Unit – I

Sequences – Series – Convergence and Divergence – Ratio test – Comparision test – Integral test – Cauchy’s root test – Rabe’s test – Absolute and conditional convergence

Unit – II

Rolle’s Theorem – Mean Value Theorem – Lagrang’s and Cauchy’s form with reminders – Radius, Centre and circle of curvatures – Evolutes and Envelopes

Unit – III

Functions of several variables – Partial Differentiation – Chain rule – Euler’s Theorem - Jacobins – Functional dependence – Taylor’s Theorem – Maxima and Minima of functions of two variables with and without constraints – Curve tracing – Cartesian, Parametric and Polar coordinates

Unit – IV

Application of integration to lengths, Volumes and surface areas – Cartesian and Polar coordinates – Double and triple integrals – change of variables – Changing the order of integration – Differential Equations of first order and first degree – Exact, Linear and Bernoulli equation.

Applications to Geometry, Law of Natural Growth and Newton’s Law of Cooling/

Unit – V

Linear Differential Equation of second and higher order with constant coefficients – Homogeneous simultaneous equations – Method of variation of parameters.

Laplace transformation of standard functions – Inverse Transforms – Convolutions theorem without proof – Transforms of periodic functions – LT of derivative and integrals – Applications of LT to ordinary differential equations.

Unit – VI

Gradients, Divergence, Curl and their related properties, Line, Surface, Volume Integrals – Potential function – work done as line integral – Curvilinear coordinates – Cylindrical and Spherical Coordinates – Expressions of Grad, Div, Curl, Spherical, Cylindrical and Polar coordinates – Green’s, Stokes and Divergence Theorems (with Proofs) and some simple problems.

Text Books

1. Advanced Engineering Mathematics – by Kreyszig E
2. Higher Engineering Mathematics – by BS Grewal
3. Engineering Mathematics – by Lazpathroy