Mathematics Books Differential Equations Books

Entropy and Partial Differential Equations

Entropy and Partial Differential Equations

Entropy and Partial Differential Equations

This note covers the following topics: Entropy and equilibrium, Entropy and irreversibility, Continuum thermodynamics, Elliptic and parabolic equations, Conservation laws and kinetic equations, Hamilton–Jacobi and related equations, Entropy and uncertainty, Probability and differential equations.

Author(s):

s213 Pages
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A First Course in Elementary Differential Equations

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.

s213 Pages
Partial Differential Equations Lectures by Joseph M. Mahaffy

Partial Differential Equations Lectures by Joseph M. Mahaffy

This note introduces students to differential equations. Topics covered includes: Boundary value problems for heat and wave equations, eigenfunctionexpansions, Surm-Liouville theory and Fourier series, D'Alembert's solution to wave equation, characteristic, Laplace's equation, maximum principle and Bessel's functions.

sNA Pages
Lectures   on Partial Differential Equations

Lectures on Partial Differential Equations

This note explains the following topics: The translation equation, The wave equation, The diffusion equation, The Laplace equation, The Schrodinger equation, Diffusion and equilibrium, Fourier series, Fourier transforms, Gradient and divergence, Spherical harmonics.

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Introduction   to Partial Differential Equations Lecture Notes

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This lecture note introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications.

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Introduction to Ordinary and Partial Differential Equations

Introduction to Ordinary and Partial Differential Equations

This note covers the following topics: Classification of Differential Equations, First Order Differential Equations, Second Order Linear Equations, Higher Order Linear Equations, The Laplace Transform, Systems of Two Linear Differential Equations, Fourier Series, Partial Differential Equations.

s234 Pages
Elementary Differential Equations With Boundary Value Problems

Elementary Differential Equations With Boundary Value Problems

This book explains the following topics: First Order Equations, Numerical Methods, Applications of First Order Equations1em, Linear Second Order Equations, Applcations of Linear Second Order Equations, Series Solutions of Linear Second Order Equations, Laplace Transforms, Linear Higher Order Equations, Linear Systems of Differential Equations, Boundary Value Problems and Fourier Expansions, Fourier Solutions of Partial Differential Equations, Boundary Value Problems for Second Order Linear Equations.

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Ordinary and Partial Differential Equations

Ordinary and Partial Differential Equations

This note explains the following topics: Existence and Uniqueness, Systems, Stability, Sturm-Liouville Theory, First Order, Quasi-Linear, Classification, Hyperbolic Problems, Elliptic Problems, Parabolic Problems.

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Notes on Partial Differential Equations

Notes on Partial Differential Equations

This book covers the following topics: Laplace's equations, Sobolev spaces, Functions of one variable, Elliptic PDEs, Heat flow, The heat equation, The Fourier transform, Parabolic equations, Vector-valued functions and Hyperbolic equations.

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Linear Partial Differential Equations and Fourier Theory

Linear Partial Differential Equations and Fourier Theory

This is a textbook for an introductory course on linear partial differential equations (PDEs) and initial/boundary value problems (I/BVPs). It also provides a mathematically rigorous introduction to Fourier analysis  which is the main tool used to solve linear PDEs in Cartesian coordinates.

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Difference Equations to Differential Equations

Difference Equations to Differential Equations

This book covers the following topics: Sequences, limits, and difference equations, Functions and their properties, Best affine approximations, Integration, Polynomial approximations and Taylor series, transcendental functions, The complex plane and Differential equations.

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Linear Differential Equations

Linear Differential Equations

This note covers the following topics: Derivatives, differential equations, partial differential equations, distributions, Cauchy-Kowalewsky theorem, heat equation, Laplace equation, Schrodinger equation, wave equation, Cauchy-Riemann equations.

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Monograph on quasilinear partial differential equations (EJDE)

Monograph on quasilinear partial differential equations (EJDE)

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Differential Equations (Dawkins P)

Differential Equations (Dawkins P)

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Entropy and Partial Differential Equations(Evans L.C pdf)

Entropy and Partial Differential Equations(Evans L.C pdf)

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A PDE Primer (Showalter R.E)

A PDE Primer (Showalter R.E)

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Analytic differential equations

Analytic differential equations

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