The cartesian coordinate system

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  • Math is an integral part of our increasingly complex daily life. Calculus for the Managerial, Life, and Social Sciences, Seventh Edition, attempts to illustrate this point with its applied approach to mathematics. Our objective for this Seventh Edition is twofold: (1) to write an applied text that motivates students and (2) to make the book a useful teaching tool for instructors. We hope that with the present edition we have come one step closer to realizing our goal.

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  • From the principles of electrical engineering it is known that the 3-phase quantities of the 3-phase AC machines can be summarized to complex vectors. These vectors can be represented in Cartesian coordinate systems, which are particularly chosen to suitable render the physical relations of the machines. These are the field-orientated coordinate system for the 3- phase AC drive technology or the grid voltage orientated coordinate system for generator systems.

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  • In Section 1.5 of the textbook, Zak introduces the Lagrangian L = K − U , which is the difference between the kinetic and potential energy of the system. He then proceeds to obtain the Lagrange equations of motion in Cartesian coordinates for a point mass subject to conservative forces, namely, d dt ∂L ∂ xi ˙ − ∂L = 0 i = 1, 2, 3. ∂xi (1)

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  • A Propos Descartes: René Descartes (March 31, 1596 – February 11, 1650), also known as Renatus Cartesius (latinized form), was a highly influential French philosopher, mathematician, scientist, and writer. Dubbed the "Founder of Modern Philosophy", and the "Father of Modern Mathematics", much of subsequent western philosophy is a reaction to his writings, which have been closely studied from his time down to the present day.

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