Assignment 4
... let γ : I → M be a nonconstant integral curve of X, where I is an open interval in R. Prove the following statements. (a) γ is an immersion. (b) If γ is not injective, then there exists a smooth embedding i : S 1 → M such that i(S 1 ) = γ(I). ...
... let γ : I → M be a nonconstant integral curve of X, where I is an open interval in R. Prove the following statements. (a) γ is an immersion. (b) If γ is not injective, then there exists a smooth embedding i : S 1 → M such that i(S 1 ) = γ(I). ...
Vector Calculus Operators
... where ψ = (ψx , ψy , ψz ). The divergence of a vector quantity is a scalar quantity. If the divergence is greater than zero, it implies a net flux out of a volume element. If the divergence is less than zero, it implies a net flux into a volume element. If the divergence is exactly equal to zero, th ...
... where ψ = (ψx , ψy , ψz ). The divergence of a vector quantity is a scalar quantity. If the divergence is greater than zero, it implies a net flux out of a volume element. If the divergence is less than zero, it implies a net flux into a volume element. If the divergence is exactly equal to zero, th ...
1 Why is a parabola not a vector space
... . Is this vector in A ? Again, for the sake of contradiction, let ...
... . Is this vector in A ? Again, for the sake of contradiction, let ...
L - Calclab
... • Cauchy-Schwarz Inequality: xT y ≤ kxk kyk. • Vectors x and y are orthogonal if xT y = 0. In this case, we write x ⊥ y. • For nonzero vectors x & y, the scalar projection α, vector projection p, and orthogonal projection q of x onto y are respectively given by xT y kyk ...
... • Cauchy-Schwarz Inequality: xT y ≤ kxk kyk. • Vectors x and y are orthogonal if xT y = 0. In this case, we write x ⊥ y. • For nonzero vectors x & y, the scalar projection α, vector projection p, and orthogonal projection q of x onto y are respectively given by xT y kyk ...