gujarat technical university BE- Sem - I

Gujarat Technological University

BE- Sem - I
Mathematics-I
• Review of limits, continuity, differentiability.
• Mean value theorem, Taylors Theorem, Maxima and Minima.
• Riemann integrals, Fundamental theorem of Calculus, Improper inte-
grals, 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 for-
mula.
• 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 Geometr