One Shot Unit-2 | Applications of PDE & Fourier Transform | Maths4 | Mohit Chauhan

📚 Welcome to the COMPLETE ONE SHOT of Unit-2 (Maths-4 – B.Tech)
This mega lecture covers the Applications of Partial Differential Equations with full concepts, derivations, and solved patterns—perfect for exams and last-minute revision! 💯✨

🧠 What’s Covered in This One-Shot Lecture?
1️⃣ Classification of Linear PDE of Second Order

🌀 Parabolic
🔥 Hyperbolic
💧 Elliptic
✔️ How to classify using standard form
✔️ Clear explanation + quick tricks

2️⃣ Method of Separation of Variables

🔹 Concept & procedure
🔹 How to split PDE into ODEs
🔹 Non-trivial solutions using constants
🔹 Full worked-out examples

3️⃣ One Dimensional Wave Equation

📈 Derivation
📌 Applying Boundary Conditions
📌 Applying Initial Conditions
📌 Obtaining Non-Trivial Solutions
✔ Examples for exam scoring

4️⃣ One Dimensional Heat Equation

🔥 Heat conduction model
📌 Use of separation of variables
📌 Fourier series solution form
📌 Finding constants using conditions

5️⃣ Laplace Equation

💠 Harmonic functions
💠 Boundary value problems
💠 Non-trivial solution technique

6️⃣ Fourier Transforms (Super Important!)

🔹 Fourier Transform
🔹 Fourier Sine Transform
🔹 Fourier Cosine Transform
🎯 Applications to solve PDE
✔ Step-by-step examples
✔ How transforms convert PDE → ODE

💡 This one-shot is perfect for:
✓ B.Tech Maths-4 Students
✓ Quick Revision
✓ University Exams
✓ Concept Building

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