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:
Functions of Several Variables, Partial Derivatives and Tangent Planes, Max
and Min Problems on Surfaces, Ordinary Differential Equations,
Parametrisation of Curves and Line Integrals and MATLAB Guide.
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.
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 lecture note introduces three main types of partial differential
equations: diffusion, elliptic, and hyperbolic. It includes mathematical
tools, real-world examples and applications.
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: 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.
This is a textbook for an introductory course on linear partial
differential equations (PDEs) and initial/boundary value problems (I/BVPs). It
also provides a mathematically rigorous introduction to Fourier analysis
which is the main tool used to solve linear PDEs in Cartesian coordinates.
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.