Introduction to Calculus and Analysis Volume II/1

By R. Courant, F. John. 2000

51 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Sliding mode control design using canonical homogeneous norm (2019, unknown): “Taking into account ∂ ∂x‖x‖d = e ∂s ∂x ∣∣ s=ln ‖x‖d the formula (7) is derived by means of Implicit Function Theorem [39] implying ∂s ∂x = − ∂‖d(−s)x‖ ∂x ∂‖d(−s)x‖ ∂s for the function s : R → R implicitly defined by the equality ‖d(−s)x‖ = 1.”
Finite-time and fixed-time stabilization: Implicit Lyapunov function approach (2015, methodology): “The conditions (C1), (C2), (C4) and the implicit function theorem Courant & John, 2000 imply that the equation Q (V , x) = 0 implicitly defines a unique function V : Rn \ {0} → R+ such that Q (V (x), x) = 0 for all x ∈ Rn \ {0}.”
Robust stabilization of MIMO systems in finite/fixed time (2016, background): “The implicit function theorem [32] provides the formula for the partial derivative @V @x D h @Q @V i 1 @Q @x .”