🐍 Python
From zero to full-stack Python — practical, exam-oriented courses for every level
🧠 AI & Neural Networks
ANN foundations through deep learning, competitive programming, and a full capstone project
∫ Complex Analysis
Complex functions, Cauchy-Riemann equations, conformal mappings, and contour integration
📊 Probability & Statistics
Distributions, curve fitting, regression, and hypothesis testing — all exam-oriented
Cauchy-Riemann Equations & Analytic Functions
Verification, construction, and the Milne-Thompson method
Pricing (per student)
Prerequisites
- Completion of Introduction to Complex Analysis (or equivalent)
- Basic understanding of partial derivatives
Overview
Deep-dives into Cauchy-Riemann equations in both Cartesian and Polar form, harmonic functions, and the construction of analytic functions using the Milne-Thompson method. Heavy emphasis on exam-style problem-solving.
Topics
| Hours | Topic | Details |
|---|---|---|
| 1–2 | C-R Equations — Cartesian Form | Derivation, verification, and solved examples. |
| 3–4 | C-R Equations — Polar Form | Conversion and applications. |
| 5–6 | Properties of Analytic Functions | Harmonic functions and Laplace's equation. |
| 7–8 | Construction of Analytic Functions | Using Cauchy-Riemann equations to construct f(z). |
| 9–10 | Milne-Thompson Method | Step-by-step construction from real or imaginary parts. |
| 11 | Problem-Solving Session | Solving textbook problems (Article 20.3, 20.4, 20.5). |
| 12 | Doubt Clearing & Revision | Addressing student queries and revising key concepts. |
Expected Outcomes
- Verify analyticity using Cauchy-Riemann equations in Cartesian and Polar form.
- Construct analytic functions from given real or imaginary parts.
- Apply the Milne-Thompson method confidently in exams.