Calculus and Analytic Geometry

Unit I: Limit and continuity, Sequence and sequential criterion for limit, Differentiation, Mean value theorems, Indeterminate forms and evaluation of limits using L’Hopital rule, Riemann Integration and fundamental theorem of calculus, Improper integrals.

Unit II: Asymptotes, Increasing and decreasing functions, Concavity and Convexity, Points of inflection, Tracing of curves.

Unit III: Taylor’s expansion and error estimates, Power series and its convergence, Functions of two variables, Partial and directional derivatives, Gradient, Maxima and Minima, Lagrange’s multiplier method.

Unit IV: Vectors in three dimensional space, dot and cross product, lines and planes in space, Tangent to curves, Normal, Green’s theorem, Gauss divergence theorem, Stokes theorem.