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.
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.
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.
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
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.
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 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,
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.
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.
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
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