Unit-I
Sequences & Series: Definition, Monotonic sequences, Bounded sequences, Convergent and
Divergent Sequences Infinite series, Oscillating and Geometric series and their Convergence, nth
Term test, Integral test, Comparison Test, Limit Comparison test, Ratio test, Root test, Alternating
series, Absolute and Conditional convergence, Leibnitz test.
Unit II
Differential Calculus: Limit Continuity and differentiability of functions of two variables, Euler’s
theorem for homogeneous equations, Tangent plane and normal. Change of variables, chain rule,
Jacobians, Taylor’s Theorem for two variables, Extrema of functions of two or more variables,
Lagrange’s method of undetermined multipliers.
Unit III
Integral Calculus: Review of curve tracing, Double and Triple integrals, Change of order of
integration. Change of variables. Gamma and Beta functions, Dirichlet’s integral; Applications of
Multiple integrals such as surface area, volumes
Unit –IV
Vector Calculus: Differentiation of vectors, gradient, divergence, curl and their physical meaning;
Identities involving gradient, divergence and curl Line and surface integrals Green’s, Gauss and
Stroke’s theorem and their applications
Unit–V
Probability and Statistics: Concept of probability, random variable and distribution function:
discrete and continuous, Binomial, Poisson and Normal Distributions.
- Teacher: Pratap Pathak