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Lecture notes files.SES #TOPICSLECTURE NOTESL1Introduction to PDEs(PDF)L2Introduction to the heat equation(PDF)L3The heat equation: Uniqueness(PDF)L4The heat equation: Weak maximum principle and introduction to the fundamental solution(PDF)L5The heat equation: Fundamental solution and the global Cauchy problem(PDF)L6Laplace’s and Poisson’s equations(PDF)L7Poisson’s equation: Fundamental solution(PDF)L8Poisson’s equation: Green functions(PDF)L9Poisson’s equation: Poisson’s formula, Harnack’s inequality, and Liouville’s theorem(PDF)L10Introduction to the wave equation(PDF)L11The wave equation: The method of spherical means(PDF)L12The wave equation: Kirchhoff’s formula and Minkowskian geometry(PDF)L13–L14The wave equation: Geometric energy estimates(PDF)L15Classification of second order equations(PDF)L16–L18Introduction to the Fourier transform; Fourier inversion and Plancherel’s theorem(PDF)L19–L20Introduction to Schrödinger’s equation(PDF)L21-L23Introduction to Lagrangian field theories(PDF)L24Transport equations and Burger’s equation(PDF)
Introduction To Fractional Differential Equations Pdf
9.1 Introduction to Linear Higher Order Equations 466 9.2 Higher Order Constant Coefficient Homogeneous Equations 476 9.3 Undetermined Coefficients for Higher Order Equations 488 9.4 Variation of Parameters for Higher Order Equations 498 Chapter 10 Linear Systems of Differential Equations 10.1 Introduction to Systems of Differential Equations 508.
