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Ordinary Differential Equations
This note covers the following topics related to Ordinary Differential Equations: Linear Constant-Coefficient, Damped Oscillator, Forced Oscillations, Series Solutions, Trigonometry via ODE's, Green's Functions, Separation of Variables, Circuits, Simultaneous Equations, Simultaneous ODE's, Legendre's Equation, Asymptotic Behavior.
Author(s): J. Nearing
33 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
Spectral Theory of Partial Differential Equations Lecture Notes
This note contains below topics, Discrete Spectrum, Continuous Spectrum.
Author(s): Richard S. Laugesen
120 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
Introduction to the Galois Theory of Linear Differential Equations
This paper expands ten lectures on the Galois theory of linear differential equations. It introduces the algebraic, analytic, and algorithmic sides of that theory by focusing on the main ideas and on examples.
Author(s): Michael F. Singer
83 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
Estimating and Assessing Differential Equation Models with Time Course Data
Ordinary differential equation models are widely used to describe chemical or biological processes. This article considers how to estimate and assess such models from time course data. The data are often noisy, and some parts of the system may not be observed.
Author(s): Samuel W. K. Wong, Shihao Yang, S. C. Kou
53 Pages
Multivariate Calculus and Ordinary Differential Equations
This note explains the following topics, Functions of Several Variables, Partial Derivatives and Tangent Planes, Max and Min Problems on Surfaces, Ordinary Differential Equations, Parametrisation of Curves and Line Integrals and MATLAB Guide.
Author(s): The University of Queensland
291 Pages