Ordinary Differential Equations Lecture Notes by Eugen J. Ionascu
Ordinary Differential Equations Lecture Notes by Eugen J. Ionascu
Ordinary Differential Equations Lecture Notes by Eugen J. Ionascu
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.
This book
explains the following topics: First Order Equations, Second Order Linear
Equations, Reduction of Order Methods, Homogenous Constant Coefficients
Equations ,Power Series Solutions, The Laplace Transform Method, Systems of
Linear Differential Equations, Autonomous Systems and Stability, Boundary
Value Problems.
This note covers the following topics: First Order Equations,
Numerical Methods, Applications of First Order Equations, Linear Second
Order Equations, Applcations of Linear Second Order Equations, Series
Solutions of Linear Second Order Equations, Laplace Transforms, Linear
Higher Order 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.
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.
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.
This lecture note introduces three main types of partial differential
equations: diffusion, elliptic, and hyperbolic. It includes mathematical
tools, real-world examples and applications.
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.
This note describes the
following topics: First Order Ordinary Differential Equations, Applications and
Examples of First Order ode’s, Linear Differential Equations, Second Order
Linear Equations, Applications of Second Order Differential Equations, Higher
Order Linear Differential Equations, Power Series Solutions to Linear
Differential Equations, Linear Systems, Existence and Uniqueness Theorems,
Numerical Approximations.
These
are the sample pages from the textbook. Topics Covered: Partial differential equations, Orthogonal functions, Fourier Series, Fourier
Integrals, Separation of Variables, Boundary Value Problems, Laplace Transform,
Fourier Transforms, Finite Transforms, Green's Functions and Special Functions.
This
elementary text-book on Ordinary Differential Equations, is an attempt to present as much of the subject as is necessary for
the beginner in Differential Equations, or, perhaps, for the student of
Technology who will not make a specialty of pure Mathematics. On account of the
elementary character of the book, only the simpler portions of the subject have
been touched upon at all ; and much care has been taken to make all the
developments as clear as possible every important step being illustrated by easy
examples.
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.