This book explains the following
topics: IFirst-order differential equations, Direction fields, existence and
uniqueness of solutions, Numerical methods, Linear equations, models,
Complex numbers, roots of unity, Second-order linear equations, Modes and
the characteristic polynomial, Good vibrations, damping conditions,
Exponential response formula, spring drive, Complex gain, dashpot drive,
Operators, undetermined coefficients, resonance, Frequency response, LTI
systems, superposition, RLC circuits, Engineering applications, Fourier
series, Operations on fourier series , Periodic solutions; resonance, Step
functions and delta functions, Step response, impulse response, Convolution,
First order systems, Linear systems and matrice, Eigenvalues, eigenvectors,
etc.

Author(s): Prof. Haynes Miller, Prof. Arthur Mattuck,
Massachusetts Institute of Technology

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 book explains the following
topics: IFirst-order differential equations, Direction fields, existence and
uniqueness of solutions, Numerical methods, Linear equations, models,
Complex numbers, roots of unity, Second-order linear equations, Modes and
the characteristic polynomial, Good vibrations, damping conditions,
Exponential response formula, spring drive, Complex gain, dashpot drive,
Operators, undetermined coefficients, resonance, Frequency response, LTI
systems, superposition, RLC circuits, Engineering applications, Fourier
series, Operations on fourier series , Periodic solutions; resonance, Step
functions and delta functions, Step response, impulse response, Convolution,
First order systems, Linear systems and matrice, Eigenvalues, eigenvectors,
etc.

Author(s): Prof. Haynes Miller, Prof. Arthur Mattuck,
Massachusetts Institute of Technology

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.

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 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.

Harry Bateman was a
famous English mathematician. In writing this book he had endeavoured to supply
some elementary material suitable for the needs of students who are studying the
subject for the first time, and also some more advanced work which may be useful
to men who are interested more in physical mathematics than in the developments
of differential geometry and the theory of functions. The chapters on partial
differential equations have consequently been devoted almost entirely to the
discussion of linear equations.

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.