A Textbook of Engineering Mathematics For UPTU (Volume - I)

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A Textbook of Engineering Mathematics is a three-volume text catering to the requirements of the three-semester compulsory undergraduate course on Engineering Mathematics offered by the Uttar Pradesh Technical University. Adapted from Peter O'Neil's Advanced Engineering Mathematics, these semester-specific volumes cover all the topicsdelineated in the UPTU syllabus and make ideal textbooks for all undergraduate engineering students. A Textbook of Engineering Mathematics, Volume I serves as a textbook for Semester I of the course on Engineering Mathematics. Beginning with successive differentiation, partial differentiation, and their applications, the book goes on to cover matrices and their applications in solving systems of linear equations. Comprehensive discussions on theory and applications of multiple integrals, gamma and beta functions, and vector calculus are also included in the book. The text is supplemented by pedagogical features such as illustrations, boxed material highlighting important theorems and definitions, solved examples including questions from previous UPTU examinations, and a large database of exercises. Lucid explanation of concepts and a simplistic approach to problem solving make for a complete undergraduate textbook. Key Features Conforms exactly to the pattern of the syllabus for the first semester Engineering Mathematics course offered by UPTU Incorporates a large number of solved and unsolved problems for each topic Elucidates all basic concepts with the aid of pedagogical features such as illustrations, definitions, and examples for easy and clear understanding Includes question papers from previous years examinations About The Author Peter V. O'Neil has more than 42 years of experience teaching mathematics to undergraduate and graduate students. For the last 30 years he has been Professor of Mathematics in the University of Alabama at Birmingham. A PhD in mathematics from Aligarh Muslim University, Santosh K. Sengar has been involved in teaching and research for over ten years. He is currently Assistant Professor in Indraprastha Engineering College, Ghaziabad (affiliated to UPTU). He has contributed several papers in national and international journals. His areas of research interest include non-linear analysis (metric fixed-point theory), differential equations, numerical analysis, and graph theory. Table Of Contents 1. Successive Differentiation and Leibniz's Theorem 2. Partial Differentiation 3.Expansion of Functions of Several Variables 4.Jacobians 5.Errors and Approximations 6. Extrema of Functions of Several Variables 7. Curve Tracing 8. Algebra of Matrices 9. Solution of Systems of Linear Equations 10. Eigenvalues, Diagonalization, and Special Matrices 11. Multiple Integrals 12. Gamma and Beta Functions 13.Vector Differential Calculus 14.Vector Integral Calculus