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Meas, MT3 B 03 CALCULUS OF SINGLE VARIABL, , , , , , , , , , Aims, Objectives and Outcomes, , , , Using the idea of definite integral developed in previous semester, the natural logarithm, function is defined and its properties are examined. This allows us to define its inverse function, namely the natural exponential function and also the general exponential function. Exponential, functions model a wide variety of phenomenon of interest in science, engineering, mathematics and, economics. They arise naturally when we model the growth of a biological population, the spread of, a disease, the radioactive decay of atoms, and the study of heat transfer problems and so on. We, also consider certain combinations of exponential functions namely hyperbolic functions that also, arise very frequently in applications such as the study of shapes of cables hanging under their own, weight., , After this, the students are introduced to the idea of improper integrals, their convergence, and evaluation. This enables to study a related notion of convergence of a series, which is practically, done by applying several different tests such as integral test, comparison test and so on. As a special, case, a study on power series- their region of convergence, differentiation and integration etc.,- is, also done., , A detailed study of plane and space curves is then taken up. The students get the idea of, parametrization of curves, they learn how to calculate the arc length, curvature etc. using, parametrization and also the area of surface of revolution of a parametrized plane curve. Students, are introduced into other coordinate systems which often simplify the equation of curves and, surfaces and the relationship between various coordinate systems are also taught. This enables, them to directly calculate the arc length and surface areas of revolution of a curve whose equation is, in polar form. At the end of the course, the students will be able to handle vectors in dealing with, the problems involving geometry of lines, curves, planes and surfaces in space and have acquired the, ability to sketch curves in plane and space given in vector valued form.