Analysis of the solutions of the equations. One of the most important techniques is the method of separation of variables. Many textbooks heavily emphasize this technique to the point of excluding other points of view. The problem with that approach is that only certain kinds of partial differential equations can be solved by it, whereas others.
Introduction To Differential Equations Book Pdf
Introduction To Differential Equations Taylor Pdf
SES # | TOPICS | LECTURE NOTES |
---|---|---|
L1 | Introduction to PDEs | (PDF) |
L2 | Introduction to the heat equation | (PDF) |
L3 | The heat equation: Uniqueness | (PDF) |
L4 | The heat equation: Weak maximum principle and introduction to the fundamental solution | (PDF) |
L5 | The heat equation: Fundamental solution and the global Cauchy problem | (PDF) |
L6 | Laplace's and Poisson's equations | (PDF) |
L7 | Poisson's equation: Fundamental solution | (PDF) |
L8 | Poisson's equation: Green functions | (PDF) |
L9 | Poisson's equation: Poisson's formula, Harnack's inequality, and Liouville's theorem | (PDF) |
L10 | Introduction to the wave equation | (PDF) |
L11 | The wave equation: The method of spherical means | (PDF) |
L12 | The wave equation: Kirchhoff's formula and Minkowskian geometry | (PDF) |
L13–L14 | The wave equation: Geometric energy estimates | (PDF) |
L15 | Classification of second order equations | (PDF) |
L16–L18 | Introduction to the Fourier transform; Fourier inversion and Plancherel's theorem | (PDF) |
L19–L20 | Introduction to Schrödinger's equation | (PDF) |
L21-L23 | Introduction to Lagrangian field theories | (PDF) |
L24 | Transport equations and Burger's equation | (PDF) |