Sequence and Series of Real Numbers: sequence – convergence – limit of sequence – non decreasing sequence theorem – sandwich theorem (applications) – L’Hospital’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 the- orem –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.

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).

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).

Course Outcomes (COs):

CO1: Understand the importance of convergence of sequences and series to learn the solutions of some physical systems that are governed by Mathematical rules.

CO2: Enable students to use these notions to choose an appropriate model that is ideal for some real life situations and solve them.

CO3: Realize the importance of the concepts like limit, continuity and differentibility in modelling and solving many practical problems.

CO4: Evaluate defenite integrals, areas of curved regions, arc length of a curve, volume and the surface area of revolution, and the center of mass in various dimensions.