Exercice Consider the circle S¹, defined by S¹ = {(x, y) = R² | x² + y² = 1}. Let U₁ = {(r,y) € S¹ r>0}, and p₁: U₁(-), with 1(x, y) = arctan, U₂ = {(r,y) Us={(1, y) Sr<0}, Sy>0}, U₁= {(r,y) € S¹|r>0}. 1. Construct functions 92, 93, and 4, such that {(U₁, 91), (U2, 42), (U3, 43), (U4, Py)} is a smooth atlas.
Exercice Consider the circle S¹, defined by S¹ = {(x, y) = R² | x² + y² = 1}. Let U₁ = {(r,y) € S¹ r>0}, and p₁: U₁(-), with 1(x, y) = arctan, U₂ = {(r,y) Us={(1, y) Sr<0}, Sy>0}, U₁= {(r,y) € S¹|r>0}. 1. Construct functions 92, 93, and 4, such that {(U₁, 91), (U2, 42), (U3, 43), (U4, Py)} is a smooth atlas.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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smooth manifold part 1
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