MTH101A - Mathematics I

Real numbers, Sequences; Series; Power series, Limit, Continuity; Differentiability, Mean value theorems and applications; Linear Approximation, Newton and Picard L-T-P-D-[C] 3-1-0-1-[4] L-T-P-D-[C] 2-0-0-0-[0] L-T-P-D-[C] 3-1-0-1-[4] 313 method, Taylor’s theorem (one variable), Approximation by polynomials, Critical points, convexity, Curve tracing, Riemann Integral, fundamental theorems of integral calculus, Improper integrals, Trapezoidal and Simpson’s rule; error bounds, Space coordinates, lines and planes, Polar coordinates, Graphs of polar equations; Cylinders, Quadric surfaces, Volume, Area, length; Continuity, Differentiability of vector functions, arc length; Curvature, torsion, Serret-Frenet formulas, Functions of two or more variables, partial derivatives Statement only, of Taylor’s theorem and criteria for maxima/Minima/saddle points, Double, triple integrals, Jacobians; Surfaces, integrals, Vector Calculus, Green, Gauss, Stokes Theorems.