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Formula Sheet-Essential Mathematical Skills and Techniques, Study notes of Mathematics

The University of SheffieldMathematics

The document is a formula sheet for the courses MAS140, MAS151, MAS152, MAS156, and MAS161. It serves as a comprehensive reference for students, covering essential mathematical formulas and results that can be quoted without proof in exams. The sheet includes key topics such as trigonometry, hyperbolic functions, series expansions (arithmetic, geometric, and binomial), differentiation rules, and integration techniques. Additionally, it provides Laplace transforms and methods for integration by parts and variable substitution. The content is well-organized, with clear sections for each topic, making it a valuable resource for students to quickly access important mathematical identities, derivatives, integrals, and series during their studies or exams.

Typology: Study notes

2024/2025

Available from 03/14/2025

charles-khama
charles-khama 🇮🇹

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Download Formula Sheet-Essential Mathematical Skills and Techniques and more Study notes Mathematics in PDF only on Docsity!

3/14/25, 9:08 PM MAS 140 151 152 Formula Sheet MAS140/151/152/156/161 Formula Sheet These results may be quoted without proof unless proofs are asked for in the questions. about:blank ‘Trigonometry sin?x+ cos?x= 1 1 + tan?x= sec?x 1 + cot?x = cosec?x 2 sin?x = 1 —cos 2x 2 cos?x = 1+c0s 2x 2 sin xcos x=sin 2x cos(x + y) = cos xcos y Fsin xsin y sin(x£y)=sin xc0s y 00s xsin y tan(x+ty) = WY) = VF tan xtan y acos x-+bsin x= Reos (x~a) 2 cos xcos y= cos(x+y) + cos(x—y) 2 sin xsin y= cos(x~y)~cos(x +y) 2 sin xcos y= sin(x +y) + sin(x—y) _ 1 tan?®(x/2) cos X= 1 + tan*(x/2) 2 tan(x/2) SxS T+ tam(x/2) tan x= Hyperbolic Functions sin x= Y(es— er) cosh x= (et +e) eon x = LX cosh x cosh x coth x= sinh x 1 ch = Senn cosh X cosh” x ~ sinh? x = 1 2 cosh’ x= 1 + cosh 2x 2 sinh” x = cosh 2x—1 2 sinh xcosh x = sinh 2x sech’x = 1 ~ tanh? x sinh x= In(x+ x2+1), all x cosh x= In(x+ x?-1),x 21 15