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
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
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 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 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 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.
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 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.
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.
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.
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
Differential Equations.