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-III. The Book encompasses the revised syllabus of 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 Director, 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
SYLLABUS MA 301 Mathematics III Unit-I Integral Transforms
Fourier Integral, Fourier Complex Transform, Fourier Sine and Cosine Transforms and Applications to Simple Heat Transfer Equation. Z-Transform and its application to solve difference equations. Unit-II Functions of a Complex Variable-I 9 Analytic Functions, C-R Equations and Harmonic Functions, Line Integral in the Complex Plane, Cauchy s Integral Formula for Derivatives of Analytic Functions, Liouvilles Theorem, Fundamental Theorem of Algebra. Unit-III Functions of a Complex Variable-II 8 Representation of a Function by Power Series, Taylor s and Laurent s Series, Singularities, Zerores and Poles, Residue Theorem, Evaluation of Real Integrals of