(BQ) Part 1 book "Numerical analysis" has contents: Fundamentals, solving equations, systems of equations, interpolation, least squares, numerical differentiation and integration, numerical differentiation and integration.
(BQ) Part 2 book "Applied numerical methods" has contents: Linear regression, fourier analysis, polynomial interpolation, splines and piecewise interpolation, numerical integration formulas, numerical integration of functions, numerical differentiation, boundary value problems,...and other contents.
(BQ) Part 1 book "Numerical analysis" has content: Mathematical preliminaries and error analysis, solutions of equations in one variable, interpolation and polynomial approximation, numerical differentiation and integration, initial value problems for ordinary differential equations, direct methods for solving linear systems.
We have attempted to write a concise modern treatment of differential equations
emphasizing applications and containing all the core parts of a course in differential
equations.Asemester or quarter course in differential equations is taught to most engineering
students (and many science students) at all universities, usually in the second
year. Some universities have an earlier brief introduction to differential equations and
others do not. Some students will have already seen some differential equations in
their science classes.We do not assume any prior exposure to differential equations.
The fifth edition of this classic book continues its excellence in teaching numerical analysis and techniques. Interesting and timely applications motivate an understanding of methods and analysis of results. Suitable for students with mathematics and engineering backgrounds, the breadth of topics (partial differential equations, systems of nonlinear equations, and matrix algebra), provide comprehensive and flexible coverage of all aspects of all numerical analysis.
This section attempts to answer some of the questions you might formulate when you turn the first page: What does this toolbox do? Can I use it? What problems can I solve?, etc.
What Does this Toolbox Do?
The Partial Differential Equation (PDE) Toolbox provides a powerful and flexible environment for the study and solution of partial differential equations in two space dimensions and time. The equations are discretized by the Finite Element Method (FEM). The objectives of the PDE Toolbox are to provide you with tools that:
• Define a PDE problem, i.e.
In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods.
Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding.
Classical differential geometry is the approach to geometry that takes full
advantage of the introduction of numerical coordinates into a geometric
space. This use of coordinates in geometry was the essential insight of Rene
Descartes that allowed the invention of analytic geometry and paved the way
for modern differential geometry. The basic object in differential geometry
(and differential topology) is the smooth manifold. This is a topological
space on which a sufficiently nice family of coordinate systems or "charts"
The goal of this book is to expose the reader to modern computational tools for
solving differential equation models that arise in chemical engineering, e.g.,
diffusion-reaction, mass-heat transfer, and fluid flow. The emphasis is placed
on the understanding and proper use of software packages. In each chapter we
outline numerical techniques that either illustrate a computational property of
interest or are the underlying methods of a computer package. At the close of
each chapter a survey of computer packages is accompanied by examples of
The present volume, compiled in honor of an outstanding historian of science,
physicist and exceptional human being, Sam Schweber, is unique in assembling
a broad spectrum of positions on the history of science by some of its leading
representatives. Readers will find it illuminating to learn how prominent authors
judge the current status and the future perspectives of their field. Students will find
this volume helpful as a guide in a fragmented field that continues to be dominated
by idiosyncratic expertise and still lacks a methodical canon.
(BQ) Part 2 book "Numerical analysis" has contents: Boundary value problems, partial differential equations, random numbers and applications, trigonometric interpolation and the FFT, compression, optimization, eigenvalues and singular values.
(BQ) Part 1 book "A first course in differential equations" has contents: Introduction to differential equations, first order differential equations, modeling with first order differential equations, higher order differential equations.
(BQ) Part 2 book "A first course in differential equations" has contents: Modeling with higher order differential equations, modeling with higher order differential equations, the laplace transform, systems of linear first order differential equations, numerical solutions of ordinary differential equations.
(BQ) Part 1 book "A first course in differential" has contents: Introduction to differential equations, first order differential equations, modeling with first-order differential equations, higher order differential equations.
(BQ) Part 2 book "A first course in differential" has contents: Modeling with higher order differential equations, series solutions of linear equations, the laplace transform, systems of linear first order differential equations, numerical solutions of ordinary differential equations.
(BQ) Part 2 book "Numerical analysis" has content: Iterative Techniques in matrix algebra, approximation theory, approximation theory, numerical solutions of nonlinear systems of equations, boundary value problems for ordinary differential equations, numerical solutions to partial differential equations.
(BQ) Part 2 book "Fundamental numerical methods and data analys" has contents: Numerical solution of differential and integral equations; least squares, fourier analysis, and related approximation norms; probability theory and statistics; sampling distributions of moments, statistical tests, and procedures.
Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods. Indeed, the area is an expanding source for novel and relevant "real-world" mathematics. In this book, the authors describe the modeling of financial derivative products from an applied mathematician's viewpoint, from modeling to analysis to elementary computation.