Bowen, Ray M.Ray M. Bowenhttp://hdl.handle.net/1969.1/25002015-01-25T14:20:16Z2015-01-25T14:20:16ZLectures on Applied Mathematics Part 1: Linear Algebrahttp://hdl.handle.net/1969.1/947722014-01-23T07:03:03Z2014-01-22T00:00:00ZLectures 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 mixtureshttp://hdl.handle.net/1969.1/912972014-09-16T06:36:12Z2014-01-22T00:00:00ZPorous 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 analysishttp://hdl.handle.net/1969.1/36092011-02-07T23:02:47Z2006-06-20T22:18:12ZIntroduction 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.
2006-06-20T22:18:12ZIntroduction to vectors and tensors, Vol 1: linear and multilinear algebrahttp://hdl.handle.net/1969.1/25022011-06-16T17:01:46Z1976-01-01T00:00:00ZIntroduction to vectors and tensors, Vol 1: linear and multilinear algebra
This work represents our effort to present the basic concepts of vector and tensor analysis. Volume I begins with a brief discussion of algebraic structures followed by a rather detailed discussion of the algebra of vectors and tensors. Volume II begins with a discussion of Euclidean Manifolds which leads to a development of the analytical and geometrical aspects of vector and tensor fields. a discussion of general differentiable manifolds. We have not included a discussion of general differentiable manifolds. However, we have included a chapter on vector and tensor fields defined on Hypersurfaces in a Euclidean Manifold.
In preparing this two volume work our intention is to present to Engineering and Science students a modern introduction to vectors and tensors. Traditional courses on applied mathematics have emphasized problem solving techniques rather than the systematic development of concepts. As a result, it is possible for such courses to become terminal mathematics courses rather than courses which equip the student to develop his or her understanding further.
As Engineering students our courses on vectors and tensors were taught in the traditional way. We learned to identify vectors and tensors by formal transformation rules rather than by their common mathematical structure. The subject seemed to consist of nothing but a collection of mathematical manipulations of long equations decorated by a multitude of subscripts and superscripts. Prior to our applying vector and tensor analysis to our research area of modern continuum mechanics, we almost had to relearn the subject. Therefore, one of our objectives in writing this book is to make available a modern introductory textbook suitable for the first in-depth exposure to vectors and tensors. Because of our interest in applications, it is our hope that this book will aid students in their efforts to use vectors and tensors in applied areas.
The presentation of the basic mathematical concepts is, we hope, as clear and brief as possible without being overly abstract. Since we have written an introductory text, no attempt has been made to include every possible topic. The topics we have included tend to reflect our personal bias. We make no claim that there are not other introductory topics which could have been included.
Basically the text was designed in order that each volume could be used in a one-semester course. We feel Volume I is suitable for an introductory linear algebra course of one semester. Given this course, or an equivalent, Volume II is suitable for a one semester course on vector and tensor analysis. Many exercises are included in each volume. However, it is likely that teachers will wish to generate additional exercises. Several times during the preparation of this book we taught a one semester course to students with a very limited background in linear algebra and no background in tensor analysis. Typically these students were majoring in Engineering or one of the Physical Sciences. However, we occasionally had students from the Social Sciences. For this one semester course, we covered the material in Chapters 0, 3, 4, 5, 7 and 8 from Volume I and selected topics from Chapters 9, 10, and 11 from Volume 2. As to level, our classes have contained juniors, seniors and graduate students. These students seemed to experience no unusual difficulty with the material.
It is a pleasure to acknowledge our indebtedness to our students for their help and forbearance. Also, we wish to thank the U. S. National Science Foundation for its support during the preparation of this work. We especially wish to express our appreciation for the patience and understanding of our wives and children during the extended period this work was in preparation.
1976-01-01T00:00:00Z