Unit-I
Sequences and Series: Sequences, Series, General properties of series, Series of positive terms,
Comparison tests, tests of Convergence D’Alembert’s ratio test, Cauchy’s nth root test, Raabe’s test,
Logarithmic test, Alternating series, Series of positive and negative terms, Absolute convergence and
Conditional convergence.
Unit-II:
Calculus of One Variable: Rolle’s theorem, Lagrange’s, Cauchy’s mean value theorems, Taylor’s
series, Curvature, Radius of curvature, Circle of curvature, Envelope of a family of curves, Evolutes and
Involutes.
Unit-III
Multivariable Calculus (Differentiation): Functions of two variables, Limits and continuity, Partial
derivatives, Total differential and differentiability, Derivatives of composite and implicit functions
(Chain rule), Change of variables, Jacobian, Higher-order partial derivatives, Taylor’s series of functions
of two variables, Maximum and minimum values of functions of two variables, Lagrange’s method of
undetermined multipliers.
Unit-IV
Multivariable Calculus (Integration): Double integrals, Change of the order of integration, Change of
Variables from Cartesian to plane polar coordinates, Triple integrals.
Unit-V
Vector Calculus: Scalar and vector fields, Gradient of a scalar field, Directional derivative, Divergence
and Curl of a vector field, Line, Surface and Volume integrals, Green’s theorem in a plane, Gauss’s
divergence theorem, Stoke’s theorem (without proofs) and their verification.
Suggested Readings:
1. R.K. Jain & S.R.K Iyengar, Advanced Engineering Mathematics, Narosa Publications, 2014.
2. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley, 9th Edition, 2012.
3. B.S. Grewal, Higher Engineering Mathematics, Khanna Publications, 43rd Edition, 2014.
4. G.B. Thomas, Maurice Weir and Joel Hass, Thomas’ Calculus, Peterson, 12th Edition,2010.
5. B.V. Ramana, Higher Engineering Mathematics, 23rd reprint, 2015.
