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  • 12:19 PM, Sunday, 17 Nov 2019


Course Undergraduate
Semester Sem. I
Subject Code MA111
Subject Title 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 – 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.

Text Books

1. Stewart, J., Calculus: Early Transcendentals, 5th ed., Brooks/Cole (2007).

2. Jain, R. K. and Iyengar, S. R. K., Advanced Engineering Mathematics, Narosa (2005).

References

1. Greenberg, M. D., Advanced Engineering Mathematics, Pearson Education (2007).

2. James, G., Advanced Modern Engineering Mathematics, Pearson Education (2004).

3. Kreyszig, E., Advanced Engineering Mathematics, 9th ed., John Wiley (2005).

4. Thomas, G. B. and Finney, R. L., Calculus and Analytic Geometry, 9th ed., Pearson Education (2003).