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 revised edition of A Textbook of Engineering Mathematics-II. The Book encompasses the revised syllabus of U.P.T.U., Lucknow and Uttrakhand Technical University, Dehradun in its 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. A.K. Khanna, Prof. R.L. Misri, Prof. R.C. Goel, Prof. Govind Prasad, Prof. B.N. Roy, Prof. Nand Lal, Prof. S.N. Singh, Dr. T.N. Singh, Dr. R.C. Singh, Dr. Rajeev Aggarwal, Dr. Madhukar Sharma and our colleagues Mr. Baboo Shahid, extended unconditionally to us. We extend our heartfelt 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, Managing Direcor, Vayu Education of India, New Delhi for taking all pains for bringing out this book.
Authors aksingh maths rediffmail.com arvind maths yahoo.co.in cmcbcs2003 yahoo.com rkmohan2k4 yahoo.com
Subject Mathematics-II UPTU Code EAS-203 Uttrakhand Technical University Code TMA-201 Unit-I Differential Equations
Ordinary differential equations of first order, Exact differential equations, Linear differential equations of nth order with constant coefficients, Complementary functions and particular integrals, Simultaneous linear differential equations, Solutions of second order differential equations by changing dependent and independent variables, Methods of variation of parameters, Applications to engineering problems without derivation . Unit-II Series Solutions and Special Functions 8 Series solutions of ODE of 2nd order with variable coefficients with special emphasis to differential equations of Legendre, and Bessel, Legendre polynomials, Bessels functions and their properties.