Calculus Syllabus
Sequence and Series of Real Numbers: sequence – convergence – limit of sequence – nondecreasing
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 – Taylors 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.

Textbooks:
1. Stewart, J., Calculus: Early Transcendentals, 7th ed., Cengage Learning (2010).
2. Jain, R. K. and Iyengar, S. R. K., Advanced Engineering Mathematics, 4th ed., Alpha
Science Intl. Ltd. (2013).
References:
1. Greenberg, M. D., Advanced Engineering Mathematics, Pearson Education (2007).
2. James, G., Advanced Modern Engineering Mathematics, 3rd ed., Pearson Education (2005).
3. Kreyszig, E., Advanced Engineering Mathematics, 10th ed., John Wiley (2011).
4. Thomas, G. B. and Finney, R. L., Calculus and Analytic Geometry, 9th ed., Pearson Education
(2003)..