What is the syllabus for integrated B.Sc B.Ed in maths major?

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.

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