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Differential Equations by MIT
This book explains the following topics: IFirst-order differential equations, Direction fields, existence and uniqueness of solutions, Numerical methods, Linear equations, models, Complex numbers, roots of unity, Second-order linear equations, Modes and the characteristic polynomial, Good vibrations, damping conditions, Exponential response formula, spring drive, Complex gain, dashpot drive, Operators, undetermined coefficients, resonance, Frequency response, LTI systems, superposition, RLC circuits, Engineering applications, Fourier series, Operations on fourier series , Periodic solutions; resonance, Step functions and delta functions, Step response, impulse response, Convolution, First order systems, Linear systems and matrice, Eigenvalues, eigenvectors, etc.
Author(s): Prof. Haynes Miller, Prof. Arthur Mattuck, Massachusetts Institute of Technology
NA 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
A Friendly Introduction to Differential Equations
This paper looks at friendly differential equations and keeps the language simple. It asks what friendly is, how equations fits, and what a student should notice. If a word in differential equations is new, the next sentence says what it means.
Author(s): Mohammed K A Kaabar
165 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
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
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