Page 1 :
Module-ll (20 hrs), , , , , , (Infinite Sequences and Series), , 7.6: Improper integrals - definition, Infinite Intervals of Integration,, Improper Integrals with Infinite Discontinuities, A Comparison Test for, Improper Integrals, , 9.1: Sequences- definition, recursive definition, Limit of a Sequence, limit laws,, squeeze theorem, Bounded Monotonic Sequences, definition, monotone, convergence theorem (only statement; its proof omitted), , 9.2: Series- defining the sum, convergence and divergence, Geometric Series,, The Harmonic Series, The Divergence Test, Properties of Convergent Series, , 9.3: The Integral Test - investigation of convergence ,integral test, The pSeries, its convergence and divergence, , 9.4: The Comparison Test- test series, The Comparison Test, The Limit, Comparison Test, , 9.5: Alternating Series- definition, the alternating series test, its proof,, examples, Approximating the Sum of an Alternating Series by S,,, , 9.6: Absolute Convergence- definition, conditionally convergent, The Ratio, Test, The Root Test, Summary of Tests for Convergence and Divergence of, Series, Rearrangement of Series, , , , , , Module-IiI (20 hrs), , , , , , 9.7: Power Series- definition, Interval of Convergence, radius of convergence,, Differentiation and Integration of Power Series, , 9.8: Taylor and Maclaurin Series- definition, Taylor and Maclaurin series of, functions, Techniques for Finding Taylor Series, , 10.2: Plane Curves and Parametric Equations- Why We Use Parametric, Equations, Sketching Curves Defined by Parametric Equations, , 10.3: The Calculus of parametric equations- Tangent Lines to Curves, Defined by Parametric Equations, Horizontal and Vertical Tangents,, , Finding © from Parametric Equations, The Length of a Smooth Curve, The, Area of a Surface of Revolution