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A First Course in Elementary Differential Equations
This note covers the following topics: Qualitative Analysis, Existence and Uniqueness of Solutions to First Order Linear IVP, Solving First Order Linear Homogeneous DE, Solving First Order Linear Non Homogeneous DE: The Method of Integrating Factor, Modeling with First Order Linear Differential Equations, Additional Applications: Mixing Problems and Cooling Problems, Separable Differential Equations, Exact Differential Equations, Substitution Techniques: Bernoulli and Ricatti Equations, Applications of First Order Nonlinear Equations, One-Dimensional Dynamics, Second Order Linear Differential Equations, The General Solution of Homogeneous Equations, Existence of Many Fundamental Sets, Second Order Linear Homogeneous Equations with Constant, Coefficients, Characteristic Equations with Repeated Roots, The Method of Undetermined Coefficients, Applications of Nonhomogeneous Second Order Linear Differential Equations.
Author(s): Marcel B. Finan
213 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
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
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
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
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
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