Introduction to Integral Calculus Ulrich L. Rohde, G. C. Jain, Ajay K. Poddar, A. K. Ghosh
The contents of each chapter are accompanied by all the necessary details. However, some useful information about certain chapters is furnished below.
Chapter 1 deals with the operation of antidifferentiation (also called integration) as the inverse processofdifferentiation. Meaningsofdifferenttermsarediscussedatlength.The comparison between the operations of differentiation and integration are discussed.
Chapter(s) 2, 3a, 3b, 4a, and 4b deal with different methods for converting the given integrals to the standard form, so that the antiderivatives (or integrals) of the given functions can be easily written using the standard results.
Chapter 5 deals with the discussion of the concept of area, leading to the concept of the definite integral and certain methods of evaluating definite integrals.
Chapter 6a deals with the first and second fundamental theorems of Calculus and their applications in computing definite integrals.
Chapter 6b deals with the process of defining the natural logarithmic function using Calculus.
Chapter 7a deals with the methods of evaluating definite integrals using the second fundamental theorem of Calculus.
Chapter 7b deals with the important properties of definite integrals established using the second fundamental theorem of Calculus and applying them to evaluate definite integrals.
Chapter 8a deals with the computation of plane areas bounded by curves. .
Chapter 8b deals with the application of the definite integral in computing the lengths of curves, the volumes of solids of revolution, and the curved surface areas of the solids of revolution. .
Chapter 9a deals with basic concepts related to differential equations and the methods of forming them and the types of their solutions. .
Chapter 9b deals with certain methods of solving ordinary differential equations of the f irst order and first degree.
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