This note covers the
following topics: The trigonometric functions, The fundamental theorem of
calculus, First-order odes, Second-order odes, constant coefficients, The
Laplace transform, Series solutions, Systems of equations, Nonlinear
differential equations, Partial differential equations.
This note describes
the following topics: First Order Differential Equations, N-th Order
Differential Equations, Linear Differential Equations, Laplace Transforms,
Inverse Laplace Transform, Systems Of Linear Differential Equations, Series
Solution Of Linear Differential Equations.
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.
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.
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.
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.
These notes are a concise understanding-based presentation of the
basic linear-operator aspects of solving linear differential equations.
Topics covered includes: Operators and Linear Combinations, Homogeneous
linear equations, Complex Exponentials and Real Homogeneous Linear
Equations, Non-homogeneous linear equations and Systems of Linear
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.