This course is a basic course offered to PG students of Engineering/Science background. It contains Fredholm and Volterra integral equations and their solutions using various methods such as Neumann series, resolvent kernels, Greenís function approach and transform methods. It also contains extrema of functional, the Brachistochrone problem, Eulerís equation, variational derivative and invariance of Eulerís equations. It plays an important role for solving various engineering sciences problems. Therefore, it has tremendous applications in diverse fields in engineering sciences.
Dr. P. N. Agrawal is a Professor in the Department of Mathematics, IIT Roorkee. His area of research includes approximation Theory and Complex Analysis. He delivered 13 video lectures on Engineering Mathematics in NPTEL Phase I and recently completed Pedagogy project on Engineering Mathematics jointly with Dr. Uaday Singh in the same Department. Further he has completed online certification course Mathematical methods and its applications jointly with Dr. S.K. Gupta of the same department. He taught the course on Integral equations and calculus of variations several times to MSc (Industrial Mathematics and Informatics) students. He has supervised nine Ph.D. theses and has published more than 160 research papers in reputed international journals of the world. Currently, he is supervising six research students.
Dr. D. N. Pandey is an Associate Professor in the Department of Mathematics, IIT Roorkee. Before joining IIT Roorkee he worked as a faculty member in BITS-Pilani Goa campus and LNMIIT Jaipur. His area of expertise includes semigroup theory, functional differential equations of fractional and integral orders. He has already prepared e-notes for course titled Ordinary Differential Equations and Special Functions under e- Pathshala funded by UGC. Also, he has published a book titled Nonlocal Functional Evolution Equations: Integral and fractional orders, LAP LAMBERT Academic Publishing AG Germany. He has delivered several invited talks at reputed institutions in India and abroad. He has guided three Ph.D. theses and has published more than 60 papers in various international journals of repute. Currently, he is supervising five research students.