SEMESTER I
MA111
CALCULUS
(2 – 1 – 0) 3 credits
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.
Textbooks:
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).
PH111
PHYSICS I
(3 – 1 – 0) 4 credits
Vectors and Kinematics: vectors, linear independence, completeness, basis, dimensionality,
inner products, orthogonality – displacement, derivatives of a vector, velocity, acceleration –
kinematic equations – motion in plane polar coordinates.
Newtonian Mechanics: momentum, force, Newton's laws, applications – dynamics of a system
of particles, conservation of momentum, impulse, center of mass.
Work and Energy: integration of the equation of motion – work energy theorem, applications –
gradient operator – potential energy and force, interpretation – energy diagrams – non‐
conservative forces – law of conservation of energy – power – particle collisions.
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