Vector Calculus [[electronic resource] /] / by Paul C. Matthews

• Record Nr.: UNINA9910480056903321
• Autore: Matthews Paul C
• Pubbl/distr/stampa: London : , : Springer London : , : Imprint : Springer, , 1998
• ISBN: 1-4471-0597-4
• Edizione: [1st ed. 1998.]
• Descrizione fisica: 1 online resource (X, 182 p. 1 illus.)
• Collana: Springer Undergraduate Mathematics Series, , 1615-2085
• Disciplina: 515/.63
• Soggetti: Applied mathematics; Engineering mathematics; Mathematical physics; Engineering; Applications of Mathematics; Theoretical, Mathematical and Computational Physics; Engineering, general
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Includes index.; "With 63 figures."
• Nota di contenuto: 1. Vector Algebra -- 1.1 Vectors and scalars -- 1.2 Dot product -- 1.3 Cross product -- 1.4 Scalar triple product -- 1.5 Vector triple product -- 1.6 Scalar fields and vector fields -- 2. Line, Surface and Volume Integrals -- 2.1 Applications and methods of integration -- 2.2 Line integrals -- 2.3 Surface integrals -- 2.4 Volume integrals -- 3. Gradient, Divergence and Curl -- 3.1 Partial differentiation and Taylor series -- 3.2 Gradient of a scalar field -- 3.3 Divergence of a vector field -- 3.4 Curl of a vector field -- 4. Suffix Notation and its Applications -- 4.1 Introduction to suffix notation -- 4.2 The Kronecker delta ?ij -- 4.3 The alternating tensor ?ijk -- 4.4 Relation between ?ijk and ?ij -- 4.5 Grad, div and curl in suffix notation -- 4.6 Combinations of grad, div and curl -- 4.7 Grad, div and curl applied to products of functions -- 5. Integral Theorems -- 5.1 Divergence theorem -- 5.2 Stokes’s theorem -- 6. Curvilinear Coordinates -- 6.1 Orthogonal curvilinear coordinates -- 6.2 Grad, div and curl in orthogonal curvilinear coordinate systems -- 6.3 Cylindrical polar coordinates -- 6.4 Spherical polar coordinates -- 7. Cartesian Tensors ; -- 7.1 Coordinate transformations -- 7.2 Vectors and scalars -- 7.3 Tensors -- 7.4 Physical examples of tensors -- 8. Applications of Vector Calculus -- 8.1 Heat transfer -- 8.2 Electromagnetism -- 8.3 Continuum mechanics and the stress tensor -- 8.4 Solid mechanics -- 8.5 Fluid mechanics -- Solutions.
• Sommario/riassunto: Vector calculus is the fundamental language of mathematical physics. It pro­ vides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. These top­ ics include fluid dynamics, solid mechanics and electromagnetism, all of which involve a description of vector and scalar quantities in three dimensions. This book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants. The book is designed to be self-contained, so that it is suitable for a pro­ gramme of individual study. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications. The physical nature of the subject is clarified with over sixty diagrams, which provide an important aid to the comprehension of the new concepts. Following the introduction of each new topic, worked examples are provided. It is essential that these are studied carefully, so that a full un­ derstanding is developed before moving ahead. Like much of mathematics, each section of the book is built on the foundations laid in the earlier sections and chapters.

Standards of mouse model phenotyping [[electronic resource] /] / edited by Martin Hrabede Angelis, Pierre Chambon, and Steve Brown

