📘 Welcome to Maths Mastery with Dr. Upasana P. Taneja!
Hello learners! I’m Dr. Upasana Taneja, passionate about simplifying higher mathematics and making it accessible for students preparing for B.Sc., M.Sc., NET, GATE, and IIT-JAM exams.
On my channel — Maths Mastery with Dr. Upasana P. Taneja — I cover advanced topics like Group Theory, Ring Theory, Real Analysis, and Complex Analysis, helping you build strong foundations and problem-solving skills.
✨ In this video, we dive into two essential concepts in Complex Analysis — Analytic Functions and the Cauchy-Riemann (CR) Equations.
You’ll learn:
✅ The definition and properties of analytic (holomorphic) functions
✅ How differentiability leads to analyticity in complex functions
✅ Derivation and interpretation of the Cauchy-Riemann equations
✅ Geometric meaning of CR equations in the complex plane
✅ Examples to check analyticity using CR equations
✅ Importance of these concepts in advanced topics like harmonic functions, contour integration, and complex mapping
By the end of this lecture, you’ll understand how to identify analytic functions and use the Cauchy-Riemann equations to verify differentiability — a key concept in Complex Analysis.
📚 Explore detailed notes and solved examples on my blog:
🔗 https://upasanataneja.blogspot.com
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