Calculus in 3D : geometry, vectors, and multivariate calculus
著者
書誌事項
Calculus in 3D : geometry, vectors, and multivariate calculus
（AMS/MAA textbooks, v. 40）
MAA Press, an imprint of the American Mathematical Society, c2018
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
Calculus in 3D is an accessible, well-written textbook for an honors course in multivariable calculus for mathematically strong first- or second-year university students. The treatment given here carefully balances theoretical rigor, the development of student facility in the procedures and algorithms, and inculcating intuition into underlying geometric principles. The focus throughout is on two or three dimensions. All of the standard multivariable material is thoroughly covered, including vector calculus treated through both vector fields and differential forms. There are rich collections of problems ranging from the routine through the theoretical to deep, challenging problems suitable for in-depth projects. Linear algebra is developed as needed. Unusual features include a rigorous formulation of cross products and determinants as oriented area, an in-depth treatment of conics harking back to the classical Greek ideas, and a more extensive than usual exploration and use of parametrized curves and surfaces.
Zbigniew Nitecki is Professor of Mathematics at Tufts University and a leading authority on smooth dynamical systems. He is the author of Differentiable Dynamics, MIT Press; Differential Equations, A First Course (with M. Guterman), Saunders; Differential Equations with Linear Algebra (with M. Guterman), Saunders; and Calculus Deconstructed, MAA Press.
目次
Coordinates and vectors
Curves and vector-valued functions of one variable
Differential calculus for real-valued functions of several variables
Integral calculus for real-valued functions of several variables
Integral calculus for vector fields and differential forms
Appendix
Bibliography
Index.
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