Matrix Vector Analysis
This outstanding text and reference applies matrix ideas to vector methods, using physical ideas to illustrate and motivate mathematical concepts but employing a mathematical continuity of development rather than a physical approach. The author, who taught at the U.S. Air Force Academy, dispenses with the artificial barrier between vectors and matrices--and more generally, between pure and applied mathematics.
Motivated examples introduce each idea, with interpretations of physical, algebraic, and geometric contexts, in addition to generalizations to theorems that reflect the essential structure. A combination of matrix and vector methods reinforces both techniques. "Applied" students learn that general theory is a natural and useful culmination of their computations, and "pure" students learn that concrete problems from the physical world have traditionally keynoted abstract intellectual pursuits.
Geared toward upper-level undergraduates, the text features approximately 50 provocative problems at each chapter's end that test students' choice of techniques. Each chapter is also followed by about 25 mental exercises that stimulate imaginative reflection. Answers are given to selected questions.
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A X B acceleration Cayley table cite a counterexample column vectors compute Consider constant coordinate system Coriolis theorem cosh cross product cylindrical deﬁned deﬁnition dependent diagonal differential equations Discuss displacement vector Divergence theorem dot product eigenvalues eigenvectors elements EXERCISE ﬁgure ﬁnd ﬁnite ﬁrst ﬁxed ﬂuid formula frame fundamental theorem Gauss reduction geometric given gradient idea identity independent of path inverse irrotational line integral linear transformation linearly independent Markov chain matrix normal notation operations orthogonal matrix particle perpendicular physical plane postulates problem projection Proof Proposition Prove or cite quadratic form real numbers rotation satisﬁes scalar calculus scalar ﬁeld scalar multiplication scalar point function signiﬁcance sinh sketch solution space solve speciﬁc spherical Stokes theorem symmetric tail tangent theorem of scalar three dimensions tion V X F variables vector ﬁeld vector point function vector space zero