Methods of Mathematical Physics II PDE     R.Courant and D.Hilbert

img1.gif I Introductory Remarks

  1. General Information about the Variety of Solutions
  2. Systems of Differential Equations
  3. Methods of Integration for Special Differential Equations
  4. Geometric Interpretation of a First Order Partial Differential Equations in Two Independent Variables  The Complete Integral
  5. Theory of Linear and Quasi-Linear Differential Equations  of First Order
  6. The Legendre Transformation
  7. The Existence Theorem of Cauchy and Kowalewsky

II General Theory of Partial Differential Equations of First Order

  1. Geometric Theory of Quasi-Linear Differential Equations in Two Independent Variables
  2.  

III Differential Equations of Higher Order

IV Potential Theory and Elliptic Differential Equations

V Hyperbolic Differential Equations in Two Independent Variables

VI Hyperbolic Differential Equations in More Than Two Independent Variables

    Part I Uniqueness,Costruction,and Geometry of Solutions

    Part II Representation of Solutions