Complex Analysis

📚 Master Complex Analysis with this syllabus-based learning app for 2025-2026! Perfect for students of BS, MS, ADS, MSc, engineers, and exam aspirants, this app is designed to help you learn Complex Analysis quickly and effectively using MCQs, notes, quizzes and detailed topics.

✔ Complete Complex Analysis syllabus

✔ MCQs and quizzes for self-assessment

✔ Easy-to-understand explanations

✔ Exam-oriented content for quick learning

✔ Inspired by classical authors Lars Valerian Ahlfors, Walter Rudin, Murray Spiegel, James Ward Brown, Ruel V. Churchill, Johan B. Conway, Alice Chang, Rami Shakarchi, George F. Simmons, Theodore W. Gamelin, Elias M. Stein in Complex Analysis

📚 Units & Topics Included:

📗 Unit 1: Basic Concepts and Complex Numbers

1. Complex Number Definition and Operations

2. Properties of Conjugate

3. Modulus and Arguments

4. Polar Form

5. Triangular Inequality

6. Locus of Point

7. Function of a Complex Variable

8. Neighbourhood of a Point

9. Limit of a Function

10. Continuity of a Function

11. Differentiability of a Function

📘 Unit 2: Analytic or Regular or Holomorphic Function

1. Analytic Function Definition

2. Cauchy-Riemann Equations

3. Harmonic Function

4. Orthogonal Trajectories

📙 Unit 3: Elementary Transcendental Functions

1. Complex Exponential Function

2. Complex Logarithmic Function

3. Complex Trigonometric Functions

4. Complex Hyperbolic Functions

📕 Unit 4: Complex Integration

1. Basic Terminology (Locus, Curve)

2. Complex Equation of a Curve

3. Line Integrals

4. Cauchy’s Theorem

5. Cauchy Integral Formula

6. Theorem: ML-Inequality with Examples

📒 Unit 5: Power Series and Related Theorems

1. Power Series Definition

2. Convergent Power Series

3. Radius and Disc of Convergence

4. Taylor Series

5. Laurent Series

6. Abel’s Theorem

📓 Unit 6: Singularities and Calculus of Residue

1. Zero of a Function

2. Singularities (Removable, Pole, Essential)

3. Residue: Definition

4. Residue Theorem

5. Application of Residue Theorem

🎯 Why Choose This App?

This app is perfect for students looking to:

• Learn Complex Analysis 2025-2026

• Quick revision before exams

• Study Complex Numbers and related topics

• Access Complex Analysis Notes & MCQs

• Prepare effectively with topics inspired by top authors of complex analysis

📥 Download Now and master Complex Analysis easily while preparing for 2025-2026 exams!