ENGINEERING MATHEMATICS-II APPLED MATHEMATICS

1 ENGINEERING MATHEMATICS -II APPLED MATHEMATICS DIPLOMA COURSE IN ENGINEERING SECOND SEMESTER Untouchability is a sin Untouchability is a crime Untouchability is a inhuman DIRECTORATE OF TECHNICAL EDUCATION GOVERNMENT OF TAMILNADU A Publication under Government of Tamilnadu Distribution of Free Textbook Programme (NOT FOR SALE) ii Government of Tamilnadu First Edition 2015 Thiru. PRAVEEN KUMAR Principal Secretary / Commissioner of Technical Education Directorate of Technical Education Guindy, Chennai- 600025 Dr. K SUNDARAMOORTHY , Phd.

2 , Additional Director of Technical Education (Polytechnics) Directorate of Technical Education Guindy, Chennai- 600025 Co-ordinator Er. , Principal Dr. Dharmambal Government Polytechnic College for Women Tharamani, Chennai 113 Convener Thiru Lecturer ( ) / MATHEMATICS Rajagopal Polytechnic College Gudiyatham Thiru Lecturer ( ) / MATHEMATICS Bharathiyar Centenary Memorial Polytechnic College Ettayapuram Thirumathi Lecturer/ MATHEMATICS Government Polytechnic College Krishnagiri Thiru NARASIMHAN Lecturer ( )/ MATHEMATICS Arulmigu Palaniandavar Polytechnic College, Palani.

3 SRINIVASAN Lecturer ( ) / MATHEMATICS Arasan Ganesan Polytechnic College Sivakasi Thiru HOD/ MATHEMATICS Adhiparasakthi Polytechnic College Melmaruvathur Thirumathi Lecturer / MATHEMATICS Rajagopal Polytechnic College Gudiyatham This book has been prepared by the Directorate of Technical Education This book has been printed on 60 Paper Through the Tamil Nadu Text book and Educational Services Corporation Reviewer Prof. Dr. E. THANDAPANI UGC EMERITUS FELLOW Ramanujan institute for Advanced Study in MATHEMATICS University of Madras, Chennai 600 005 Authors iii FOREWORD We take great pleasure in presenting this book of MATHEMATICS to the students of polytechnic colleges.

4 This book is prepared in accordance with the new syllabus under M scheme framed by the Directorate of Technical Education, Chennai. This book has been prepared keeping in mind, the aptitude and attitude of the students and modern method of education. The lucid manner in which the concepts are explained, make the teaching and learning process more easy and effective. Each chapter in this book is prepared with strenuous efforts to present the principles of the subject in the most easy to understand and the most easy to workout manner.

5 Each chapter is presented with an introduction, definitions, theorems, explanation, solved examples and exercises given are for better understanding of concepts and in the exercises, problems have been given in view of enough practice for mastering the concept. We hope that this book serve the purpose keeping in mind the changing needs of the society to make it lively and vibrating. The language used is very clear and simple which is up to the level of comprehension of students. We extend our deep sense of gratitude to Thiru.

6 R. Sornakumar Coordinator and Principal, Dr. Dharmambal Government Polytechnic College for women, Chennai and to Thiru Sankar, Convener and Lecturer / SG, Rajagopal Polytechnic College, Gudiyattam who took sincere efforts in preparing and reviewing this book. Valuable suggestions and constructive criticisms for improvement of this book will be thankfully acknowledged. AUTHORS iv 30022 ENGINEERING MATHEMATICS II DETAILED SYLLABUS UNIT I: ANALYTICAL GEOMETRY Chapter - EQUATION OF CIRCLE 5 Hrs.

7 Equation of circle given centre and radius. General equation of circle finding centre and radius. Equation of circle on the line joining the points and as diameter. Simple Problems. )1,1(yx(x ,y )22 Chapter - FAMILY OF CIRCLES 4 Hrs. Concentric circles, contact of two circles(Internal and External) -Simple problems. Orthogonal circles (results only). Problems verifying the condition . Chapter - INTRODUCTION TO CONIC SECTION 5 Hrs.

8 Definition of a Conic, Focus, Directrix and Eccentricity. General equation of a conic (statement only). Condition for conic (i) for circle: and (ii) for pair of straight line: (iii) for parabola: (iv) for ellipse: and (v) for hyperbola: . Simple Problems. 022222 cyfxgybyxhxaba 0 h0 cfgfbhgha02 bah02 bah02 bahUNIT II: VECTOR ALGEBRA I Chapter - VECTOR - INTRODUCTION 5 Hrs. Definition of vector - types, addition, and subtraction of Vectors, Properties of addition and subtraction.

9 Position vector. Resolution of vector in two and three dimensions. Directions cosines, Direction ratios. Simple problems. Chapter - SCALAR PRODUCT OF VECTORS 5 Hrs. Definition of Scalar product of two vectors Properties Angle between two vectors. Simple Problems. Chapter - APPLICATION OF SCALAR PRODUCT 4 Hrs. Geometrical meaning of scalar product. Work done by Force. Simple Problems. UNIT III: VECTOR ALGEBRA II Chapter - VECTOR PRODUCT OF TWO VECTORS 5 Hrs.

10 Definition of vector product of two vectors. Geometrical meaning. Properties Angle between two vectors unit vector perpendicular to two vectors. Simple Problems. Chapter - APPLICATION OF VECTOR PRODUCT OF TWO VECTORS & SCALAR TRIPLE PRODUCT 5 Hrs. Definition of moment of a force. Definition of scalar product of three vectors Geometrical meaning Coplanar vectors. Simple Problems. v Chapter - VECTOR TRIPLE PRODUCT & PRODUCT OF MORE VECTORS 4 Hrs.