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Chapter 11 on vectors and geometry of space offer a solid foundation for understanding basic vector functions and operations (dot and cross product, projection and components, etc.), 3-D geometrical shapes (paraboloid, hyperboloids of 1 or 2 sheets, etc.), as well as applications for both, also cylindrical and spherical coordinates.
Chapter 12 on vector-valued functions initiates the idea of rate, velocity, and acceleration vectors and their relationship including vector differentiation, tangent and normal vectors, and arc length and curvature.
Chapter 13 does a wonderful job introducing functions of several variables, using limits, differentials, partial differentiation rules, gradients, max/minimization, and applications.
Chapter 14 on multiple integration is much easier to understand using this text than others. Lots of physics applications using area, volume, center of mass, moment of inertia, and change of variables.
Chapter 15 returns to vectors with topics such as curl (with physical interpretation), divergence, line and surface integrals, Green's thm, Stoke's thm, flux, and parametric surfaces.
Chapter 16 concludes the text by introducing differential equations. Basic concepts, separation of variables, exactness, homogenous equations, and power series solutions offer both as a learning tool and as somewhat of a refresher course.
Overall, the book is very well-written, from the introduction which illustrates the many advantages of calculus over algebra, the insight into careers using mathematics, to the appendices with proofs of theorems, basic differentian rules and answers to odd-numbered exercises (even exercises for the first 10 chapters), this book is a work of art for any math and/or science student.
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But little focus is really paid to this very powerful Clan that influenced not only Scotland, but England during this period. Alan Young finally brings Clan Comyn out of the shadows and places there in their rightful position as the most powerful family in Scotland in the 13th Century.
Young covers the rising of Bruce and Wallace and how it was impacted or changed by Clan Comyn; follows through to the Comyns roles as the later Guardians of Scotland; their role in John de Balliols Kingship; up through the murder of John Comyn by Bruce or his supports and the fallout.
Maybe a little more history than the casual read would enjoy, but for someone interested in ALL the history and understanding what happened then, this is a MUST!!
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