Integral Calculus(Paperback)

The book consist of nine chapters. In chapter 1, we have discussed indefinite integration which includes basic terminology of integration, methods of evaluating the integration of several types as well as Integration of Rational and Irrational functions. Chapter 2 deals with the introduction and properties of definite integrals as well as summation of series. While chapter 3 deals with the Reduction formula of several types. In chapter 4, we have discussed introduction of Beta and Gamma functions, transformation, reduction, and relations of Beta and Gamma functions. In chapter 5, we have discussed the evaluation of double integral in cartesian and polar coordinates, change of order of integration, applications, evaluation of triple integral, Dirichlet’s Integral. While in chapter 6, we have discussed introduction and convergence of improper integrals. In chapter 7, Areas of curves in cartesian and polar coordinates are discussed. While in chapter 8, Rectification, Volume, and Surface of Solid Revolution in cartesian, polar and parametric equation also Intrinsic equation in cartesian, polar and parametric equation are discussed. Chapter 9 deals with Leibnitz’s differentiation under integral sign. Integral calculus is a branch of applied mathematics concerning mathematical models (mathematical methods and techniques) that are typically used in sciences, engineering, and industry.

Integration of Rational Irrational Fractions • Definite Integral • Reduction Formula • Beta and Gamma Functions • Multiple Integrals • Improper Integrals • Rectification, Volume and Surface of Solid Revolutions • Differentiation Under Integrals Sign.

Dr. Mukesh Kumar is presently working as an Associate Professor in the Department of Mathematics at Graphic Era University, Dehradun, India. He received M. Phil. Degree in Mathematics from Indian Institute of Technology, Roorkee, India and Ph.D. Degree from HNBG Central University, Srinagar and has an experience of more than 13 years. His fields of specialization are inventory control, supply chain management and operations research. He has published 19 research papers in national and international reputed journals as well as presented many papers in national and international conferences. He has guided two Ph.D. students in the field of operations research. He is also on the editorial board of many National and International journals and reviewer of many national and international journals. He is an author/co-author six books viz. Mathematical Foundation of Computer Science, Engineering Mathematics for Semesters I and II, Engineering Mathematics for Semesters III and IV and Business Mathematics.

Dr. Anubhav Pratap Singh is working as assistant Professor (Senior scale) in Department of Mathematics at SGRR PG College affiliated with HNB Garwhal Central University, Srinagar. He obtained M.Phil. in Mathematics from  IIT, Roorkee, and Ph. D. in Mathematics from CCS University, Meerut, UP, He received M.Sc. in Mathematics and undergraduation from H.N.B. Garwhal University, Srinagar. He has 10 years postgraduate teaching experience and guided six Ph.D. students in the field of operations research. He has published many research papers in national and international reputed journals as well as presented many papers in national and international conferences.

Dr. Ashok Kumar is working as an assistant professor in the Department of Mathematics at H.N.B. Garhwal University (A Central University), Srinagar, Garhwal, Uttarakhand. He has completed his M.Sc. (Applied Mathematics)  and Ph.D. in Mathematics from the Department of Mathematics, Indian Institute of Technology, Roorkee. He has worked as an assistant professor in Government W. PG College, Kandhla, Muzaffarnagar, UP and after it he worked as an assistant professor in the department of mathematics NIT, Jalandhar, Punjab. His research area are Computational Fluid Dynamics, Hydrodynamic Stability, Spectral Method and Spectral Element Methods. He has been completed one UGC STARTUP Research Project and one DST-SERB project is running on Hydrodynamic stability in Vertical pipe filled with porous medium. He has published 12 research paper in international peer review journals and 06 articles in National and International conferences organized in India and abroad.