Lecture Notes

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)

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