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Geometric Morphometrics for Biologists is an introductory textbook for a course on geometric morphometrics, written for graduate students and upper division undergraduates, covering both theory of shape analysis and methods of multivariate analysis. It is designed for students with minimal math background; taking them from the process of data collection through basic and more advanced statistical analyses. Many examples are given, beginning with simple although realistic case-studies, through examples of complex analyses requiring several different kinds of methods. The book also includes URL’s for free software and step-by-step instructions for using the software.

* Accessible, student-tested introduction to sophisticated methods of biological shape analysis
* Detailed instructions for conducting analyses with freely available, easy to use software
* Numerous illustrations; including graphical presentations of important theoretical concepts and demonstrations of alternative approaches to presenting results
* Many realistic examples, both simple and complex, from on-going research
* Comprehensive glossary of technical terms

The first edition of Geometric Morphometrics for Biologists has been the primary resource for teaching modern geometric methods of shape analysis to biologists who have a stronger background in biology than in multivariate statistics and matrix algebra. These geometric methods are appealing to biologists who approach the study of shape from a variety of perspectives, from clinical to evolutionary, because they incorporate the geometry of organisms throughout the data analysis. The second edition of this book retains the emphasis on accessible explanations, and the copious illustrations and examples of the first, updating the treatment of both theory and practice. The second edition represents the current state-of-the-art and adds new examples and summarizes recent literature, as well as provides an overview of new software and step-by-step guidance through details of carrying out the analyses.

• Contains updated coverage of methods, especially for sampling complex curves and 3D forms and a new chapter on applications of geometric morphometrics to forensics
• Offers a reorganization of chapters to streamline learning basic concepts
• Presents detailed instructions for conducting analyses with freely available, easy to use software
• Provides numerous illustrations, including graphical presentations of important theoretical concepts and demonstrations of alternative approaches to presenting results

Engineering drawing is the "instrument of communication" upon which the designer must place all information necessary to define a new product. Computer-aided design (CAD) courses often involve teaching solid modelling software, and we view CAD as an engineering communication tool for manufacturing. As the technology of engineering design is in transition from paper drawings to solid models, its education must address the challenge of covering both technologies. Geometry of design integrates drafting technology based on experience with engineering design education. This workbook has evolved from the course “Computer-Aided Graphics and Design” at the University of Florida, and many pages of this textbook can be used for student assignments. In order to help students to familiarize themselves with the manufacturing field experience, most assignments are to be submitted in the form of complete working drawings of the parts and assembly. The first three chapters introduce basic engineering drawing definitions and practices. The following four chapters cover design and descriptive geometry, and subsequent chapters move on to dimensions, assembly line design and surface development.

Geometry with Trigonometry Second Edition is a second course in plane Euclidean geometry, second in the sense that many of its basic concepts will have been dealt with at school, less precisely. It gets underway with a large section of pure geometry in Chapters 2 to 5 inclusive, in which many familiar results are efficiently proved, although the logical frame work is not traditional. In Chapter 6 there is a convenient introduction of coordinate geometry in which the only use of angles is to handle the perpendicularity or parallelism of lines. Cartesian equations and parametric equations of a line are developed and there are several applications. In Chapter 7 basic properties of circles are developed, the mid-line of an angle-support, and sensed distances. In the short Chaper 8 there is a treatment of translations, axial symmetries and more generally isometries. In Chapter 9 trigonometry is dealt with in an original way which e.g. allows concepts such as clockwise and anticlockwise to be handled in a way which is not purely visual. By the stage of Chapter 9 we have a context in which calculus can be developed. In Chapter 10 the use of complex numbers as coordinates is introduced and the great conveniences this notation allows are systematically exploited. Many and varied topics are dealt with , including sensed angles, sensed area of a triangle, angles between lines as opposed to angles between co-initial half-lines (duo-angles). In Chapter 11 various convenient methods of proving geometrical results are established, position vectors, areal coordinates, an original concept mobile coordinates. In Chapter 12 trigonometric functions in the context of calculus are treated.

New to this edition:

• The second edition has been comprehensively revised over three years
• Errors have been corrected and some proofs marginally improved
• The substantial difference is that Chapter 11 has been significantly extended, particularly the role of mobile coordinates, and a more thorough account of the material is given

• Provides a modern and coherent exposition of geometry with trigonometry for many audiences across mathematics
• Provides many geometric diagrams for a clear understanding of the text and includes problem exercises for many chapters
• Generalizations of this material, such as to solid euclidean geometry and conic sections, when combined with calculus, would lead to applications in science, engineering, and elsewhere