Vectors, Tensors and the Basic Equations of Fluid Mechanics
Title | Vectors, Tensors and the Basic Equations of Fluid Mechanics PDF eBook |
Author | Rutherford Aris |
Publisher | Courier Corporation |
Pages | 322 |
Release | 2012-08-28 |
Genre | Mathematics |
ISBN | 048613489X |
Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.
Basic Equations of the Mass Transport Through a Membrane Layer
Title | Basic Equations of the Mass Transport Through a Membrane Layer PDF eBook |
Author | Endre Nagy |
Publisher | Elsevier |
Pages | 342 |
Release | 2012 |
Genre | Science |
ISBN | 0124160255 |
With a detailed analysis of the mass transport through membrane layers and its effect on different separation processes, this book provides a comprehensive look at the theoretical and practical aspects of membrane transport properties and functions. Basic equations for every membrane are provided to predict the mass transfer rate, the concentration distribution, the convective velocity, the separation efficiency, and the effect of chemical or biochemical reaction taking into account the heterogeneity of the membrane layer to help better understand the mechanisms of the separation processes. The reader will be able to describe membrane separation processes and the membrane reactors as well as choose the most suitable membrane structure for separation and for membrane reactor. Containing detailed discussion of the latest results in transport processes and separation processes, this book is essential for chemistry students and practitioners of chemical engineering and process engineering. Detailed survey of the theoretical and practical aspects of every membrane process with specific equations Practical examples discussed in detail with clear steps Will assist in planning and preparation of more efficient membrane structure separation
Basic Linear Partial Differential Equations
Title | Basic Linear Partial Differential Equations PDF eBook |
Author | François Treves |
Publisher | Academic Press |
Pages | 493 |
Release | 1975-08-08 |
Genre | Mathematics |
ISBN | 0080880258 |
Basic Linear Partial Differential Equations
Basic Partial Differential Equations
Title | Basic Partial Differential Equations PDF eBook |
Author | David. Bleecker |
Publisher | CRC Press |
Pages | 974 |
Release | 2018-01-18 |
Genre | Mathematics |
ISBN | 1351086987 |
Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving reasonably smooth, predictable changes of measurable quantities. This text enables the reader to not only find solutions of many PDEs, but also to interpret and use these solutions. It offers 6000 exercises ranging from routine to challenging. The palatable, motivated proofs enhance understanding and retention of the material. Topics not usually found in books at this level include but examined in this text: the application of linear and nonlinear first-order PDEs to the evolution of population densities and to traffic shocks convergence of numerical solutions of PDEs and implementation on a computer convergence of Laplace series on spheres quantum mechanics of the hydrogen atom solving PDEs on manifolds The text requires some knowledge of calculus but none on differential equations or linear algebra.
Basic Theory of Ordinary Differential Equations
Title | Basic Theory of Ordinary Differential Equations PDF eBook |
Author | Po-Fang Hsieh |
Publisher | Springer Science & Business Media |
Pages | 480 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461215064 |
Providing readers with the very basic knowledge necessary to begin research on differential equations with professional ability, the selection of topics here covers the methods and results that are applicable in a variety of different fields. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, while the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history, and hints and comments for many problems are given throughout. With 114 illustrations and 206 exercises, the book is suitable for a one-year graduate course, as well as a reference book for research mathematicians.
Basic Mathematics
Title | Basic Mathematics PDF eBook |
Author | Serge Lang |
Publisher | |
Pages | 475 |
Release | 1988-01 |
Genre | Mathematics |
ISBN | 9783540967873 |
Basic Global Relative Invariants for Nonlinear Differential Equations
Title | Basic Global Relative Invariants for Nonlinear Differential Equations PDF eBook |
Author | Roger Chalkley |
Publisher | American Mathematical Soc. |
Pages | 386 |
Release | 2007 |
Genre | Mathematics |
ISBN | 0821839918 |
The problem of deducing the basic relative invariants possessed by monic homogeneous linear differential equations of order $m$ was initiated in 1879 with Edmund Laguerre's success for the special case $m = 3$. It was solved in number 744 of the Memoirs of the AMS (March 2002), by a procedure that explicitly constructs, for any $m \geq3$, each of the $m - 2$ basic relative invariants. During that 123-year time span, only a few results were published about the basic relative invariants for other classes of ordinary differential equations. With respect to any fixed integer $\, m \geq 1$, the author begins by explicitly specifying the basic relative invariants for the class $\, \mathcal{C {m,2 $ that contains equations like $Q {m = 0$ in which $Q {m $ is a quadratic form in $y(z), \, \dots, \, y{(m) (z)$ having meromorphic coefficients written symmetrically and the coefficient of $\bigl( y{(m) (z) \bigr){2 $ is $1$.Then, in terms of any fixed positive integers $m$ and $n$, the author explicitly specifies the basic relative invariants for the class $\, \mathcal{C {m, n $ that contains equations like $H {m, n = 0$ in which $H {m, n $ is an $n$th-degree form in $y(z), \, \dots, \, y{(m) (z)$ having meromorphic coefficients written symmetrically and the coefficient of $\bigl( y{(m) (z) \bigr){n $ is $1$.These results enable the author to obtain the basic relative invariants for additional classes of ordinary differential equa