Definition, Classification & Formation Of PDE | JRF EXPRESS | Lec- 1 | IFAS

Definition, Classification & Formation Of PDE explained with clear concepts and exam-focused approach. Master PDE classification, order and degree, linear and nonlinear PDE concepts for CSIR NET JRF. Covers PDE formation tricks, PYQs, and problem‑solving strategies.

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⏳ Lecture Timeline:
[00:00:00] – Introduction to PDE & Shortcut Tricks
[00:02:44] – Intro to PDE & Order Concept
[00:03:43] – Order of PDE: Highest Derivative
[00:04:54] – Degree of PDE: Conditions
[00:06:00] – Degree Not Defined Cases
[00:06:07] – Example: Degree Calculation
[00:07:59] – Question 1: Order & Degree
[00:09:13] – Question 2: Order & Degree
[00:10:35] – Question 3: Degree of PDE
[00:11:20] – Question 4: Order of PDE
[00:12:19] – Question 5: Degree of PDE
[00:14:29] – Linear PDE Conditions
[00:15:37] – Example: Non‑linear PDE
[00:16:37] – Question 6: Identify Linear PDE
[00:18:30] – Question 7: Non‑linear PDE
[00:19:43] – Question 8: Non‑linear (Multiplication)
[00:24:49] – Linear 1st Order PDE Form
[00:25:25] – Semi‑linear PDE Concept
[00:26:54] – Quasi‑linear PDE Concept
[00:28:28] – Question 9: Quasi‑linear PDE
[00:29:39] – Question 10: Linear PDE Example
[00:30:58] – Question 11: Semi‑linear PDE
[00:31:29] – Formation of PDE (Elimination)
[00:32:09] – Question 12: PDE of Spheres Family
[00:38:34] – Question 13: PDE from z = ax + by
[00:45:43] – Homework: PDE Formation
[00:47:00] – Question 14: Verify PDE Solution
[00:55:38] – Complete Session (PDE Basics & Classification)

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📖 Topics Covered in This Lecture:
• PDE Definition, Order and Degree Concepts
• Linear, Semi‑Linear, Quasi‑Linear PDE Classification
• Nonlinear PDE Formation Tricks & PYQs
• Deriving PDE by Eliminating Arbitrary Functions
• Harmonic Conjugate and Cauchy Integral Problems

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📚 Lecture Summary:
In this session, IFAS Expert Faculty focuses on the definition, classification, and formation of PDE with an exam‑oriented approach. Core concepts like order and degree of PDE, conditions for linearity, and semi‑linear/quasi‑linear types are detailed. Problem‑solving tricks for PDE formation from geometric surfaces and elimination of arbitrary functions are demonstrated. The lecture provides a strong foundation in PDE definition and classification, preparing students for CSIR NET JRF with confidence.

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🎓 This lecture is highly beneficial for students preparing for:
✅ CSIR NET Mathematical Science ✅ GATE Mathematics ✅ SET Mathematics
✅ TIFR Mathematics ✅ PhD Entrance Exams

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✅ CSIR NET June 2024: 2000+ Selections (AIR 3, 10, 13...)
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