📘 Course Title: Complex Analysis

Code: 29017-AUX

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🏁 Introduction:

Complex Analysis is a central branch of mathematics, exploring the behavior of functions of a complex variable.
It provides essential tools used across physics, engineering, and advanced mathematical modeling.

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✨ Course Description:

This course offers a comprehensive journey through the world of complex functions, starting from the basic properties of complex numbers to the advanced theory of analytic functions and singularities.
Students will learn to solve complex integrals, understand convergence of complex series, and apply these concepts to real-world problems in physics, engineering, and finance.

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🎯 Target Audience:

• Mathematics, Physics, and Engineering students.

• Researchers in applied sciences.

• Enthusiasts interested in mastering functions of a complex variable.

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📚 What You Will Learn:

• Represent and manipulate complex numbers geometrically and algebraically.

• Analyze analytic functions and use Cauchy-Riemann equations.

• Evaluate integrals in the complex plane with Cauchy’s Integral Theorem.

• Expand functions using Taylor and Laurent series.

• Identify and classify singularities and compute residues.

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🧑‍🏫 Instruction Methodology:

• 🎥 Interactive Lectures (with real-world applications).

• 📝 Solved Examples and Exercises.

• 🧠 Concept Visualization (graphs and transformations).

• 🛠️ Hands-on Mini Projects.

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🧩 Main Modules:

1️⃣ Complex Numbers

• 🔵 Geometric Representation

• 🔵 Complex Transformations

2️⃣ Analytic Functions

• 🧠 Cauchy-Riemann Equations

• 🧠 Exponential and Power Series

3️⃣ Integration in the Complex Plane

• 🔗 Line Integrals

• 🔗 Cauchy’s Integral Theorem

4️⃣ Infinite Series and Singularities

• ♾️ Laurent Series

• ♾️ Poles, Residues, and Singular Points

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🎒 Materials Included:

• 📘 Comprehensive Lecture Notes (PDFs)

• 📊 Visual Presentations and Graphs

• 📈 Problem Sets and Detailed Solutions

• 📹 Recorded Video Lectures

• 🧩 Practice Projects and Case Studies

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🕒 Course Duration:

• 8 weeks — Two lectures per week.

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📈 Level:

• Advanced (Recommended background: calculus, linear algebra).

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