This note covers the following topics: Notion of ODEs, Linear ODE of
1st order, Second order ODE, Existence and uniqueness theorems, Linear equations
and systems, Qualitative analysis of ODEs, Space of solutions of homogeneous
systems, Wronskian and the Liouville formula.
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.
This note explains the following topics: Solving various types of
differential equations, Analytical Methods, Second and n-order Linear
Differential Equations, Systems of Differential Equations, Nonlinear Systems and
Qualitative Methods, Laplace Transform, Power Series Methods, Fourier Series.
Goal of this
note is to develop the most basic ideas from the theory of partial
differential equations, and apply them to the simplest models arising from
physics. Topics covered includes: Power Series, Symmetry and Orthogonality,
Fourier Series, Partial Differential Equations, PDE’s in Higher Dimensions.
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 note covers the
following topics: First Order Equations and Conservative Systems, Second Order
Linear Equations, Difference Equations, Matrix Differential Equations, Weighted
String, Quantum Harmonic Oscillator, Heat Equation and Laplace Transform.
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 book covers the following topics: Geometry and a Linear Function,
Fredholm Alternative Theorems, Separable Kernels, The Kernel is Small, Ordinary
Differential Equations, Differential Operators and Their Adjoints, G(x,t) in the
First and Second Alternative and Partial 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.
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