21MAT106 CALCULUS MATHEMATICS PAPER – I–

Unit I-

The Precise definition of a Limit, One-Sided Limits and Limits at Infinity, Infinite Limits and Vertical Asymptotes, Continuity, Tangents and Derivatives.

Unit II-

Extreme values of Functions, The Mean Value Theorem, Monotonic Functions and the First Derivative Test, Concavity and Curve Sketching, Integration-Riemann Sum, Definite integrals, The Fundamental Theorem of Calculus.

Unit III-

Functions in Several Variables, Limits and Continuity in Higher Dimensions, Partial Derivatives, Chain Rule, Directional Derivatives and Gradients, Tangent Planes and Differentials, Extreme Values and Saddle Points, Lagrange Multipliers.

Unit IV-

Line integrals, Vector fields, Work, Circulation and Flux, Path Independence, Potential Functions and Conservative Fields, Green’s Theorem in the Plane.

Unit V-

Surface Areas and Surface Integrals, Parameterized Surfaces, Orientation of Surfaces, Stoke’s Theorem and Divergence Theorem.

TEXTBOOKS:

1. G.B. Thomas and R.S. Finney, Calculus, 11th Edition, Pearson, 2009.

REFERENCES:

1. Monty J. Strauss, Gerald J. Bradley and Karl J. Smith, Calculus, 3rd Edition, 2002.
2. Dennis G. Zill and Michael R.Cullen, Advanced Engineering Mathematics, 2nd edition, CBS Publishers, 2012.
3. Srimanta Pal and Subhodh C Bhunia, Engineering Mathematics, 9th edition, John Wiley and Sons, 2012.
4. James Stewart, Calculus: Early Transcendentals, 8th Edition, Cengage (India), 2016.