About the Book

Engineering Mathematics is an essential tool for describing and analyzing engineering processes and systems. Mathematics also enables precise representation and communication of knowledge. Engineering Mathematics II fulfils the need for a book that not only effectively explains the concepts but also aids in visualizing the underlying geometric interpretation. Every chapter has easy to follow explanations of the theory and numerous step-by-step solved problems and examples. Extreme care has been taken to provide careful and correct mathematics, outstanding exercises and helpful worked examples. ·Matrix and Linear Systems ·Ordinary Differential Equations - I ·Ordinary Differential Equations - II ·Partial Differential Equations - I ·Partial Differential Equations - II

About the Author

Dr. R. N. Yadava, Raman Research Fellow and a founder member of RRL (CSIR) Bhopal, has served CSIR as Director Gr. Sci. and executed a variety of research projects at National and International levels. He has supervised Research Scholars and PG Students for their Ph.D. and M.Tech. thesis, respectively. He has been invited to deliver technical talks in esteemed universities of USA, Canada, UK, Germany, The Netherlands, Thailand, Korea, Australia, etc. Dr. Anil Goyal has taught various subjects as per curriculum to the students of M.Sc., M.Tech., M.C.A. and B.E. He has also supervised research fellows for their Ph.D. thesis. He has published a number of research papers in international and national journals. Dr. Ramakant Bharadwaj is Head of the Department of Mathematics in TIT. He has published research papers in journals of international repute and also presented research papers in national and international conferences. Dr. Sarvesh Kumar Agrawal has published a number of research papers in international and national journals and participated in many national and international conferences.

Table of Contents:
Preface About the Authors Unit I Matrix and Linear Systems Chapter 1 Matrices 1.1 Introduction 1.2 Types of Matrices 1.3 Matrix Operations 1.4 Elementary Row Operations 1.5 Row Equivalent Matrices 1.6 Order of a Minor 1.7 Rank of a Matrix 1.8 Echelon Form of a Matrix 1.9 Normal (Canonical) Form of a Matrix 1.10 Solution of Simultaneous Linear Equations and Consistency of Equations 1.11 Eigenvalues and Eigenvectors 1.12 Some Important Theorems 1.13 The Cayley–Hamilton Theorem Unit II Ordinary Differential Equations - I Chapter 2 Ordinary Differential Equations of First Order and First Degree 2.1 Introduction 2.2 Order and Degree of Differential Equations 2.3 Formation of Differential Equations 2.4 Solution of Differential Equations 2.5 Variable-Separable Form of Differential Equations 2.6 Equations Reducible to Variable-Separable Form 2.7 Homogeneous Differential Equations 2.8 Equations Reducible to Homogenous Forms 2.9 Linear Differential Equations 2.10 Equations Reducible to the Linear Form (Bernoulli’s Equation) 2.11 Exact Differential Equations 2.12 Equations Reducible to Exact Forms Chapter 3 Higher Order Linear Differential Equations with Constant Coefficients 3.1 Introduction 3.2 The Differential Operator D 3.3 Auxiliary Equations 3.4 Rules for Finding the Complimentary Function 3.5 Rules for Finding the Particular Integral Unit III Ordinary Differential Equations - II Chapter 4 Homogeneous and Simultaneous Differential Equations 4.1 Cauchy’s Homogeneous Linear Differential Equation 4.2 Legendre’s Linear Differential Equation 4.3 Simultaneous Differential Equations Chapter 5 Second-Order Linear Differential Equations with Variable Coefficients 5.1 Introduction 5.2 Complete Solution When One Integral of C.F. Is Known 5.3 One Integral of C.F. by Inspection 5.4 Removal of First Derivative 5.5 Change of Independent Variable 5.6 Method of Variation of Parameters Unit IV Partial Differential Equations - I Chapter 6 Partial Differential Equations 6.1 Introduction 6.2 Formation of Partial Differential Equations 6.3 Solutions of Partial Differential Equations 6.4 Linear Partial Differential Equations of First Order: Lagrange’s Method 6.5 Non-Linear Partial Differential Equations of First Order 6.6 Charpit’s Method Unit V Partial Differential Equations - II Chapter 7 Partial Differential Equations with Constant Coefficients 7.1 Liner Partial Differential Equations with Constant Coefficients 7.2 Solution of Homogeneous Linear Partial Differential Equations 7.3 Rules for Finding the Complementary Function 7.4 Rules for Finding the Particular Integral 7.5 Solution of Non-Homogeneous Linear Partial Differential 7.6 Method for Finding Complementary Function 7.7 Reducible Form of Homogeneous Linear Partial Differential Equation Chapter 8 Separation of Variables 8.1 Introduction 8.2 Method of Separation of Variables