On the Review of Riemann’s Line and Double (Surface) Integrals

Main Article Content

Eziokwu, C. Emmanuel


In this work on Riemann’s integral, we discuss the integral for real valued function defined and bounded on finite intervals and then also for unbounded functions in finite intervals. We also extended the notion of integrals in another dimension. The interval  is replaced by a curve in two dimensional plane described by a vector valued function  and the integrand is vector function  defined and unbounded in this curve. The resulting integral is called the line integral or a contour integral and is denoted by  or by some similar symbol where the dot purposely suggest an inner product of two vectors. The curve is called a path of integration.

Double integrals, finite closed interval, line integral, paths, partition of a rectangle, piecewise smooth path, scalar function.

Article Details

How to Cite
Emmanuel, E. C. (2020). On the Review of Riemann’s Line and Double (Surface) Integrals. Asian Research Journal of Current Science, 2(1), 1-13. Retrieved from https://globalpresshub.com/index.php/ARJOCS/article/view/803
Review Article


Ejike UBCO. A postgraduate lecture note in functional analysis. Federal University of Technology Owerri, Nigeria; 1991.

Riez F, Nagy B. Functional analysis dover publications. Inc. New York; 1990.

Chidume CE. An iterative process for Nonlinear Lipschitzian strongly accretive mapping in L^p Spaces. Journal of Mathematical Analysis and Applications. 1990;152(2):453-461.

Vatsa BS. Principles of mathematical analysis” CBS Publishers & Distributors, New Delhi, India; 2002.

Trench WF. Instructors solution manual introduction to real analysis. National Mathematical Center, Abuja, Nigeria; 2010.

Trench WF. Introduction to real analysis. National Mathematical Center Abuja, Nigeria; 2010.

Eke A. Fundamental Analysis. Acena Publishers, Enugu, Nigeria; 1991.

Royden HL. Real analysis” Prentice Hall of India, New Delhi, India; 2008.

Argyros IK. Approximate solution of operator equations with applications. World Scientific Publishing Co. Plc Ltd; 2005.

Ukpong K. Undergraduate real analysis lecture notes. Federal University of Technology, Yola, Nigeria; 1987.

Atkin RJ, Fox N. An introduction to the theory of elasticity. Longman, London and New York; 1980.

Rama BB, Rao VD. Advanced dynamics Narosa Publishing House, New Delhi; 2005.

Altman M. Contractors and contractor directions theory and applications (A new approach to solving equations). Marcel Dekker Inc. New York and Basel; 1977.