• Record Nr.: UNINA9910830451103321
• Pubbl/distr/stampa: Weinheim, : Wiley-VCH, c2006
• ISBN: 1-282-30244-2; 9786612302442; 3-527-61194-0; 3-527-60870-2
• Descrizione fisica: 1 online resource (359 p.)
• Altri autori (Persone): Hrabé de AngelisMartin; ChambonPierre; BrownStephen D. M
• Disciplina: 599.353135
• Soggetti: Mice as laboratory animals; Mice - Genetics; Transgenic mice; Phenotype
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Standards of Mouse Model Phenotyping; Foreword; Table of Contents; Preface; 1 Characterizing Hearing in Mice; 1.1 Introduction; 1.2 Behavioral Tests of Hearing; 1.3 Physiological Tests of Hearing; 1.4 Anatomy of the Ear; 1.5 Conclusions; Acknowledgements; 2 Molecular Phenotyping: Gene Expression Profiling; 2.1 Why this Screen? Medical and Biological Relevance; 2.2 Examples: Diseases of Mouse and Man; 2.3 Diagnostic Methods: History and State of the Art; 2.4 Technical Requirements for Screening Protocols (Short): First and Second Line Approaches; 2.5 Logistics (Whom, When, How Many, Why); 2.5.1 Choice of Platform2.5.2 Biological Samples; 2.6 Trouble Shooting; 2.6.1 Preparation of Hybridization Target; 2.6.2 Critical Issues of Chip Hybridization; 2.6.3 Image Processing and Array Design; 2.7 Short-term Outlook; 3 Screening for Bone and Cartilage Phenotypes in Mice; 3.1 Introduction; 3.1.1 The Skeleton; 3.1.2 Skeletal Development in the Embryo; 3.1.3 Growth and Maintenance of Bone and Cartilage; 3.1.4 ; Diseases Involving Cartilage and Bone; 3.1.5 The Mouse as a Model for Skeletal Diseases; 3.2 Screening Protocols; 3.2.1 Morphological Analysis; 3.2.1.1 Protocol; 3.2.2 X-Ray Analysis3.2.2.1 General; 3.2.2.2 Imaging; 3.2.2.3 X-Ray Analysis; 3.2.2.4 Protocol; 3.2.3 DXA-Analysis; 3.2.3.1 General; 3.2.3.2 Advantages; 3.2.3.3 Disadvantages; 3.2.3.4 Small Animal Applications; 3.2.3.5 Precision and Accuracy; 3.2.3.6 Considerations; 3.2.3.7 Protocol; 3.2.4 Biochemical Bone Markers; 3.2.4.1 Clinical Utility of Biochemical Markers of Bone Turnover in Small Animals; 3.2.4.2 Mouse Markers of Bone Turnover/Metabolism and Hormonal Regulation; 3.2.4.3 Variability/Sensitivity/Sample Choice; 3.2.4.4 Which Markers Should be Used During the Screen?; 3.2.5 Advanced Small Animal Imaging Techniques3.2.5.1 pQCT; 3.2.5.2 μCT; 3.2.5.3 μMRI; 3.2.5.4 Whole-mount Skeletal Preparations; 3.2.5.5 Histomorphometry; 3.2.5.6 Miscellaneous; 3.2.5.7 Order of the Tests; 3.3 Conclusion; List of Abbreviations; Appendix; μCT Volumetric Data Processing; MRI Principles; 4 Clinical Chemical Screen; 4.1 Introduction; 4.1.1 Relevance of the Screen; 4.1.2 Biology and Medical Application; 4.1.2.1 Biology of Clinical Chemical Parameters; 4.1.2.2 Medical Application; 4.2 Diseases in Mouse and Humans; 4.2.1 Diagnostic Impact of Clinical Chemistry; 4.2.2 Clinical Chemistry in Selected Disorders4.2.2.1 Hypercholesterolemia; 4.2.2.2 Albuminuria; 4.2.2.3 Acute Myeloid Leukemia (AML); 4.3 Clinical Chemistry as Diagnostic Tool; 4.3.1 History; 4.3.2 State of the Art; 4.4 Technical Requirements and Screening Protocols; 4.4.1 Technical Requirements; 4.4.1.1 Blood Collection; 4.4.1.2 Sample Preparation; 4.4.1.3 Sample Analysis; 4.4.2 Screening Protocols; 4.4.2.1 Primary Screen; 4.4.2.2 Secondary Screen; 4.4.2.3 Tertiary Screen; 4.5 Logistics of the Screen; 4.5.1 General Considerations; 4.5.2 Lessons from ENU Mutants; 4.6 Trouble Shooting; 4.6.1 Factors Interfering In Vivo
• Sommario/riassunto: This is the first book in the field of mouse genetics to provide comprehensive and standardized methods for the characterization of laboratory mice. The editor is Director of the German Mouse Clinic and member of the Project Committee of the German National Genome Research Network and provides here a brief introduction to the mouse as a model for diseases and functional analysis of genes and proteins. Throughout, he focuses on the characterization of mouse models using the latest phenotyping methods, with the different areas presented in a clearly structured and easily accessible manner.