About this eBook
This is a textbook for Engineering Mathematics I 2nd edition for Engineering Students of Visveswaraya Technological University, introduced from the year 2014 2015. The topics included are Differential Calculus, Vector Calculus, Integral Calculus, Differential Equations and Linear Algebra. Each topic contains several solved problems to elucidate the concepts. Some of these examples have appeared in the various University examinations. The problems are solved in simple steps as can be understood by students. Assignment problems with answers appear at the end of each topic. Both theory and problems have been explained using necessary diagrams. Each topic is presented with care and it is hoped that the book will meet the requirements of the students and the teachers. Suggestions for further improvement of the book are welcome. I am indebted to my professors, colleagues and students, who have directly or indirectly contributed to this work. I express my thanks with gratitude to Dr. Venugopal K. R, UVCE, Dr. T. Basavaraju, Dr. Shivaprasad. B. Dandagi, UBDTCE , Dr. Ejanul Haque, Dr. Lakshmi Narayanachari. K, SVIT, Dr. M. Sankar, EPCET, Dr. D.V. Chandrashekar, VKIT, Dr. Hariprasad SSSMCE, Dr. C. Vinay, JSSATE, Dr. G. S. Prasad, RRCE, Dr. M. Suresha, VIT, Dr. Siddalinga Prasad, SIT, Mr. Krishna, Sri K. G. Jagadeesh, Dr. K. M. Niranjan, Dr. Ravichandra Nayakar, Dr. Mahesh, Smt. Mamatha, UBDTCE for their advice and help while preparing this book. I also express my sincere thanks to my wife Dr. Bharathi. K and my children Rithvik. P.R and Manasa. P.R for their continuous support and encouragement. I express my sincere thanks to Sanguine Technical Publishers, Bangalore for publishing the book in such an excellent form, and Interline Publishing, Bangalore for online publication of this book. I also express my sincere thanks to Mr. Sathish for keen interesting in typesetting the book. September 2014
Neural fm 2014 9 2 20 09 page v 1
Neural fm 2014 9 2 20 09 page vi 2
It gives me great pleasure in writing a foreword to this book on Engineering Mathematics by Dr. Pandurangappa C. I know the author for over two decades as my student and has earned a good reputation as a teacher. The results and properties on speci c topics have been stated in the form of theorems and followed by the proofs. This really helps the students to understand the meaning of the results and properties. A large number of solved examples on each topic are also given. In each exercise, a large number of graded problems are given for rigorous practice. In addition, this book also contains the required preliminaries that the students have studied earlier. This helps the students to brush up the requisite preliminaries and glance through the current topics for the examination purposes. I am con dent that the above book will be of great help to the teachers also in selecting the graded problems from worked out examples and exercises for effective teaching.