By H.S. Gangwar, Dr. Prabhakar Gupta

Show description

Read or Download A Textbook of Engineering Mathematics: v. 1 PDF

Best textbook books

The History of Poland Since 1863 (Cambridge Russian, Soviet and Post-Soviet Studies)

This is often an account of the evolution of Poland from stipulations of subjection to its reconstruction in 1918, improvement within the years among the 2 international Wars, and reorganisation after 1945. It starts off at a time while Poland was once nonetheless struggling with the legacy of the eighteenth-century walls and pressured with difficulties of significant ethnic minorities, insufficient agrarian reforms and slow business improvement sustained via international capital.

Give Me Liberty!: An American History, Volume 2 (3rd Edition)

A transparent, concise, modern, authoritative background through one of many prime historians within the country.
Give Me Liberty! is the major ebook available in the market since it works within the lecture room. A single-author ebook, supply Me Liberty! bargains scholars a constant technique, a unmarried narrative voice, and a coherent point of view during the textual content. Threaded during the chronological narrative is the subject of freedom in American historical past and the numerous conflicts over its altering meanings, its limits, and its accessibility to numerous social and financial teams all through American background. The 3rd version areas American background extra absolutely in an international context. The pedagogy can also be more suitable within the 3rd version, with a Visions of Freedom function in each one bankruptcy and extra huge end-of-chapter overview exercises.

Note to mods: this isn't a dupe, it's the moment quantity.

AS-Level Mathematics Edexcel: Complete Revision & Practice

Taken from retail AZW4 utilizing KindleUnpack

This ebook is stuffed with transparent revision notes and examination perform questions for AS Maths scholars. It covers the C1, C2, S1, M1 and D1 modules for the Edexcel examination, and it’s effortless to learn and revise from - everything’s defined easily and punctiliously. each few pages there are fast warm-up questions, a few exam-style questions and on the finish of every module there are perform examination papers (answers on the back). There’s additionally a sprinkling of jokes to lighten the temper. It’s precisely what you want to arrange in your tests!

Extra resources for A Textbook of Engineering Mathematics: v. 1

Sample text

B x + yg . 1 4 1 + y4 I Fx JK GH 1 5 1 I JK + y5 . xy 3. cos–1 6. cos–1 F xI GH y JK F xI GH y JK + cot–1 + cot–1 FG y IJ. H xK FG y IJ . H xK F x + y I , show that x ∂u + y ∂u = 3. , 2000) GH x + y JK ∂y ∂x ∂u 9 ∂u I F I F 8. U. (AG), 2005] 20 ∂x F xI F xI ∂z ∂z 9. If z = x y sin G y J + log x – log y, show that x +y = 6x y sin G y J . H K H K ∂x ∂y 4 4 7. U. , 2003] ∂ ∂ ∂ u u u 10. If u = x3 + y3 + z3 + 3xyz; show that x +y +z = 3u. ∂x ∂y ∂z 11. If u = cos–1 LM x − y OP , prove that x Nx + y Q ∂u ∂u + y ∂y = 0.

If u = x3 + y3 + z3 + 3xyz; show that x +y +z = 3u. ∂x ∂y ∂z 11. If u = cos–1 LM x − y OP , prove that x Nx + y Q ∂u ∂u + y ∂y = 0. ∂x 12. If u = log [(x2 + y2)/(x + y)], prove that x 13. If u = sin–1 {(x2 + y2)/(x + y)}, show that x 14. If u = sin–1 {(x + y)/( x + ∂u ∂u + y ∂y = 1. , 2008) ∂u ∂u + y ∂y = tan u. ∂x y )}. Show that x ∂u 1 ∂u + y ∂y = tan u. 2 ∂x ∂u 1 ∂u + y ∂y = sin 2u. 2 ∂x 16. If u is a homogeneous function of degree n, show that 15. If u = tan–1 [(x2 + y2)/(x + y)], then prove that x ∂ 2u ∂ 2u ∂u .

Ii) x2 + y2 Thus, from (i) and (ii), we get ∂2 f ∂2 f = . Hence proved. ∂x∂y ∂y∂x Example 6. If V = (x2 + y2 + z2)–1/2, show that ∂ 2V ∂ 2V ∂ 2V + + = 0. 2 ∂y ∂x 2 ∂z 2 Sol. Given V = (x2 + y2 + z2)–1/2. (i) 1 (x2 + y2 + z2)–3/2 2x = – x (x2 + y2 + z2)–3/2 2 LM RS 3 ex NT 2 = – x – 2 + y2 + z2 j –5/2 UV e W ⋅ 2x + x 2 + y 2 + z 2 = 3x2 (x2 + y2 + z2)–5/2 – (x2 + y2 + z2)–3/2 = (x2 + y2 + z2)–5/2 [3x2 – (x2 + y2 + z2)] or and ∂ 2V = (x2 + y2 + z2)–5/2 (2x2 – y2 – z2) ∂x 2 Similarly from (i), we can find j –3/2.

Download PDF sample

Rated 4.50 of 5 – based on 28 votes