📘 Course Title: Mathematical Physics

Code: 29021-AUX

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🏁 Introduction:

Mathematical Physics forms the backbone of theoretical and applied physics by using rigorous mathematical methods to model and analyze physical systems. It plays a vital role in fields like mechanics, quantum theory, relativity, and thermodynamics.

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✨ Course Description:

This course offers an in-depth exploration of the mathematical tools and concepts necessary for understanding classical mechanics, quantum mechanics, general relativity, and statistical physics. Students will gain both theoretical knowledge and practical skills to tackle advanced scientific problems.

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🎯 Target Audience:

• Students of Physics, Applied Mathematics, and Engineering.

• Researchers aiming for careers in theoretical or experimental physics.

• Professionals seeking a deeper understanding of mathematical models in physics.

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📚 What You Will Learn:

• Apply Lagrangian and Hamiltonian formulations to classical systems.

• Solve the Schrödinger equation and understand operator theory in quantum mechanics.

• Grasp the mathematical structure of spacetime and Einstein’s field equations.

• Analyze thermal systems using concepts of statistical distributions and classical thermodynamics.

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🧑‍🏫 Instruction Methodology:

• 📖 Theoretical lectures combined with real-world physical examples.

• 🧮 Problem-solving workshops.

• 🖥️ Interactive simulations and visualizations.

• 📚 Weekly assignments, quizzes, and mini-projects.

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🧩 Main Modules:

1️⃣ Classical Mechanics

• ⚙️ Lagrange’s Equations

• ⚙️ Hamilton’s Equations

• ⚙️ Dynamical Systems and Stability Analysis

2️⃣ Quantum Mechanics

• 🔬 Schrödinger Equation: Formulation and Solutions

• 🔬 Operators, Eigenvalues, and Matrix Representations

3️⃣ General Relativity

• 🌌 Geometry of Spacetime

• 🌌 Einstein’s Field Equations and their Physical Implications

4️⃣ Thermodynamics and Statistical Mechanics

• ♨️ Statistical Distributions (Maxwell-Boltzmann, Bose-Einstein, Fermi-Dirac)

• ♨️ Classical Thermodynamics Principles and Laws

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🎒 Materials Included:

• 📘 Comprehensive Lecture Notes

• 🧠 Problem Sets with Detailed Solutions

• 🖥️ Access to Simulation Tools

• 🎥 Recorded Lectures for Review

• 📑 Mini Research Project Guidelines

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🕒 Course Duration:

• 10 weeks — 2 sessions per week (Each session: 2 hours).

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📈 Level:

• Advanced (Requires prior knowledge in calculus, linear algebra, and basic classical/quantum physics).

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