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: 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.
covers the following topics: Geometrical Interpretation of ODE, Solution of
First Order ODE, Linear Equations, Orthogonal Trajectories, Existence and
Uniqueness Theorems, Picard's Iteration, Numerical Methods, Second Order Linear
ODE, Homogeneous Linear ODE with Constant Coefficients, Non-homogeneous Linear
ODE, Method of Undetermined Coefficients, Non-homogeneous Linear ODE, Method of
Variation of Parameters, Euler-Cauchy Equations, Power Series Solutions:
Ordinary Points, Legendre Equation, Legendre Polynomials, Frobenius Series
Solution, Regular Singular Point, Bessle Equation, Bessel Function, Strum
Comparison Theorem, Orthogonality of Bessel Function, Laplace Transform, Inverse
Laplace Transform, Existence and Properties of Laplace Transform, Unit step
function, Laplace Transform of Derivatives and Integration, Derivative and
Integration of Laplace Transform, Laplace Transform of Periodic Functions,
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 book covers the following topics: 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 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 book covers the following
topics: Sequences, limits, and difference equations, Functions and their properties,
Best affine approximations, Integration, Polynomial approximations and Taylor
series, transcendental functions, The complex plane and Differential equations.