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# Calculus-I, II, III: Calculus II

Calculus used for counting and calculations, like on an abacus) is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations

## Course Outline

Techniques of integration: Integrals of elementary, hyperbolic, trigonometric, logarithmic and  exponential functions.

Integration by parts, substitution and partial fractions. Approximate integration. Improper integrals. Gamma functions.

Applications of integrals:   Area between curves, average value. Volumes. Arc length.

Area of a surface of revolution. Applications to Economics, Physics, Engineering and Biology.

Infinite series: Sequences and series. Convergence and absolute convergence.

Tests for convergence: divergence test, integral test, p- series test, comparison test, limit comparison test, alternating series test, ratio test, root test. Power series. Convergence of power series.

Representation of functions as power series. Differentiation and integration of power series. Taylor and McLaurin series. Approximations by Taylor polynomials.

Conic  section,  parameterized  curves

and  polar  coordinates:

Curves  defined  by  parametric equations. Calculus  with  parametric curves: tangents, areas, arc length.

Polar coordinates. Polar curves, tangents to polar curves. Areas and arc length in polar coordinates.