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Elementary Differential Equations
This note covers the following topics: First Order Equations, Numerical Methods, Applications of First Order Equations, Linear Second Order Equations, Applcations of Linear Second Order Equations, Series Solutions of Linear Second Order Equations, Laplace Transforms, Linear Higher Order Equations.
Author(s): William F. Trench
663 Pages 
This note contains below topics, some linear algebra, but these references are not essential and can be skimmed, can safely be dropped, while still covering chapters 4 and 5, does not depend on, except that the PDEs section 6 5 makes a few references to, and maybe.
Author(s): Jiri Lebl
466 Pages
An Introduction to Partial Differential Equations
This book contains below topics, First notions, PDEs as mathematical models of physical systems, Initial and boundary conditions, Numerical methods, First order PDEs, Classification of equations Characteristics, Adjoint differential operators, Initial and boundary value problems in bounded domains, The SturmLiouville problem and Fourier series, Integral transforms, Projects.
Author(s): Per Kristen Jakobsen
226 Pages
Spectral Theory of Partial Differential Equations Lecture Notes
This note contains below topics, Discrete Spectrum, Continuous Spectrum.
Author(s): Richard S. Laugesen
120 Pages
Symmetries of Ordinary Differential Equations A Short Introduction
This book contains below topics, Basic notions and facts, Local oneparameter orbital symmetry groups, Multiparameter symmetries and invariant sets, Linear symmetries and normal forms, background on power series.
Author(s): Sebastian Walcher
68 Pages
Introduction to Stochastic Differential Equations SDEs for Finance
This book contains below topics, Financial Introduction, Brownian Motion and Stochastic Calculus, The BlackScholes Theory, The BlackScholes Greeks, Exotic Options, Implied Volatility and LocalVolatility Fits, Stochastic Volatility, Stochastic Control, A Martingales and Stopping Times, B Some Notes on Fourier Transforms.
Author(s): Andrew Papanicolaou
103 Pages
This note contains below topics, THE SOBOLEV SPACES AND THE BOUNDARY VALUE PROBLEMS, CAUCHY PROBLEM FOR PDEs AND STABILITY ESTIMATES, III CARLEMAN ESTIMATES AND UNIQUE CONTINUATION PROPERTIES.
Author(s): Sergio Vessella
799 Pages
Rough path theory and an introduction to rough partial differential equations
This book contains below topics, Frequently used notation, The tensor product, Spaces of rough paths, Integration against rough paths, Compositions of paths with functions, Rough differential equations, Brownian motion as a rough path, Stochastic differential equations, Rough partial differential equations, Another approach to rough partial differential equations.
Author(s): Stefan Tappe
62 Pages
A Concise Introduction to Control Theory for Stochastic Partial Differential Equations
This note contains below topics, Control systems governed by stochastic partial differential equations, Controllability and observability for stochastic evolution equations some simple results, Controllability of stochastic partial differential equations stochastic transport equations, Controllability of stochastic partial differential equations stochastic parabolic equations, Controllability of stochastic partial differential equations stochastic hyperbolic equations, Stochastic linear quadratic optimal control problems openloop optimal control, Stochastic linear quadratic optimal control problems optimal feedback control, Stochastic linear quadratic optimal control problems deterministic coefficients, Pontryagin type maximum principle for controlled stochastic evolution equations, A sufficient condition for an optimal control.
Author(s): Qi Lü, Xu Zhang
112 Pages