Syllabus

Sequence and Series of Real Numbers: sequence – convergence – limit of sequence – non decreasing sequence theorem – sandwich theorem (applications) – L'Hopital's rule – infinite series – convergence –geometric series – tests of convergence (nth term test, integral test, comparison test, ratio and root test) –alternating series and conditional convergence – power series.

Differential Calculus: functions of one variable – limits, continuity and derivatives – Taylor’s theorem– applications of derivatives– curvature and asymptotes– functions of two variables– limits and continuity–partial derivatives– differentiability, linearization and differentials–extremum of functions – Lagrange multipliers.

Integral Calculus: lower and upper integral – Riemann integral and its properties – the fundamental theorem of integral calculus – mean value theorems – differentiation under integral sign – numerical Integration‐ double and triple integrals – change of variable in double integrals – polar and spherical transforms – Jacobian of transformations.