Elementary Different

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Solutions to the Exercises in Elementary Differential Geometry

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Solutions to the Exercises in Elementary Differential Geometry Chapter 1 1.1.1 It is a parametrization of the part of the parabola with x ≥ 0. 1.1.2 (i) γ(t) = (sec t, tant) with −π/2 < t < π/2 and π/2 < t < 3π/2. Note that γis defined on the union of two disjoint intervals: this corresponds to the fact that the hyperbola y2 − x2 = 1 is in two pieces, where y ≥ 1 and where y ≤ −1. (ii) γ(t) = (2 cost, 3 sint). 1.1.3 (i) x + y = 1. (ii) y = (lnx)2. 1.1.4 (...

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Elementary Different • Elementary Different