analytic with proof https://www.youtube.com/watch?v=neg-lVku0oA Extension of Cauchy's Integral Theorem (detailed proof) https://www.youtube.com/watch?v=spdAwITNkbY Cauchy's Integral Formula (Proof) https://www.youtube.com/watch?v=ZQCtNuIr55k Cauchy-Riemann equations (c-r equations)...necessary condition for analytic function https://www.youtube.com/watch?v=CCMnwZHcW6w Polar form of C-R Equations (Proof by 2 different Methods) https://www.youtube.com/watch?v=heWCBmh38Uk Cauchy Integral Theorem https://www.youtube.com/watch?v=-d9-V7-2lPE Conformal Mapping (complex analysis) https://www.youtube.com/watch?v=XvLnHIPsWqY Milne Thomson Method (Detailed proof in Hindi) https://www.youtube.com/watch?v=UKPAR8pQz2Y Epsilon Delta Definition of Limit...detailed explanation in Hindi https://www.youtube.com/watch?v=wzT403sa5oE Examples on Epsilon Delta Definition of Limit (for 1 variable functions) https://www.youtube.com/watch?v=NqwieokSeqE limit of bivariate function in Hindi...logical explanation with 2 different Examples https://www.youtube.com/watch?v=h94Xm-nzDYo Limit of Bivariate Functions Examples https://www.youtube.com/watch?v=d94IVoEgI48 Epsilon-Delta Definition of Limit example for two variable functions https://www.youtube.com/watch?v=bAD1E1hc6JI Epsilon-Delta definition of limit trigonometry related example https://www.youtube.com/watch?v=kL2yVY7q2xo Maxima and Minima For two variable functions (Extreme Values of a function) https://www.youtube.com/watch?v=dodoqu6zvMw Example related to extreme values https://www.youtube.com/watch?v=FyHWo8ZhpLE Extreme Values Trigonometry related Example https://www.youtube.com/watch?v=H0ofuQL8jOk Maxima and Minima for 1 variable functions (class 12) https://www.youtube.com/watch?v=dksu5SZZ80A ORTHOGONAL CIRCLES (condition with proof) https://www.youtube.com/watch?v=9qgdzvoQhoo Rolle's Theorem and Mean Value Theorem https://www.youtube.com/watch?v=U5sGFf0DjLs PLAYLISTS LINK : 1. Cauchy integral formula and proof    • Cauchy Integral Theorem and Formula   2. Maxima & Minima (Extreme Values)    • Maxima & Minima (Extreme Values)   3. ε-δ Definition of Limit    • ε-δ Definition of Limit   4. BSc Mathematics    • BSc Mathematics