Maths Spl

Unit-1
Inequalities involving arithmetic, geometric, and harmonic means, Cauchy-Schwarz
inequality. Unit-2
Sequences: Cauchy sequence, Cauchys General principle of convergence, Subsequences, Convergence and divergence of monotonic sequences, Sandwich theorem. Infinite series: statements of basic properties of infinite series (without proofs), Convergence, Absolute and conditional convergences. Tests for convergence: Comparison test, Ratio test, Raabes test, Leibnitzs test. Unit-3
Functions of one variable: Limit, Continuity, Differentiability, Rolls Theorem, Mean value
theorems and applications, Taylors theorem. Unit-4
Critical points, convexity, curvature of plane curves, Asymptotes. Curve tracing: tracing of catenary, cissoids, asteroid, cycloid, folium of Descartes, cardioid, lemniscate. Unit-5
Functions of two or more variables: Limit, Continuity, Partial derivatives, Eulers theorem on
homogeneous functions, Differentiability, Chain rule, Directional derivatives, Gradient
vectors and Tangent planes, Taylors theorem (statement only), Criteria for
Maxima/Minimal/Saddle points, Lagranges method of multipliers.