# A Textbook of Engineering Mathematics-I, 2nd Edition by H.S. Gangwar, Dr. Prabhakar Gupta

By H.S. Gangwar, Dr. Prabhakar Gupta

Written for the scholars of BTech I yr of UP Technical collage, Lucknow and different states, this publication discusses intimately the innovations and strategies in Engineering arithmetic.

**Read Online or Download A Textbook of Engineering Mathematics-I, 2nd Edition PDF**

**Best textbook books**

**Elementary Linear Algebra with Applications (9th Edition)**

Notice: The ISBN indexed refers back to the hardcover liberate. The dossier is from the book liberate, which has all of the unique content material from the publication, in addition to numerous extra chapters.

This vintage therapy of linear algebra provides the basics within the clearest real way, reading easy rules by way of computational examples and geometrical interpretation. It proceeds from well-known options to the surprising, from the concrete to the summary. Readers always compliment this amazing textual content for its expository kind and readability of presentation.

* The purposes model incorporates a large choice of attention-grabbing, modern applications.

* transparent, obtainable, step by step factors make the fabric crystal clear.

* demonstrated the difficult thread of relationships among structures of equations, matrices, determinants, vectors, linear alterations and eigenvalues.

**Physics for Scientists and Engineers with Modern Physics**

PHYSICS FOR SCIENTISTS AND ENGINEERS finds the sweetness and straightforwardness of physics whereas highlighting its crucial position in different disciplines, from engineering to medication. This confirmed textual content positive aspects the Serway hallmarks of concise writing, conscientiously thought-out challenge units, global type labored examples, and modern academic pedagogy.

**Fundamentals of Fluid Mechanics (6th Edition)**

The number 1 textual content in its box, basics of Fluid Mechanics is revered via professors and scholars alike for its complete topical assurance, its assorted examples and homework difficulties, its software of the visible element of fluid mechanics, and its robust specialize in studying. The authors have designed their presentation to permit for the slow improvement of scholar self assurance in challenge fixing.

This cutting edge textbook is the 1st to combine studying and reminiscence, behaviour, and cognition. It makes a speciality of interesting human study in either reminiscence and studying (while additionally bringing in vital animal stories) and brings the reader brand new with the newest advancements within the topic. scholars are inspired to imagine severely: key theories and matters are checked out intimately; descriptions of experiments comprise why they have been performed and the way reading the strategy may help assessment competing viewpoints.

- Investigating Astronomy: A Conceptual View of the Universe
- Scientific American Biology for a Changing World (2nd Edition)
- Advanced Statistical Methods for the Analysis of Large Data-Sets (Studies in Theoretical and Applied Statistics / Selected Papers of the Statistical Societies)
- Practical Business Statistics (6th Edition)
- Machine Learning For Financial Engineering (Advances in Computer Science and Engineering: Texts)

**Additional resources for A Textbook of Engineering Mathematics-I, 2nd Edition**

**Sample text**

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 . (a) x 2 + y ∂x∂y = (n – 1) ∂x ∂x ∂ 2u ∂u ∂ 2u . (b) y 2 + x ∂x∂y = (n – 1) ∂y ∂y 48 A TEXTBOOK OF ENGINEERING MATHEMATICS—I FG y IJ , show that x ∂u + y H xK ∂x LM x + y OP , prove that x 1 8 . If u = sin M MN x + y PPQ 17. If u = f –1 1 4 1 4 1 6 1 6 2 2 0 . Verify Euler’s theorem for f = 2 1 . If u = y2 ∂ 2u 1 ∂ 2u ∂ 2u 2 2 + 2xy + y 2 = 144 tan u [tan u – 11]. 2 ∂ ∂ x y ∂y ∂x 5 ∂u ∂u +y = tan u if u = sin–1 2 ∂x ∂y 1 9 .

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. ∂x 12. If u = log [(x2 + y2)/(x + y)], prove that x 13.

F x, y + δy − f x, y δy ∂z ∂z ∂f is also denoted by or fx similarly ∂y is denoted ∂x ∂x ∂f by ∂y or fy. The partial derivatives for higher order are calculated by successive differentiation. Thus, ∂2 f ∂ 2z = ∂x 2 ∂x 2 = fxx, ∂2z ∂2 f = = fyy ∂y 2 ∂y 2 ∂2z ∂2 f = ∂x∂y ∂x∂y = fxy, ∂2 f ∂2z = = fyx and so on. ∂y∂x ∂y∂x ∂z ∂z and : ∂ y ∂x Let z = f(x, y) represents the equation of a surface in xyzcoordinate system. Suppose APB is the curve which a plane through any point P on the surface O to the xz-plane, cuts.