Contents

• First order PDEs
  • Classification of first order PDEs
  • Formation of first order PDE
  • General solution of quasi-linear equations
  • Integral surface passing through a given curve
  • First order nonlinear PDEs
    • Cauchy's method of characteristics
    • Compatible system of PDEs
  • Charpit's method
    • Special type I: First order PDEs involving only and
    • Special type II: PDEs not involving the independent variables explicitly
    • Special type III: Separable PDEs
    • Special type IV: Clairaut equations
  • Explore further
  
  
• Second order PDEs
  • Basics
  • Transformation
  • Invariance of the type of PDE
  • Canonical forms
    • Canonical form of hyperbolic equations
    • Canonical form of parabolic equations
    • Canonical form of elliptic equations
  
  
• The Method of Separation of Variables
  • Parabolic Equations
    • Heat Equation: Homogeneous Dirichlet boundary conditions
    • Insulated endpoint conditions(Neumann BVP)
  • Wave equation
    • Solution of one-dimensional wave equations by canonical transformation
    • D'Alembert's solution of wave equation
    • Vibrating string : variable separation method
    • Elliptic equations