Geometrical representation of addition, subtraction, multiplication and division of complex numbers Illustrations of graphing standard quadric surfaces like cone, ellipsoid Reflection properties of parabola, ellipse and hyperbolaĬlassification of quadratic equations representing lines, parabola, ellipse and hyperbolaĭifferentiation of vector valued functions, gradient, divergence, curl and their geometrical interpretation Techniques for sketching parabola, ellipse and hyperbola Their use in polynomial approximation and error estimationįormation and solution of Differential equations arising in population growth, radioactive decay, administration of medicine and cell division
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Partial differentiation upto second orderĬomputation of Taylor’s Maclaurin’s series of functions such as ex, log(1 + x), sin (2x), cos x Graphs and Level Curves of functions of two variables Graphs of simple concrete functions such as polynomial, trigonometric, inverse trigonometric, exponential, logarithmic and hyperbolic functions arising in problems or chemical reaction, simple pendulum, radioactive decay, temperature cooling/heating problem and biological rhythms Illustration of proof of convergence of some simple sequences such as (–1)n /n, I/n2, (1+1/n)n, sin n/n, xn with 0 < x < 1 For instance, the sequence arising from Tower of Hanoi game, the Fibonacci sequence arising from branching habit of trees and breeding habit of rabbitsĬonvergence of a sequence and algebra of convergent sequences. Volumes Sequences to be introduced through the examples arising in Science beginning with finite sequences, followed by concepts of recursion and difference equations. Properties of continuous functions including intermediate value theoremĬauchy mean value theorem with geometrical interpretationsĭefinitions and techniques for finding asymptotes singular points Limit and continuity of a function: (ε-δ and sequential approach).
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