Stokes

LONDON, June 13 (Reuters) - Ben Stokes is well aware of the threat posed by World Test Championship winners Australia but says England have "found something that works" and will not back down from their high-risk, high-reward style of play in the upcoming Ashes series. Stokes and coach Brendon 'Baz' McCullum have ushered in a fearless approach that has injected fresh excitement into test cricket with England winning 11 of their last 13 tests under the duo. Stokes ruled out discarding that 'Bazball' approach in the Ashes opener at Edgbaston from Friday. "We know the threat that Australia pose, no matter who they are playing against, they are a very good team but we've found something that works and has been successful," Stokes told BBC Test Match Special. "That doesn't change with the opposition." Australia crushed India by 209 runs in the WTC final at The Oval on Sunday and have not parted with the Ashes since reclaiming the urn in 2017-18. Stokes said there was no point in adopting a more measured approach against their arch-rivals. "Nothing is going to change because we've had unbelievable success with it," he said. "If we were to change anything from the last 12 months because we find ourselves in an Ashes series, then anything from the last 12 months will have been completely pointless." About Reuters • About Reuters , opens new tab • Careers , opens new tab • Reuters News Agency , opens new tab • Brand Attribution Guidelines , opens new tab • Reuters Leadership , open...

[ "article:topic", "Stokes\u2019 Theorem", "surface independent", "Faraday\'s Law", "curl vector fields", "Interpretation of Curl", "authorname:openstax", "license:ccbyncsa", "showtoc:no", "program:openstax", "licenseversion:40", "source@https://openstax.org/details/books/calculus-volume-1", "author@Gilbert Strang", "author@Edwin \u201cJed\u201d Herman" ] \( \newcommand\) • • • • • • • • • • • • • • • • • Learning Objectives • Explain the meaning of Stokes’ theorem. • Use Stokes’ theorem to evaluate a line integral. • Use Stokes’ theorem to calculate a surface integral. • Use Stokes’ theorem to calculate a curl. In this section, we study Stokes’ theorem, a higher-dimensional generalization of Green’s theorem. This theorem, like the Fundamental Theorem for Line Integrals and Green’s theorem, is a generalization of the Fundamental Theorem of Calculus to higher dimensions. Stokes’ theorem relates a vector surface integral over surface \(S\) in space to a line integral around the boundary of \(S\). Therefore, just as the theorems before it, Stokes’ theorem can be used to reduce an integral over a geometric object \(S\) to an integral over the boundary of \(S\). In addition to allowing us to translate between line integrals and surface integrals, Stokes’ theorem connects the concepts of curl and circulation. Furthermore, the theorem has applications in fluid mechanics and electromagnetism. We use Stokes’ theorem to derive Stokes’ Theorem Stokes’ theorem says we can calculate th...

Σ, its boundary ∂Σ and the normal vector n. Stokes' theorem, Kelvin–Stokes theorem fundamental theorem for curls or simply the curl theorem, R 3 , then ∬ Σ ( ( ∂ F z ∂ y − ∂ F y ∂ z ) d y d z + ( ∂ F x ∂ z − ∂ F z ∂ x ) d z d x + ( ∂ F y ∂ x − ∂ F x ∂ y ) d x d y ) = ∮ ∂ Σ ( F x d x + F y d y + F z d z ) . , then ∮ ∂ Σ F ⋅ d Γ = ∬ Σ ∇ × F ⋅ d 2 Σ . . Proof [ ] The proof of the theorem consists of 4 steps. We assume Elementary proof [ ] First step of the elementary proof (parametrization of integral) [ ] As in ψ and γ be as in that section, and note that by change of variables ∮ ∂ Σ F ( x ) ⋅ d Γ = ∮ γ F ( ψ ( γ ) ) ⋅ d ψ ( γ ) = ∮ γ F ( ψ ( y ) ) ⋅ J y ( ψ ) d γ be an orthonormal basis in the coordinate directions of R 2. Recognizing that the columns of J y ψ are precisely the partial derivatives of ψ at y, we can expand the previous equation in coordinates as ∮ ∂ Σ F ( x ) ⋅ d Γ = ∮ γ F ( ψ ( y ) ) J y ( ψ ) e u ( e u ⋅ d y ) + F ( ψ ( y ) ) J y ( ψ ) e v ( e v ⋅ d y ) = ∮ γ ( ( F ( ψ ( y ) ) ⋅ ∂ ψ ∂ u ( y ) ) e u + ( F ( ψ ( y ) ) ⋅ ∂ ψ ∂ v ( y ) ) e v ) ⋅ d y Second step in the elementary proof (defining the pullback) [ ] The previous step suggests we define the function P ( u , v ) = ( F ( ψ ( u , v ) ) ⋅ ∂ ψ ∂ u ( u , v ) ) e u + ( F ( ψ ( u , v ) ) ⋅ ∂ ψ ∂ v ( u , v ) ) e v are defined as follows, ∮ ∂ Σ F ( x ) ⋅ d l = ∮ γ P ( y ) ⋅ d l = ∮ γ ( P u ( u , v ) e u + P v ( u , v ) e v ) ⋅ d l We have successfully reduced one side of Stokes' theorem to a 2-dimensi...

Could Ben Stokes or Cameron Green decide the outcome of the men's Ashes? Men's Ashes 2023 - first Test Venue: Edgbaston Dates: 16-20 June Coverage: Live text commentary and in-play video clips on the BBC Sport website & app, plus BBC Test Match Special on BBC Sounds and BBC Radio 5 Sports Extra. Daily Today at the Test highlights on BBC Two and BBC iPlayer from 19:00 BST. "Will England's style of play work against Australia?" is a question being asked so often, Ben Stokes is fed up of answering it. With the help of Cricviz, BBC Sport has taken a closer look at all the key battlegrounds. Can England 'Bazball' the Australian attack? The most obvious place to start. England's upturn in fortunes under captain Stokes and coach Brendon McCullum has been built on some breathtaking batting that has laid waste to attacks in Manchester, Multan and Mount Maunganui. In the 13 Tests England have played since Stokes and McCullum took over last year, they have scored their runs at 4.85 an over, more than a whole run faster than the next swiftest scorers - Australia on 3.56. Their most notable achievements include chasing 299 in 50 overs to beat New Zealand at Trent Bridge, knocking off 378 inside 77 overs to defeat India on the same Edgbaston ground that will host Friday's Ashes opener, then piling on 506-4 on a stunning first day against Pakistan in Rawalpindi. England's batting strike-rate by length vs pace under McCullum & Stokes Length Average Strike-rate Full 41.30 94 Good 33.06 52 ...