BE - Semester -1 - Mathematics -1

• Review of limits, continuity, differentiability.
• Mean value theorem, Taylors Theorem, Maxima and Minima.
• Riemann integrals, Fundamental theorem of Calculus, Improper integrals,
applications to area, volume.
• Convergence of sequences and series, power series.
• Partial Derivatives, gradient and directional derivatives, chain rule,
maxima and minima, Lagrange multipliers.
• Double and Triple integration, Jacobians and change of variables formula.
• Parametrization of curves and surfaces, vector Fields, line and surface
integrals.
• Divergence and curl, Theorems of Green, Gauss, and Stokes.

Texts/References

1. Hughes-Hallett et al., Calculus - Single and Multivariable (3rd Edition),
John-Wiley and Sons (2003).

2. James Stewart, Calculus (5th Edition), Thomson (2003).

3. T. M. Apostol, Calculus, Volumes 1 and 2 (2nd Edition), Wiley Eastern
1980.

4. G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry

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