🐍 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
Complex Integration & Cauchy's Theorem
Line integrals, Cauchy's theorem, and the integral formula
Pricing (per student)
Prerequisites
- Completion of Introduction to Complex Analysis and Cauchy-Riemann Equations (or equivalent)
- Understanding of contour integration concepts
Overview
Covers complex line integrals, Cauchy's theorem, and Cauchy's integral formula — with strong emphasis on exam-level problem-solving. Students evaluate contour integrals and apply the integral formula to find derivatives of analytic functions.
Topics
| Hour | Topic | Details |
|---|---|---|
| 1 | Line Integral of a Complex Function | Definition, examples, and properties. |
| 2 | Evaluation of Line Integrals | Direct integration and parameterisation. |
| 3 | Cauchy's Theorem | Statement, proof outline, and applications. |
| 4 | Simply vs. Multiply Connected Domains | Explanation with diagrams and examples. |
| 5 | Cauchy's Integral Formula | Statement, proof outline, and applications. |
| 6 | Problem-Solving (Article 20.12, 20.13, 20.14) | Solving standard exam problems on Cauchy's theorem. |
| 7 | Derivatives via Cauchy's Integral Formula | Finding higher-order derivatives of analytic functions. |
| 8 | Zeros, Singularities & Residues (Intro) | Overview — zeroes, poles, residues. |
| 9 | Additional Problem-Solving Session | Further practice with complex integration problems. |
| 10 | Recap & Doubt Clearing | Revision and timed Q&A session. |
Expected Outcomes
- Evaluate line integrals of complex functions.
- Apply Cauchy's theorem and integral formula confidently.
- Solve exam-level problems on complex integration.