1. 1. Introduction
   1. A function e.g f(x,y) or z(x,y)
2. 2. Second Partial Derivatives
   1. Taking two consecutive partial derivatives with respect to the same variable
   2. Standard Notation
      1. fxx
      2. fyy
3. 3. Mixed Partial Derivatives
   1. Taking partial derivatives with respect to one variable, and then take another partial derivative with respect to a different variable
   2. Standard Notation
      1. fyx
      2. fxy
   3. Del Notation
   4. Subscript Notation
4. 4. Higher Partial Derivatives
   1. Mixed partial derivatives give same result whenever :
      1. f, fx, fy, fxy, fyx
   2. Third and higher order :
      1. fyyx
      2. fyyxx
5. Engineering Applications
   1. Mechanics of Fluid : Ideal Flow
   2. Finite Element Method or Analysis
   3. Mechanics of Materials : Macaulay's Beam Deflection
6. Example Questions
   1. Second Partial Derivatives
      1. Subtopic 1
   2. Mixed Partial Derivatives
      1. Subtopic 1
   3. Function more than three variable
      1. Subtopic 1
7. Other
   1. Figure of Mixed Partial Derivatives
      1. Subtopic 1