Bowen, Ray M.
http://hdl.handle.net/1969.1/2500
Ray M. Bowen2015-05-27T20:00:23ZLectures on Applied Mathematics Part 2: Numerical Analysis
http://hdl.handle.net/1969.1/153759
Lectures on Applied Mathematics Part 2: Numerical Analysis
This book is designed to be a continuation of the textbook, Lectures on Applied Mathematics Part I: Linear Algebra which can also be downloaded at http://rbowen.tamu.edu. This textbook evolved from my teaching an undergraduate Numerical Analysis course to Mechanical Engineering students at Texas A&M University. That course was one of the courses I was allowed to teach after my several years out of the classroom. It tries to utilize rigorous concepts in Linear Algebra in combination with the powerful computational tools of MATLAB to provide undergraduate students practical numerical analysis tools. It makes extensive use of MATLAB's graphics capabilities and, to a limited extent, its ability to animate the solutions of ordinary differential equations. It is not a textbook that tries to be comprehensive as a source of MATLAB information. It does contain a large number of links to MATLAB's extensive online resources. This information has been invaluable to me as this work was developed. The version of MATLAB used in the preparation of this textbook is MATLAB 2014b. This version implements a new graphics system. As a result, when earlier versions are utilized with this textbook, small changes in the script may be required to cause the script in the textbook to execute.
2015-03-24T00:00:00ZLectures on Applied Mathematics Part 1: Linear Algebra
http://hdl.handle.net/1969.1/94772
Lectures on Applied Mathematics Part 1: Linear Algebra
Chap. 1: Elementary Matrix Theory; Chap. 2: Vector Spaces;
Chap. 3: Linear Transformations;
Chap. 4: Vector Spaces with Inner Product; Chap. 5: Eigenvalue Problems; Chap. 6: Additional Topics Relating to Eigenvalue Problems
It is common for Departments of Mathematics to offer a junior-senior level course on Linear Algebra. This book represents one possible course. It evolved from my teaching a junior level course at Texas A&M University during the several years I taught after I served as President. I am deeply grateful to the A&M Department of Mathematics for allowing this Mechanical Engineer to teach their students.
This book is influenced by my earlier textbook with C.-C Wang, Introductions to Vectors and Tensors, Linear and Multilinear Algebra. This book is more elementary and is more applied than the earlier book. However, my impression is that this book presents linear algebra in a form that is somewhat more advanced than one finds in contemporary undergraduate linear algebra courses. In any case, my classroom experience with this book is that it was well received by most students. As usual with the development of a textbook, the students that endured its evolution are due a statement of gratitude for their help.
2014-01-22T00:00:00ZPorous Elasticity: Lectures on the elasticity of porous materials as an application of the theory of mixtures
http://hdl.handle.net/1969.1/91297
Porous Elasticity: Lectures on the elasticity of porous materials as an application of the theory of mixtures
This work was originally planned as a textbook exploiting the structure of the Theory of Mixtures as the basis for the study of porous elasticity. The decision to write this book was made approximately thirty years ago! At that time, I was a faculty member in Mechanical Engineering at Rice University. It is an understatement to observe that it has taken awhile to complete, even partially, this project. I encountered a lot of diversions along the way. Not the least of which was an eight year period where I served as President of Texas A&M University. Prior to that time, I was a Dean of Engineering at Kentucky, an administrator at the National Science Foundation and a Provost and Interim President at Oklahoma State University. During my time as an administrator, I never lost my ambition to prepare this textbook. On occasion, during periods of relative calm or, at the other extreme, during periods of great stress, I would find comfort in returning to my manuscript. It would take someone not trained in Engineering to understand why I would find comfort thinking about this book when caught up in the tangles of university administration. This work is organized into ten chapters. It begins in Chapter 1 with a brief review of classical porous media models. Chapter 2 introduces the essentials of the theory of mixtures. Chapters 3,4 and 5 exploit the theory of mixtures to formulate various models of porous elastic materials. Chapter 6 is concerned with establishing connections between the formulation given in this work and other important formulations. Chapters 7, 8,9 and 10 contain various calculations which utilize the models formulated in earlier chapters.
2014 Version
2014-01-22T00:00:00ZIntroduction to vectors and tensors, Vol 2: vector and tensor analysis
http://hdl.handle.net/1969.1/3609
Introduction to vectors and tensors, Vol 2: vector and tensor analysis
This is the second volume of a two-volume work on vectors and tensors. Volume 1 is concerned with the algebra of vectors and tensors, while this volume is concerned with the geometrical aspects of vectors and tensors. This volume begins with a discussion of Euclidean manifolds. The principal mathematical entity considered in this volume is a field, which is defined on a domain in a Euclidean manifold. The values of the field may be vectors or tensors. We investigate results due to the distribution of the vector or tensor values of the field on its domain. While we do not discuss general differentiable manifolds, we do include a chapter on vector and tensor fields defined on hypersurfaces in a Euclidean manifold.
2006-06-20T22:18:12Z