About this eBook
Preface Mathematics has proved itself as a fundamental discipline for all branches of Engineering and Technology with ever-spreading applications in all spheres. Thus, the need for conceptualizing the framework followed by rational applications becomes imperative. In order to cater to the needs, we feel extremely happy to put forward the first edition of A Textbook of Engineering Mathematics. The Book encompasses the revised syllabus of U.P.T.U., Lucknow and U.T.U. in their totality ranging from preliminary concepts to more advanced and contemporary issues. Written in a very descriptive and lucid manner, the book is self explanatory and poses least challenge to conceptualize topics. Besides covering all units of the prescribed syllabus, this book not only clarifies concepts but also leads readers to be prepared for university examinations. We welcome feedback, suggestions and reviews from teachers and students to achieve our mission of imparting quality education. The book in its first edition, we hope, will meet needs of the teachers and students equally well. We acknowledge all supports and guidance of Prof. O.P. Singh, Prof. D.S. Chauhan, Prof. A.K. Khare, Prof. R.C. Goyal, Prof. Govind Prasad, Prof. B.N. Roy, Prof. Nand Lal, Prof. S.N. Singh, Prof. Prem Hari Sharma, Dr. T.N. Singh, Dr. R.C. Singh, Dr. Rajeev Aggarwal , Dr. Madhukar Sharma, Mr. Shahid Baboo, Dr. K. Alam and Mr. Anshu Kumar extended unconditionally to us. We extend our heartful gratitude to Mr. P.K. Gupta, Chairman, Sharda Group of Institutions for his kind support and encouragement while drafting this book. Our thanks are due to the Dr. Rajiv Kumar Jain for taking all pains for bringing out this book.
SYLLABUS U.P. TECHNICAL UNIVERSITY, LUCKNOW Revised Syllabus w.e.f. the Session 2008-2009 Semester-I Class Work Exam. Total Duration of Exam.
50 Marks 100 Marks 150 Marks 3 Hours
Unit I Differential Calculus I Leibnitz theorem, Partial differentiation, Eulers theorem, Curve tracing, Change of variables, Expansion of function of several variables. Unit II Differential Calculus II Jacobian, Approximation of errors, Exterma of functions of several variables,