Ordinary Differential Equations and Dynamical Systems
Ordinary Differential Equations and Dynamical Systems
Ordinary Differential Equations and Dynamical Systems
The aim of this book is to give a self contained introduction to the
field of ordinary differential equations with emphasis on the dynamical systems
point of view while still keeping an eye on classical tools as pointed out
before. Covered topics are: Newton’s equations, Classification of differential
equations, First order autonomous equations, Qualitative analysis of first order
equations, Initial value problems, Linear equations, Differential equations in
the complex domain, Boundary value problems, Dynamical systems, Planar dynamical
systems, Higher dimensional dynamical systems, Local behavior near fixed points,
Chaos, Discrete dynamical systems, Discrete dynamical systems in one dimension,
Periodic solutions, Chaos in higher dimensional systems.
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.
The contents of
this book include: A short mathematical review, Introduction to odes,
First-order odes , Second-order odes, constant coefficients, The Laplace
transform, Series solutions, Systems of equations, Nonlinear differential
equations, Partial differential equations.
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 main ideas to solve certain differential equations, such us
first order scalar equations, second order linear equations, and systems of
linear equations. It uses power series methods to solve variable
coefficients second order linear equations. Also introduces Laplace
transform methods to find solutions to constant coefficients equations with
generalized source functions.
This
note explains the following topics: What are differential equations,
Polynomials, Linear algebra, Scalar ordinary differential equations, Systems of
ordinary differential equations, Stability theory for ordinary differential
equations, Transform methods for differential equations, Second-order boundary
value problems.
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 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.